A rescue material distribution optimization method and system considering psychological factors of disaster victims

Abstract

The application provides a rescue material distribution optimization method and system considering the psychological factors of disaster victims, and relates to the technical field of data processing.The method comprises the following steps: processing the obtained basic data of a disaster rescue scene to obtain a basic data set containing supply points, disaster points, material types, stock, demand and transportation time; based on the basic data set, a multi-objective optimization model integrating a prospect theory is constructed, the multi-objective optimization model contains a first objective function of minimizing the total transportation time, and a second objective function of maximizing the overall psychological satisfaction based on a prospect value function and a probability weight function; the multi-objective optimization model is subjected to normalization and weighted aggregation processing, and the two objective functions of the first objective function and the second objective function are converted into a single objective comprehensive utility minimization problem.The application can realize the collaborative scheduling and fair and efficient allocation of rescue materials.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to an optimized method and system for the distribution of relief supplies that takes into account the psychological factors of disaster victims. Background Technology

[0002] In existing technologies, the optimization problem of relief material distribution is typically described and solved using mathematical programming and optimization models. The core design principles largely revolve around the objective efficiency of relief efforts. The core optimization objective focuses on minimizing total delivery time, total transportation cost, or unmet demand under various constraints such as transport capacity, material inventory, and transportation time limits, thereby maximizing the demand fulfillment rate of relief materials and improving the overall operational efficiency of emergency rescue. While this type of technical solution has developed a relatively mature modeling and solution system over a long period and can meet the basic efficiency requirements of emergency rescue to a certain extent, it generally neglects the social attributes of relief material distribution and the subjective psychological needs of disaster-stricken groups, making it difficult to adapt to the complex decision-making environment in disaster scenarios.

[0003] To further improve the social impact of relief supplies distribution and reduce the negative effects caused by unfair distribution, some existing technologies have begun to introduce fairness-related objective functions or constraints into optimization models, attempting to achieve a balance between relief efficiency and fair distribution. Among them, Chen et al. comprehensively considered the uncertainty of transportation time, fluctuations in the amount of donations, and the impact of secondary disasters, and introduced a satisfaction evaluation mechanism based on the quantity of materials allocated and transportation time. With the maximization of system utility and the coordination of vertical and horizontal equity as the core objectives, they constructed a multi-cycle relief material distribution optimization model. Mao et al. introduced a cost function that can characterize the perceived suffering of disaster victims, constructed a comparative penalty mechanism from the perspective of two-dimensional equity to quantify the negative effects of unfair distribution, and constructed a relief material allocation and placement decision model that takes into account both efficiency and equity, with the goal of minimizing the overall social cost of relief. Yang Qian et al. used the analytic hierarchy process to assign weights to the urgency of needs at different disaster sites, and constructed a constrained emergency material vehicle route optimization model with the goal of minimizing the response time of the emergency rescue process, the penalty for delivery delays, and the rate of unmet needs. Wu Peng et al. constructed a disaster victim psychological suffering function and used it as the core judgment criterion for the fairness of relief actions, and constructed a mixed integer nonlinear programming model for the problem of post-disaster emergency facility site selection and material allocation that takes into account both equity and efficiency.

[0004] While the aforementioned technical solutions incorporating fairness constraints mitigate the shortcomings of traditional purely efficiency-oriented models to some extent, they still suffer from inherent technical limitations: First, these solutions typically assume a passive and uniform response from disaster-stricken groups to the arrival of relief supplies, failing to adequately characterize the individual differences in behavioral patterns and psychological states among different victims. This homogenization assumption is severely inconsistent with the heterogeneous nature of disaster-stricken groups in actual disaster scenarios. Second, these methods provide relatively simplified descriptions of victims' behavior and psychological reactions, often employing linear or fixed proportional relationships to depict their responses to resource availability or scarcity, thus failing to capture their psychological responses. Third, this type of solution fails to fully recognize that in actual rescue operations, the psychological perception of relief supplies by disaster victims does not depend solely on the absolute quantity they receive, but is also profoundly influenced by their own expected level and the results of horizontal comparisons between their receiving levels and those of other disaster victims. When disaster victims perceive themselves as being in a relatively unfavorable or unfair distribution state, their psychological losses are often significantly amplified, leading to dissatisfaction, anxiety, and even collective emotional reactions. The aforementioned linear model cannot accurately characterize this amplification effect of psychological losses, ultimately resulting in the optimized distribution plan being out of touch with the actual rescue decision-making situation and the real psychological needs of disaster victims.

[0005] Prospect theory, a classic theory specifically designed to describe individual decision-making behavior under risk and uncertainty, emphasizes the core characteristics of individual decision-making: reference dependence and loss aversion. It accurately characterizes individuals' asymmetric psychological responses to gains and losses in relative gain-loss situations, possessing natural theoretical applicability in depicting individual perceptions of fairness and relative deprivation. It has already been maturely applied in multiple fields such as finance, marketing, and environmental policy. In recent years, to more accurately characterize the psychological response characteristics of disaster victims, some existing technologies have begun to introduce prospect theory into the field of relief material distribution. However, related technical solutions still have significant shortcomings: most research focuses on modeling the selection of relief routes or the risk preferences of relief decision-makers; only a small number of technical solutions focus on using prospect theory to characterize the psychological response mechanisms of disaster victims during the material distribution process. Furthermore, all related studies have varying degrees of technical deficiencies, failing to form a complete, implementable, and adaptable technical solution for complex relief scenarios.

[0006] Specifically, Guo Qing'e constructed a satisfaction function for material supply points and material receiving points based on prospect theory, and used a prospect value function to describe the psychological gains and losses perceived by different nodes in the process of obtaining or giving materials. Based on this, she established a relief material allocation model that considers both distribution efficiency and psychological fairness. However, this study mainly analyzes the sharing and allocation of materials under deterministic conditions and determines the transportation routes from distribution centers to disaster-stricken points using a shortest path algorithm. It has relatively limited consideration of the inherent uncertainty of disaster scenarios and the dynamic changes in the psychological perceptions of disaster victims, and cannot adapt to the actual relief scenarios with multiple uncertainties after a disaster. Ma Bin et al. combined prospect theory with unfairness aversion theory to introduce emergency material allocation problems, constructing a disaster victim psychological satisfaction function from the two dimensions of material delivery time and allocation fairness, and using a prospect value function to describe the asymmetric perception of gains and losses by disaster victims. This study analyzed the evolutionary process and stability of different strategy combinations by constructing an evolutionary game model between the government and disaster-stricken groups. However, its research focuses on the evolutionary analysis of strategic behavior and has not formed a model for complex allocation with multiple supply points, multiple disaster-stricken points, multiple materials, and multiple constraints. The unified optimization modeling and solution framework for disaster relief decision-making cannot directly generate feasible relief material distribution plans. Gong Zaiwu et al. introduced the psychological cost factor of disaster victims into the multi-period emergency material dispatch problem, analyzed the relationship between resource constraints, dispatch timing and disaster victims' psychological feelings under the framework of uncertain planning, and characterized the cumulative effect of psychological costs through multi-period modeling. However, the psychological factors of disaster victims in this study are mainly characterized by deterministic psychological costs or penalty functions, and do not systematically describe the reference dependence and subjective risk perception mechanism of disaster victims in uncertain environments from the perspective of prospect theory. It cannot accurately restore the real psychological decision-making logic of disaster victims in uncertain disaster scenarios. Yang et al. introduced prospect theory into the problem of relief resource allocation and dispatch, used prospect value functions to characterize the differences in the psychological perception of disaster victims regarding resource acquisition results, and explored the impact of different resource allocation schemes on system performance under the framework of scenario analysis. However, this study mainly focuses on analysis based on given or objective probability conditions, and does not further characterize the subjective weighting behavior of disaster victims regarding the probability of uncertain events. It fails to fully cover the core connotation of prospect theory, resulting in an essential lack of characterization of the psychological perception of disaster victims.

[0007] In summary, existing technical solutions that incorporate prospect theory into the decision-making process for the distribution or allocation of relief supplies still suffer from three major technical shortcomings, failing to meet the decision-making needs of actual emergency rescue scenarios: First, at the level of psychological perception modeling, existing technologies mainly focus on using the prospect value function in prospect theory to characterize the asymmetric psychological perception of gains and losses among disaster victims. However, they lack a systematic and complete characterization of the probability weight function in prospect theory, which is used to describe the subjective probability perception of uncertain events. This results in incomplete and inaccurate modeling of the psychological perception of disaster victims, and an inability to truly reproduce the subjective decision-making and psychological response mechanisms of disaster victims in uncertain disaster scenarios. At the same time, related studies mostly focus on single materials or equivalent materials, and fail to conduct unified modeling and collaborative optimization for the differences in demand attributes, psychological perception weights, transportation and storage constraints of various relief materials. This makes it impossible to adapt to the core needs of joint distribution of multiple types of relief materials in actual disaster relief.

[0008] Second, at the level of optimizing goal construction, existing technologies either focus only on single efficiency goals such as transportation time and cost, or only on single-goal optimization of allocation fairness and psychological perception. They fail to construct a multi-goal unified optimization framework that simultaneously takes into account the efficiency goal of minimizing total transportation time and the fairness goal of maximizing overall psychological satisfaction based on the complete prospect theory. This makes it impossible to achieve synergistic optimization of rescue efficiency and psychological fairness for disaster victims. Ultimately, the optimization schemes either fail to meet the time urgency requirements of emergency rescue or are detached from the real psychological needs of the disaster-stricken groups, making it difficult to implement in actual rescue operations.

[0009] Third, at the model-solving algorithm level, after introducing nonlinear factors such as psychological perception, the problem of optimizing the distribution of relief supplies transforms into a complex NP-hard optimization problem with high dimensions, multiple constraints, and strong nonlinearity. Existing solutions for this type of problem mostly rely on traditional heuristic algorithms or conventional evolutionary algorithms. On the one hand, these algorithms often require customized design based on the specific problem structure, resulting in limited applicability and scenario expansion capabilities, making it difficult to stably apply in real-world relief scenarios with multiple supply points, multiple disaster sites, multiple supplies, and multiple constraints. On the other hand, traditional algorithms generally suffer from slow convergence speed, poor convergence stability, large fluctuations in solution quality, and a tendency to get trapped in local optima when solving such high-dimensional nonlinear optimization problems. They are unable to quickly output stable, high-quality relief supply distribution solutions that balance efficiency and psychological fairness under the extremely urgent requirements of emergency relief.

[0010] Furthermore, existing technologies have not yet formed a complete and feasible method for optimizing the delivery of relief supplies, encompassing the entire process from basic data processing in disaster relief scenarios, construction of multi-objective optimization models, multi-objective normalization and aggregation processing, generation of feasible initial solutions, iterative optimization of improved algorithms, to decoding and outputting the final delivery plan. This makes it impossible to provide complete and direct technical support for on-site decision-making in emergency rescue. Summary of the Invention

[0011] The technical problem to be solved by this invention is to provide a method and system for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims. This method and system can achieve coordinated scheduling and fair and efficient allocation of relief supplies, thereby improving the overall effectiveness and social acceptance of relief work.

[0012] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: Firstly, a method for optimizing the distribution of relief supplies that takes into account the psychological factors of disaster victims, the method comprising: The basic data obtained from the disaster relief scenario are processed to obtain a basic dataset containing supply points, disaster-stricken areas, types of materials, inventory, demand, and transportation time. Based on the basic dataset, a multi-objective optimization model integrating prospect theory is constructed. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. The multi-objective optimization model is normalized and weighted aggregation to transform the first objective function and the second objective function into a single-objective comprehensive utility minimization problem. To address the single-objective comprehensive utility minimization problem of transformation, a joint matrix encoding and hybrid strategy are used to generate an initial population, resulting in an initial feasible solution set that satisfies all constraints. An improved genetic algorithm is run iteratively to optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a convergent population of optimized solutions is finally obtained. From the converged population of optimized solutions, select the individual with the smallest comprehensive utility function value for decoding, and output the final relief material distribution plan and resource sharing plan.

[0013] Secondly, an optimized relief supplies distribution system that takes into account the psychological factors of disaster victims includes: The basic data processing module is used to process the basic data acquired in the disaster relief scenario to obtain a basic dataset containing supply points, disaster-stricken points, types of materials, inventory, demand, and transportation time. The model building module is used to construct a multi-objective optimization model that integrates prospect theory based on the basic dataset. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. The aggregation and transformation module is used to perform normalization and weighted aggregation processing on the multi-objective optimization model, so as to transform the two objective functions, the first objective function and the second objective function, into a single-objective comprehensive utility minimization problem; The coding and strategy coordination module is used to generate an initial population by employing joint matrix coding and hybrid strategies for the single-objective comprehensive utility minimization problem of transformation, thereby obtaining an initial feasible solution set that satisfies all constraints. The iterative optimization module is used to run an improved genetic algorithm to iteratively optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a convergent population of optimized solutions is finally obtained. The matching output module is used to select the individual with the smallest comprehensive utility function value from the converged optimization solution population for decoding, and output the final relief material distribution plan and resource sharing plan.

[0014] The above-described solution of the present invention has at least the following beneficial effects: Because it employs a multi-objective optimization model based on fusion prospect theory, including a first objective function that minimizes the total transportation time, and a second objective function that integrates the probability weight function and prospect value function to maximize overall psychological satisfaction, coupled with normalized weighted aggregation processing, joint matrix encoding and hybrid strategies to generate the initial population, and improved genetic algorithms with tournament selection, uniform crossover, directed mutation, elite preservation and diversity maintenance mechanisms, it overcomes the technical problems of existing relief material distribution technologies that fail to systematically characterize the psychological characteristics of disaster victims in uncertain environments, such as reference dependence, nonlinear gain and loss perception, and low solution efficiency and poor convergence stability in complex scenarios with multiple resources and regions. This allows for accurate reconstruction of actual rescue decision-making scenarios, achieving coordinated scheduling and fair and efficient allocation of relief materials. It ensures both the efficiency of rescue transportation and fully considers the satisfaction and fairness perception of disaster victims, enabling the algorithm to quickly converge and output high-quality stable solutions in rescue scenarios ranging from small to large scales, effectively improving the overall effectiveness and social acceptance of rescue work. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating an optimized method for the distribution of relief supplies that takes into account the psychological factors of disaster victims, as provided in an embodiment of the present invention.

[0016] Figure 2 This is a schematic diagram of an optimized relief supplies distribution system that takes into account the psychological factors of disaster victims, provided by an embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram of the distribution matrix X.

[0018] Figure 4 This is a diagram illustrating the cross-operation of the delivery matrix X.

[0019] Figure 5 This is a schematic diagram of the mutation operation of the delivery matrix X.

[0020] Figure 6 Examples of objective function value boundaries in verification scenarios of different scales.

[0021] Figure 7 Example of the mean overall utility with different weights (all verification scenarios).

[0022] Figure 8 Examples of overall utility variance settings with different weights (all validation scenarios).

[0023] Figure 9 Example of sensitivity analysis of foreground theory parameters (Scenario M1).

[0024] Figure 10 Example of sensitivity analysis of foreground theory parameters (Scenario M2). Detailed Implementation

[0025] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0026] like Figure 1 As shown, an embodiment of the present invention proposes an optimized method for the distribution of relief supplies that takes into account the psychological factors of disaster victims. The method includes the following steps: Step 1: Process the basic data of the disaster relief scenario to obtain a basic dataset containing supply points, disaster-stricken areas, types of materials, inventory, demand, and transportation time. Step 2: Based on the basic dataset, construct a multi-objective optimization model that integrates prospect theory. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. Step 3: Normalize and weighted aggregate the multi-objective optimization model to transform the first objective function and the second objective function into a single-objective comprehensive utility minimization problem; Step 4: For the single-objective comprehensive utility minimization problem of transformation, a joint matrix encoding and hybrid strategy are used to generate an initial population, resulting in an initial feasible solution set that satisfies all constraints. Step 5: Run the improved genetic algorithm to iteratively optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a converged optimized solution population is finally obtained. Step 6: Select the individual with the smallest comprehensive utility function value from the converged optimization solution population, decode it, and output the final relief material distribution plan and resource sharing plan.

[0027] In this embodiment of the invention, the invention fully integrates the core connotations of prospect theory to construct an optimization model. On the one hand, through the prospect value function, it accurately portrays the asymmetric psychological reactions, reference dependence characteristics, and loss aversion characteristics of disaster victims to the gains and losses of relief supplies. This breaks through the limitations of existing technologies that use linear / proportional relationships to simplify the description of psychological reactions, and can effectively restore the amplified psychological loss effect caused by the relative unfair distribution of disaster victims, accurately portraying the relative deprivation and fairness perception of different disaster victim groups. On the other hand, the system introduces the probability weight function in prospect theory to fully portray the subjective weighting behavior of disaster victims in uncertain disaster environments, such as the timeliness of material delivery and the probability of resource acquisition. This makes up for the core shortcomings of existing technologies, such as incomplete application of prospect theory, focusing only on the value function while ignoring subjective probability perception, and failing to restore the true risk decision-making mechanism of disaster victims. Meanwhile, the modeling framework of this invention can perform differentiated modeling based on the demand attributes, urgency, and psychological perception weight differences of different categories of relief supplies such as food, drinking water, and medical supplies. This enables unified modeling and collaborative optimization of multiple categories of supplies, breaking through the limitations of existing technologies that assume single / equivalent supplies. It can fully adapt to the core needs of joint distribution of multiple categories of supplies in actual disaster relief. Furthermore, this invention breaks the strong assumption of homogeneous responses among disaster-stricken groups in existing technologies. It is compatible with the heterogeneous characteristics of psychological expectation levels, demand levels, and loss degrees of different disaster-stricken locations and different disaster-stricken groups. This allows the optimization model to truly reflect the differentiated psychological responses of disaster-stricken groups, avoiding the problem of insufficient fairness in allocation schemes caused by homogeneous modeling. This fundamentally reduces the risk of dissatisfaction, anxiety, and even collective negative emotions among disaster-stricken people caused by unfair allocation.

[0028] This invention breaks through the technical bottleneck of existing technologies that either focus solely on transportation efficiency or unilaterally on allocation fairness, failing to achieve synergistic optimization of both. It simultaneously constructs a dual-core optimization objective: minimizing the total transportation time as the first objective function, firmly upholding the core bottom line that "time is life" in emergency rescue and ensuring the timeliness of relief material delivery; and maximizing the overall psychological satisfaction of the disaster-stricken group based on the complete prospect theory as the second objective function, anchoring the social attributes of rescue work and the needs of the masses, and ensuring the fairness and psychological suitability of material allocation. Meanwhile, this invention effectively eliminates the numerical magnitude difference between the two different objectives, transportation time and psychological satisfaction, by normalizing the dual objective function. This avoids the optimization bias caused by an excessively large proportion of a single objective, ensuring that both core objectives are fully considered during the optimization process. Through weighted aggregation, the dual-objective optimization problem is transformed into a single-objective comprehensive utility minimization problem, significantly reducing the complexity of the model solution. Furthermore, the weight coefficients of the two objectives can be flexibly adjusted according to different disaster types, rescue stages, emergency response levels, and on-site control requirements, achieving dynamic adaptation of the optimization focus. For example, during the critical 72-hour rescue period after a disaster, the weight of the transportation time objective can be increased to prioritize the rapid delivery of medical and relief supplies. In the post-disaster resettlement phase, the weight of the psychological satisfaction objective can be increased to ensure the fairness of material distribution and social order stability. This completely solves the problems of fixed optimization objectives, poor scenario adaptability, and inability to match the differentiated needs throughout the entire rescue cycle in existing technical models.

[0029] This invention addresses the NP-hard and complex optimization problem arising from the introduction of psychological perception nonlinearity. It proposes a comprehensive improvement to the traditional genetic algorithm, resolving its core shortcomings: slow convergence speed, poor convergence stability, susceptibility to local optima, and large fluctuations in solution quality. Firstly, considering the three-dimensional decision variable characteristics of multiple supply points, multiple disaster points, and multiple materials, a joint matrix encoding mechanism is designed. This integrates core decision variables such as material allocation, cross-node transportation volume, supply point resource sharing, and transportation path matching into a unified encoding structure. This achieves complete and compact encoding of decision variables, avoiding the problems of dimensional redundancy, complex constraint handling, and the generation of infeasible solutions inherent in traditional encoding methods, significantly reducing the algorithm's solution dimensionality and computational complexity. Secondly, an initial population is generated using a combination of joint matrix encoding and a hybrid strategy, integrating the advantages of random generation and heuristic rule generation, ensuring 100% initial population quality. It satisfies all constraints such as material inventory, transportation capacity, and demand ceiling, achieving a 100% feasible solution rate. Simultaneously, it ensures global diversity of the initial population, solving the problems of low feasible solution rate and insufficient diversity in traditional initial population generation methods, which lead to slow algorithm convergence and long iteration cycles. This enables the rapid generation of high-quality initial feasible solutions under highly time-sensitive emergency rescue conditions. Thirdly, through optimized selection, crossover, and mutation operations combined with elite retention and diversity maintenance mechanisms, the entire process of genetic algorithm iteration is optimized. Selection and elite retention strategies ensure the stable inheritance of high-quality solutions, effectively accelerating algorithm convergence. Crossover, mutation, and population diversity maintenance operations avoid premature convergence and getting trapped in local optima during algorithm iteration, significantly improving the algorithm's convergence stability and global optimality of solutions. Meanwhile, the solution algorithm framework of this invention does not require large-scale customization for different scenarios. It can flexibly adapt to different numbers of supply points, disaster sites, material categories, and complex constraints such as different transport capacity limits, transport time limits, material inventory, and demand levels. Its scenario expansion capability and applicability are far superior to existing targeted solution algorithms. It can stably and quickly output high-quality optimized solutions in actual rescue scenarios with multiple resources, multiple regions, and multiple constraints.

[0030] This invention constructs a complete closed-loop technical process, covering the entire decision-making chain from basic data collection and standardization processing in disaster relief scenarios, construction of multi-objective optimization models, multi-objective normalization and weighted aggregation processing, generation of initial feasible solution populations, iterative optimization using improved genetic algorithms, to the final optimal solution decoding, output of relief material distribution plans and resource sharing plans. It requires no additional auxiliary models, complex manual intervention, or multi-system integration, and can directly connect with basic data collected at the emergency relief site. It can quickly output complete, actionable solutions that are detailed down to the quantity of each type of material delivered from each supply point to each disaster-stricken area, transportation route matching, and cross-supply point resource sharing. This solves the pain point of existing technologies, which tend to focus on theoretical analysis and strategy evolution research, and fail to form a complete and implementable decision-making process that cannot directly serve emergency relief site decision-making. Meanwhile, the entire process design of this invention has strong fault tolerance and compatibility, and can be compatible with dynamic scenario changes such as transportation channel repair, material donation and replenishment, and updated needs of disaster-stricken areas during disaster relief. By re-entering the updated basic data, new optimization solutions can be quickly generated through iteration. It can adapt to the dynamically changing on-site environment during emergency rescue and provide emergency management departments with a full-cycle, operable, and highly reliable distribution decision-making tool.

[0031] The optimized solution output by this invention not only strictly meets the hard constraints such as transportation time, material inventory, transport capacity limitations, and demand guarantee, but also fully considers the psychological expectations and fairness perceptions of different disaster-stricken groups. It can maximize the balance between rescue efficiency and the psychological satisfaction of disaster-stricken groups under limited rescue resources. Through precise modeling and optimization of the psychological perceptions of disaster-stricken groups, it effectively avoids the problem of "prioritizing timeliness over fairness" caused by purely efficiency-oriented solutions, reduces negative emotions among disaster-stricken people caused by unequal distribution and a sense of relative deprivation, and prevents group emotional fluctuations and conflicts from the source, ensuring the smooth progress of rescue operations. At the same time, through dual-objective collaborative optimization, it avoids the problems of insufficient rescue timeliness and low material turnover efficiency caused by purely fairness-oriented solutions, achieving the globally optimal allocation of limited rescue resources. This invention maintains the bottom line of efficiency in emergency rescue while also considering the livelihood attributes and social value of rescue work, effectively improving the recognition and satisfaction of disaster-stricken people with rescue efforts.

[0032] In a preferred embodiment of the present invention, step 1 above may include: Step 1.1: Collect and aggregate raw disaster relief data from different data sources to obtain a raw data set. The raw data includes geographic location information, inventory reports, demand assessment reports, and road network status information. Specifically, this includes collecting geographic location information such as latitude and longitude, and administrative boundaries of supply points (hereinafter referred to as supply points, representing a geographical area, such as a reserve warehouse or material distribution center) and disaster-stricken areas (hereinafter referred to as disaster-stricken areas, representing a geographical area, such as disaster-stricken townships or villages) to determine the supply area set. I= {1 , 2 , … ,m}(in m (Indicates the number of supply areas) and the set of disaster-stricken areas J= {1 , 2 , … ,n}(in n (Indicates the number of affected areas); retrieve inventory reports from the inventory management terminals of each supply point to obtain supply area data. i China Resources k stock r ik ,in k Belongs to the collection of relief supplies K ={1 , 2 , …, s}, s To determine the types and quantities of supplies, and simultaneously collect initial inventory data from each disaster-stricken area, we can obtain the disaster-stricken area data. j China Resources k initial inventory r jk Needs assessment reports were compiled through on-site investigations in disaster areas and reports from grassroots levels to determine the affected areas. j Resources k demand d jk Then, road network status information is obtained, including road capacity and damage status, to provide basic data for subsequent calculation of transportation time. All the collected information is classified and summarized to form a raw data set.

[0033] Step 1.2 involves validating and cleaning the original dataset to remove outliers and missing items, resulting in cleaned and standardized data. This includes: performing range checks on all data points in the original dataset to ensure all parameters conform to the logic of the actual rescue scenario; specifically, data related to transportation time must be greater than 0, and material inventory must be... r ik Initial inventory r jk Demand d jkData must be greater than or equal to 0; any negative or other outliers will be discarded. Logical validation will be performed to determine the demand at each affected location. d jk Whether the data is within a reasonable range, avoiding extreme demand data far exceeding the region's carrying capacity, and for outliers exceeding the reasonable range, using box plots to determine anomaly thresholds and removing data exceeding the thresholds; regarding missing inventory data... r ik or r jk The data is filled by the average inventory of corresponding materials at similar supply points or disaster-stricken points. For missing transportation time data, it is supplemented by referring to the average unit transportation time of similar road sections based on the geographical distance and road network type between the corresponding two points, and finally, the cleaned and standardized data is obtained.

[0034] Step 1.3 involves performing standardization and quantification processing on the cleaned and normalized data to convert non-numerical information into numerical parameters in a unified format, resulting in a standardized parameter set. Specifically, this includes: quantifying the non-numerical information in the cleaned and normalized data; quantifying the road network status as smooth, slow, and congested to traffic efficiency coefficients of 1.0, 0.6, and 0.3 respectively, which will be used to adjust the transportation time calculation results; converting the latitude and longitude coordinates in the geographic location information to Cartesian coordinates and calculating the supply area... i to the disaster area j The straight-line distance, combined with the road network traffic efficiency coefficient, yields the unit transportation time. t ij Similarly, calculate the disaster-stricken area l to the disaster area j Unit transportation time t lj ,in Based on the importance of the supplies, the weights of different types of supplies, such as medical supplies, food, and drinking water, were determined. w k Quantified as a value between 1 and 3, with higher importance resulting in a larger weight value; a security requirement coefficient is set. θ =0.8 indicates that meeting 80% of the demand at the disaster-stricken area is the safe threshold; clarify the relevant parameters of prospect theory, including the parameters of the revenue curve. α =0.88, loss curve parameters β =0.88, Profitability Coefficient γ =1, Loss Coefficient φ =2.25 (φ>1, reflecting loss aversion characteristics), probability weight parameters δ =0.61, converting all non-numerical information into numerical parameters in a unified format, forming a standardized parameter set.

[0035] Step 1.4: Based on the preset data structure template, the standardized parameter set is integrated and correlated to ultimately generate a structured basic dataset. Specifically, the preset data structure template uses a three-dimensional framework centered on supply area, disaster-stricken area, and material type, and is divided into three related modules: a basic information module, a material supply and demand module, and a transportation information module. The basic information module stores the supply area set. I= {1 , 2 , … ,m Collection of disaster-stricken areas J= {1 , 2 , … ,n} Collection of types of relief supplies K ={1 , 2 , …, s The basic attributes of the resource supply and demand module include unique identifiers for each region, geographic coordinates, and material type classification labels. The module is designed with fields based on the region-material correspondence to associate and store supply areas. i China Resources k stock r ik Disaster-stricken areas j China Resources k initial inventory r jk and demand d jk and resources k Importance weight w k Safety requirement coefficient θ Equivalent parameters; the transportation information module is designed with fields based on the combination of origin and destination, specifically storing supply areas. i to the disaster area j Unit transportation time t ij Disaster-stricken areas l to the disaster area j ( (unit transportation time) t lj Traffic-related parameters, etc.

[0036] During the integration process, each data point in the standardized parameter set is first filled into the corresponding module according to the field definition. Cross-module associations are established through unique regional identifier codes and material type labels to ensure that the material inventory in the supply area can be accurately matched with the needs and transportation time of the corresponding disaster-stricken area; for example, the supply area i resources k Existing stock r ik With the disaster-stricken areas jresources k Demand d jk Unit transportation time t ij Through the supply area i Disaster-stricken areas j ,resource k The three-dimensional index is associated and bound; finally, the integrity of the integrated data is verified to confirm that the relevant parameters of each region and each material are complete and the association logic is correct, and finally a structured basic dataset is generated to provide a standardized and directly usable data source for subsequent data calls.

[0037] In a preferred embodiment of the present invention, step 2 above may include: Step 2.1: Based on the basic dataset, extract and define the sets and parameters required for the model to obtain the model parameter set. The required sets include the supply point set, the disaster-affected point set, and the material type set. The required parameters include transportation time, material inventory, demand, material weight, and safety requirement coefficient. Specifically, this involves accurately extracting three core sets from the structured basic dataset, including the supply area set... I= {1 , 2 , … ,m}, m The number of supply areas, such as reserve warehouses and distribution centers for donated materials, is determined by extracting unique identifier codes from the basic information modules in the basic dataset; the set of disaster-stricken areas... J= {1 , 2 , … ,n}, n The number of affected areas, such as affected townships and villages, is determined by the geographical coordinates of the basic information module; the types of relief supplies are also included. K ={1 , 2 , … ,s}, s The types and quantities of supplies, such as medical supplies, food, and drinking water, are determined based on the supply type classification labels in the basic dataset; quantitative parameters are extracted for each type and the units are standardized, all in pieces or tons, for the supply area. i to the disaster area j Unit transportation time t ij Disaster-stricken areas l to the disaster area j ( (unit transportation time) t lj Extracted from the transportation information module, supply area i China Resources k stock rik Disaster-stricken areas j China Resources k initial inventory r jk Disaster-stricken areas j Resources k demand d jk Extracted from the supply and demand module, resources k Importance weight w k The weighting was determined using a combination of expert scoring and the analytic hierarchy process (AHP). Medical supplies were weighted at 3, food and drinking water at 2, and other daily necessities at 1. The safety requirement coefficient was... θ =0.8, set with reference to safety requirements standards in the rescue field; preset prospect theoretical parameters, referencing existing empirical research and psychological analysis results of rescue scenarios, determine the parameters of the benefit curve. α =0.88, loss curve parameters β =0.88, Profitability Coefficient γ =1, Loss Coefficient φ =2.25 (greater than 1, reflecting loss aversion), probability weight parameter δ =0.61, organize and summarize all sets, parameters and unit information to form a clearly labeled set of model parameters that can be directly called.

[0038] Step 2.2: Based on the model parameter set, establish a mathematical expression with the objective of minimizing the total transportation time, resulting in the first objective function. Specifically, this includes: based on the model parameter set and considering the material flow pattern of direct delivery from the supply area to the disaster-stricken area combined with mutual assistance and sharing between disaster-stricken areas in actual rescue efforts, constructing a first objective function to minimize the total transportation time. This first objective function comprehensively calculates two types of transportation time: the direct delivery time from the supply area to the disaster-stricken area and the transportation time for resource sharing between disaster-stricken areas. The mathematical expression strictly follows the actual logistics logic of the rescue scenario, specifically: ; in, Indicates from the supply area i to the disaster area j Delivery resources k The quantity corresponds to the transportation volume of the direct delivery route; Indicates from the disaster area l to the disaster area j ( (To avoid meaningless self-sharing and resource sharing) k The quantity corresponds to the transportation volume of the mutual assistance route in the disaster-stricken area; the three-layer summation symbols cover all material types and supply / disaster areas respectively, ensuring that the total transportation time is calculated without omission and achieving precise optimization of overall transportation efficiency.

[0039] Step 2.3: Based on the model parameter set and the preset foreground theoretical parameters, calculate the core parameters used to characterize psychological perception; the core parameters include the subjective perception probability obtained based on the probability weight function, and the psychological perception value obtained based on the foreground value function, specifically including: first calculating resources k Global supply probability This parameter reflects the resources k The degree of supply and demand tension, the molecular level of resources in all disaster-stricken areas k The total demand, i.e. All disaster-stricken areas received relief supplies. k The sum of demands; the denominator is resources. k The total supply, i.e. The sum of the supply area inventory and the initial inventory at the disaster-stricken area is expressed mathematically as follows: ; Then based on and probability weight parameters δ The probability of subjective perception is calculated using a probability weighting function. To depict the disaster victims' demand for resources k Subjective judgments about whether supplies can be successfully delivered, such as a low probability of supply but the disaster victims may subjectively exaggerate the scarcity, can be expressed by the following formula: ; Then calculate the gap between the actual amount obtained and the security requirements. ,in It is a disaster area j Resources k Initial inventory, It is all supply areas to j Delivery k Total amount of supplies It is all other disaster-stricken areas to j Shared k Total amount of supplies yes j right k The safety requirements are met to satisfy 80% of the demand, as shown in the formula: ; Finally based on Using prospect theory parameters, the perceived value is calculated through the prospect value function. :when hour, j right k When the actual amount obtained meets or exceeds safety requirements, the psychological perception is a benefit, expressed as: ;when When the actual amount obtained does not meet the safety requirements, the psychological perception is a loss, expressed as: It accurately depicts the non-linear psychological reactions of disaster victims to the gains and losses of resources.

[0040] Step 2.4: Integrating the weight of resources, subjective perception probability, and psychological perception value, construct a mathematical expression aimed at maximizing overall psychological satisfaction, thus obtaining the second objective function. This function specifically includes: the resource importance weights in the integrated model parameter set. w k Calculated subjective perception probability With psychological perceived value Construct a second objective function that maximizes overall psychological satisfaction; where, w k Determined through expert scoring combined with the analytic hierarchy process, such as emergency medications. w k =3. Drinking water w k =2.5, Convenience Foods w k =2, used to distinguish the importance of different materials in psychological perception; It reflects the disaster victims' subjective judgment on the possibility of resource availability. It reflects the psychological feelings brought about by actual gains and losses, with positive values ​​for gains and negative values ​​for losses. Multiplying these three values ​​together can accurately quantify the psychological satisfaction of a single disaster-stricken point with a single type of material; the objective function covers all material types through double summation. With all disaster-stricken areas To ensure a comprehensive assessment of overall psychological satisfaction, the mathematical expression is: ; The logic behind this function is that the overall psychological satisfaction is the sum of the psychological contributions of various materials to each disaster-stricken area. It takes into account both the differences in the importance of materials and the subjective probability perception and non-linear gain-loss response of the disaster victims, thus conforming to the psychological characteristics of the disaster-stricken groups in actual rescue operations.

[0041] Step 2.5 defines the decision variables of the model and sets constraints on resource supply, regional sharing, and the scope of demand satisfaction based on the model parameter set. Specifically, this includes determining the two core decision variables of the model: Indicates from the supply area i to the disaster area j Delivery resources k Quantity, Indicates from the disaster area l to the disaster area j ( Shared resources k The quantities, both of which must be non-negative real numbers, cannot be negative and decimals such as 0.5 tons are supported; four constraints are set based on the model parameter set: the supply capacity constraint is: ; Ensure that the total distribution volume of various resources in each supply area does not exceed its actual inventory, avoiding over-allocation that could lead to resource shortages; shared resource constraints are: ; in It is a disaster area l Resources k Net surplus, constraints ensure l Only their own surplus resources can be shared without affecting their own needs; the restriction prohibiting self-sharing is as follows: ; To avoid unnecessary transportation costs caused by disaster-stricken areas sharing resources with themselves; the scope of demand satisfaction is constrained as follows: ; Ensure that the actual satisfaction rate of various resources in the disaster-stricken area is not lower than the safety threshold. θ =0.8, to avoid severe shortages, and not exceeding 1, to avoid waste of resources.

[0042] Step 2.6 integrates the first objective function, the second objective function, decision variables, and constraints to form a multi-objective optimization model incorporating prospect theory. Specifically, this includes: before integrating the multi-objective optimization model, verifying the consistency of each core element: firstly, verifying the suitability of the objective function and decision variables, confirming the first objective function... T Second objective function S The core independent variables in the data are all decision variables. (Supply Area) i to the disaster area j Delivery resources k (quantity) and (Disaster area) l to the disaster area j Shared resources k Quantity, ( ), and all summation dimensions K , I , J The first step is to ensure a complete match with the set definition in the model parameter set; the second step is to verify the correlation between constraints and parameters, confirming the relevant constraints among the four constraints, including supply capacity constraints and shared resource constraints. r ik (Supply Area) i resources k (existing stock) d jk (Disaster area) j resources k Parameters such as demand are all derived from the model parameter set, and there are no conflicts in formula symbols and value ranges; thirdly, the closed-loop nature of psychological perception-related elements is verified to confirm the second objective function. π( p k (Subjective perceived probability) v (Δ jk The calculation logic of (psychologically perceived value) fully follows step 2.3 and is consistent with the parameters of prospect theory. α , β The calls to etc. were all complete.

[0043] After verification, systematic integration is carried out according to the hierarchical logic of variables, objectives, and constraints: The first step is to integrate the decision variables. , Bind to two objective functions, explicitly , The value of directly determines the total transportation time. T and overall psychological satisfaction S The calculation results, and the optimization directions of the two objective functions. T minimize, S The first step is to clearly distinguish the variables through symbolic logic; the second step is to bind the constraints to the decision variables, thus... Define an upper limit for the value of supply capacity constraints, for Define the value rules for shared resource constraints and prohibition of self-sharing constraints, and associate them with the scope constraints of demand satisfaction. , The first step is to match the actual needs of the disaster-stricken area, ensuring that the values ​​of decision variables always remain within the feasible domain that aligns with the actual rescue situation. The second step is to encapsulate and integrate the model framework, determining that the model input is the set of model parameters from step 2.1, and the output is the set of parameters that satisfy all constraints. , The optimal solution, the core optimization objective of the model, is to minimize the total transportation time under four constraints. T Maximize overall psychological satisfaction S .

[0044] After integration, adaptability calibration is performed based on actual rescue scenarios: considering road network characteristics such as mountain road transport time for different disaster scenarios including mountain floods and earthquakes. t ij Large fluctuations and demand characteristics for supplies, such as the weight of medical supplies after an earthquake. w k Higher, confirming the model can be improved by adjusting parameters such as t ij , w k Adaptable to different scenarios; designed for small-scale operations m <5、 n <10 and large scale m ≥10、 nIn ≥20 rescue scenarios, the model's summation dimensions and constraint calculation logic were verified to be adaptable, with no missing dimensions or computational redundancy issues. Finally, the model's applicable boundaries were clarified, namely, that the model is applicable to rescue material distribution scenarios with multiple supply points, multiple disaster sites, and multiple material types, and must be run on the generated structured basic dataset to ensure the model's practicality and feasibility. Through the above-mentioned hierarchical integration and scenario calibration, the final multi-objective optimization model that integrates prospect theory not only retains the core requirement of optimizing rescue transportation efficiency, but also accurately portrays the psychological perception of disaster-stricken groups through relevant elements of prospect theory, while ensuring the feasibility of the solution through constraints. The logical closed loop of each element and the clear correlation of parameters fully adapt to the decision-making needs of rescue material distribution in complex disaster scenarios.

[0045] In a preferred embodiment of the present invention, step 3 above may include: Step 3.1: Determine the boundary of the value range of the first objective function and the second objective function, and obtain the reference maximum and reference minimum values ​​for each objective function. Specifically, this includes: combining the initial population assessment and the analysis of the characteristics of the rescue problem, accurately determining the first objective function (total transportation time). T ) and the second objective function (overall psychological satisfaction) S The value range boundary of ) is defined to ensure that the boundary covers the value range of all feasible solutions; for the total transportation time T The reference values ​​are cross-validated in two ways: one is based on the initial population assessment, calculating the values ​​for 50 to 100 randomly generated feasible solutions. T The maximum value among the values ​​is taken as the reference maximum value. The minimum value is used as a reference minimum value. Second, based on the analysis of the problem characteristics, referencing the maximum value. The maximum unit transportation time from all supply areas to disaster-stricken areas and between disaster-stricken areas ( , ) and maximum possible delivery volume, sharing volume ( , The sum of the products of ), with reference to the minimum value. For the minimum unit of transportation time ( , The sum of the products of the minimum necessary delivery quantity and the shared quantity (the transportation quantity that meets the lower limit of demand); for overall psychological satisfaction. S Reference maximum value To ensure that the psychological perceived value of all types of resources in all disaster-stricken areas reaches its optimal Δ jk The sum when ≥0 and maximized, referencing the minimum value. In all disaster-stricken areas, the availability of various resources has fallen short of safety requirements. jkThe sum is less than 0 and minimized. This is combined with practical examples of small-scale rescue scenarios, such as a scenario with 3 supply areas, 5 disaster sites, and 2 types of resources. =7.7250、 , , Calibration is performed to ultimately determine the reference maximum and minimum values ​​for each objective function, providing a precise basis for normalization.

[0046] Step 3.2: Based on the reference maximum and minimum values ​​of each objective function, normalize the output values ​​of the first and second objective functions respectively to obtain the normalized transportation time index and psychological satisfaction index. Specifically, this includes: normalizing the actual output values ​​of the two objective functions based on the determined reference boundaries to eliminate dimensional differences and make transportation time and psychological satisfaction comparable; for the total transportation time index, the normalization formula is as follows: ,in The actual total transportation time for the current delivery plan is calculated using the first objective function and then normalized. The value range is strictly limited to [0,1]. The closer the value is to 0, the closer the transportation time of the plan is to the optimal level. For the overall psychological satisfaction index, since the original goal is to maximize it, reverse normalization logic is used to ensure that it is consistent with the optimization direction of the transportation time index. The formula is: ,in The actual overall psychological satisfaction with the current plan is calculated using the second objective function, and then normalized. The value range is also [0,1], and the closer the value is to 0, the higher the original psychological satisfaction. For example, in a small scenario with 3 supply areas, 5 disaster points, and 2 types of relief supplies, , , ,but If the plan , , ,but Finally, the normalized transportation time index was obtained. With psychological satisfaction index .

[0047] Step 3.3 involves setting relative importance weights for transportation time and psychological satisfaction based on decision-making needs, resulting in a set of weighting coefficients. Specifically, this includes scientifically setting the transportation time weight based on the actual decision-making needs and objective priorities of the rescue scenario. w t And psychological satisfaction weight w s The weights must meet the constraints. w t≥0、 w s ≥0 and w t + w s =1, ensuring the rationality and exclusivity of weight allocation; the weight setting is mainly based on the rescue stage, disaster type, and resource characteristics: if it is during the golden 72-hour rescue period after an earthquake, transportation efficiency has the highest priority and can be set to 1. w t =0.75、 w s =0.25; If the disaster is in the post-disaster reconstruction phase, it is necessary to focus on both the fairness of distribution and the satisfaction of the affected groups, and a setting can be made. w t =0.25、 w s =0.75; In conventional rescue scenarios or multi-objective balanced optimization needs, the overall effect is better when considering both transportation time and psychological satisfaction in most large-scale scenarios. Therefore, the balanced weighting is recommended. w t =0.5、 w s =0.5; Meanwhile, based on practical application patterns, increasing the weight of transportation time usually improves the stability of the solution. The weight can be fine-tuned according to the stability requirements of the decision-making process. For example, in large-scale rescue scenarios with high stability requirements, involving more than 10 supply areas and more than 20 disaster-stricken points, the weight can be adjusted. w t Adjusted to 0.6 w s =0.4, ultimately forming a set of weighting coefficients that fit actual needs.

[0048] Step 3.4 involves using the aforementioned weighting coefficients to perform a linear weighted combination of the normalized transportation time index and the psychological satisfaction index, forming a single-objective comprehensive utility function. This specifically includes using determined weighting coefficients. w t As a weight for transportation time, w s As a weight for psychological satisfaction, satisfying w t + w s =1, for the normalized transport time index With psychological satisfaction index A linear weighted combination is used to construct a logically rigorous single-objective comprehensive utility function that aligns with the needs of rescue decision-making; the function formula strictly follows the multi-objective transformation logic, specifically: in, This item directly reflects the contribution of transportation efficiency to overall utility. The shorter the transportation time, the better; the smaller the value of this item, the more conducive it is to optimizing the overall utility. This reflects the contribution to psychological satisfaction, because Using reverse normalization, , The smaller the value, the higher the original psychological satisfaction. The higher the satisfaction level, the smaller the corresponding value can be achieved through subtraction. U The value is completely consistent with the optimization direction of transportation time, achieving synergistic optimization of the two objectives.

[0049] To further illustrate with a real-world example: If a rescue mission is in its routine phase, a balanced weighting approach is used. w t =0.5、 w s =0.5, corresponding to the solution data for small-scale scenarios in step 3.2. , Then the overall utility of the plan The calculation process clearly demonstrates the balancing effect of the weights on the two indicators. When a rescue scenario prioritizes transportation efficiency, such as... w t =0.75, the proportion of transportation time in the overall utility index increases, ensuring the core need for fast delivery; when the focus needs to be on psychological satisfaction, such as w s =0.75, then by weighting the values ​​to strengthen the perception of fairness and psychological needs, the final comprehensive utility function is formed. U This will become a unified standard for evaluating the merits of different solutions, providing a clear evaluation basis for subsequent algorithm solutions.

[0050] Step 3.5 defines the optimization objective as minimizing the single-objective comprehensive utility function, thus transforming the multi-objective optimization model into a single-objective comprehensive utility minimization problem. Specifically, this includes: defining the optimization objective as minimizing the single-objective comprehensive utility function, i.e. min:U This process achieves a deep transformation from a multi-objective optimization model to a single-objective problem, while fully preserving the core requirements of the original dual objectives, forming a logical closed loop. The core logic of this transformation lies in... U The value of combines the optimization level of transportation time and psychological satisfaction: when U When taking the minimum value, Normalized transit time approaches 0, meaning the total transit time is close to the reference minimum. Transportation efficiency reaches its optimal level; at the same time Normalized psychological satisfaction approaches 0, corresponding to the original psychological satisfaction. Approaching the reference maximum value This ensures that the psychological perception of the affected groups reaches its optimal level, achieving a synergistic optimization of efficiency and fairness.

[0051] By combining parameter constraints and scene characteristics, the boundary of the transformed single-objective problem is further determined: U The range of values ​​is determined by both the weighting coefficient and the normalization index. Worst delivery time When psychological satisfaction is optimal U=w t ;when Optimal transportation time When psychological satisfaction is at its worst U=−w s ,therefore U The range of values ​​for is [− w s , w t The boundary is clear and controllable, which can effectively narrow the search range of subsequent algorithms, avoid invalid searches, and improve solution efficiency. In addition, this transformation is highly compatible with the improved genetic algorithm in step 5: the fitness function of the algorithm can be directly adopted using comprehensive utility. U No additional multi-target adaptation mechanism needs to be designed; it can be achieved through search. U The minimum value can be used to quickly locate the optimal solution; at the same time, combined with w t The algorithm enhances the stability of the solution by increasing the weight. The transformed single-objective problem can maintain solution stability under different weight settings, avoiding solution quality fluctuations caused by multi-objective conflicts. This ensures that in complex rescue scenarios with multiple resources and regions, the algorithm can efficiently output optimized solutions that balance transportation efficiency and psychological satisfaction.

[0052] In a preferred embodiment of the present invention, step 4 above may include: Step 4.1: Based on the supply points, disaster-stricken points, and material types defined in the multi-objective optimization model, design a joint matrix coding structure to obtain a coding framework for representing individual complete solutions. This coding framework includes a three-dimensional delivery matrix representing the direct delivery volume and a three-dimensional sharing matrix representing the resource sharing volume between regions. Specifically, it includes: a set of supply areas defined in the multi-objective optimization model... I ={1 , 2 , … ,m}, Collection of disaster-stricken areas J ={1 , 2 , … ,n} and collection of relief supplies types K ={1 , 2 , … ,sA joint matrix encoding structure of a 3D delivery matrix and a 3D shared matrix is ​​designed to form a solution individual encoding framework that can be directly adapted to subsequent genetic algorithm operations; wherein, the 3D delivery matrix... The dimension strictly corresponds to the number of supply areas. m ×Number of disaster-stricken areas n × Quantity of Material Types s Each element in the matrix All are non-negative real numbers, and their values ​​range from [0, 1 / 2] to [0, 1 / 2 r ik [, meaning not exceeding the supply area] i Resources k The inventory is specifically designed for accurate recording of supplies from the supply area. i to the disaster area j The direct delivery volume ensures that every direct shipment has a clear, quantifiable record; a three-dimensional shared matrix. The dimension is the number of disaster-stricken areas initiated by sharing. n × Number of disaster-stricken areas to be shared n × Quantity of Material Types s Matrix elements Also a non-negative real number, its range of values ​​is... , For the disaster-stricken area l Resources k The net surplus, and mandatory satisfaction l=j hour This completely eliminates meaningless self-sharing behavior; the two matrices form a closed loop through the material flow path: the distribution matrix covers one-way direct transportation from the supply area to the disaster area, and the sharing matrix covers two-way mutual assistance transportation from the disaster area to the disaster area. Together, they completely represent all the key information of a relief material distribution plan, and the coding structure supports element-level precise modification during subsequent genetic operations such as crossover and mutation, ensuring the feasibility and effectiveness of the algorithm operation.

[0053] Step 4.2: Based on the three-dimensional delivery matrix in the coding framework, multiple different direct delivery schemes are generated using various allocation strategies to obtain a set of delivery schemes. These multiple allocation strategies include random allocation based on demand ratio, heuristic allocation based on spatiotemporal efficiency, and completely random allocation. Specifically, based on the three-dimensional delivery matrix X in the coding framework, three differentiated allocation strategies are used to generate multiple sets of direct delivery schemes. The three strategies generate initial delivery schemes in approximately equal proportions, ensuring population diversity while avoiding the local optimum trap caused by a single strategy. The first strategy is a random allocation strategy based on demand ratio: for each supply area... i resources k First calculate the disaster-stricken areas j Resources k Demand share ,in Resources for all disaster-stricken areas k The total demand is calculated, and if the total demand is 0, then the allocation ratio is 0; then a multinomial distribution is constructed based on this ratio. The allocation ratio for each disaster-stricken area was determined through random sampling; finally, the sampling ratio was compared with the supply area. i resources k Existing stock r ik Multiply, we get x ijk and verify If the quantity exceeds the limit, the allocation will be reduced proportionally to ensure that supply capacity constraints are not violated.

[0054] The second approach is a heuristic allocation strategy based on spatiotemporal efficiency: first, allocate resources by weight. w k Sort all resource types in descending order, allocating resources with higher weights first; for each priority resource, calculate the allocation for each disaster-stricken area. j The overall priority score is: ; in The current safety demand satisfaction rate is represented by a higher score, indicating higher transportation efficiency and more urgent demand. Disaster-stricken areas are ranked from highest to lowest score, and resources are prioritized for allocation to the highest-scoring areas. The allocation amount is calculated based on the remaining stock in the supply areas and the safety demand gap in the disaster-stricken areas. The smaller value in the distribution is used to allocate resources and update the remaining stock in the supply area. This process is repeated until resources are allocated or there is no demand gap. The third approach is a completely random allocation strategy: using a Beta(0.5, 0.5) distribution to generate resources for each disaster-stricken area. j For the supply area i resource k The distribution ratio is characterized by generated values ​​concentrated at both ends of 0 and 1, ensuring random diversity while also allowing for extreme distributions to cover more feasible solutions. The generated ratio values ​​are normalized to ensure the sum of the ratios for all affected areas is 1, and then compared with the supply area... i resources k Existing stock r ik Multiply, we get x ijk ,make sure This makes full use of the resources in the supply area; after all the delivery plans generated by the three strategies are summarized, a set of delivery plans covering different allocation logics is formed.

[0055] Step 4.3: For each direct delivery scheme in the set of delivery schemes, calculate and fill the corresponding sharing matrix according to the material inventory, demand and transportation time constraints to obtain the corresponding resource sharing scheme, thereby forming a complete solution. Specifically, for each direct delivery scheme in the set of delivery schemes, i.e. the determined three-dimensional delivery matrix X, calculate and fill the corresponding sharing matrix Y accurately according to the process of calculating the supply and demand gap, matching the supply and demand relationship, and iteratively allocating and filling, to ensure that the sharing scheme meets all constraints. The first step is to accurately calculate the net surplus and net deficit for each disaster-stricken area. l and each resource k Calculate net surplus ,like Then, a value of 0 indicates that no shared resources are available; for each disaster-stricken area j and each resource k Calculate the net deficit + ,like The first step is to set the value to 0, indicating that no additional resources are needed. The second step is to establish a supply-demand matching relationship: for each type of resource... k Disaster-stricken areas with a net surplus greater than 0 are categorized into the supplier group. L k Disaster-stricken areas with a net deficit greater than 0 are categorized as demand-side groups. J k ;right L k Each supplier l and J k Each demand side j Calculate the transportation time t lj , and according to t lj The first step is to sort the suppliers and demanders in ascending order to form a priority matching list; the second step is to iteratively allocate and fill the matrix: according to the order of the matching list, starting from the suppliers... l To the demand side j Allocate resources k Allocation amount Updated immediately after allocation = , ;like Then remove the supplier from L k Removed from the middle, if Then the demand side will be from J k Remove from the middle; repeat this iterative process until... L k empty or J kEmpty; for suppliers, demanders, and resource combinations without sharing behavior, the corresponding y ljk Setting it to 0 completes the filling of the shared matrix Y, which, together with the delivery matrix X, constitutes a complete and constrained solution.

[0056] Step 4.4 involves aggregating and verifying all generated individual solutions to ensure that each individual satisfies all constraints set by the multi-objective optimization model of the fusion prospect theory. This ultimately forms an initial feasible solution set that satisfies all constraints. Specifically, this includes: aggregating all generated individual solutions of the delivery matrix X + shared matrix Y in sequence to form an initial solution set. The set size is determined based on the problem size: 50 to 80 individuals for small scenarios, 80 to 120 individuals for medium scenarios, and 120 to 150 individuals for large scenarios, ensuring sufficient population diversity. Subsequently, a process of hierarchical verification, targeted repair, and secondary verification based on constraint type is used to verify whether each individual solution satisfies all constraints of the multi-objective optimization model, ensuring the validity of the initial feasible solution. The first step is hierarchical constraint verification: first verifying simple constraints, prohibiting self-sharing constraints. First, check if all diagonal elements in the shared matrix are 0. If any non-zero values ​​exist, set them to 0. Then, verify the core constraints: supply capacity constraints, shared resource constraints, and demand fulfillment range constraints, for each supply area. i and resources k ,check For each disaster-stricken area l and resources k ,check For each disaster-stricken area j and resources k The verification formula is as follows: ; The second step is to specifically address the violations by individual entities: such as those that violate supply capacity constraints. According to each disaster-stricken area j Distribution ratio reduce Ensure that the sum after reduction equals If the shared resource constraints are violated Reduced based on the proportion of shared volume Alternatively, the shared route with the longest transit time may be cancelled first; if the requirement to meet the demand is violated, the time limit may be lower than 100%. θIf the value is higher than 1, the corresponding sharing matrix is ​​readjusted, and resources are supplemented from the adjacent surplus area; if the value is higher than 1, the delivery volume or sharing volume is reduced, and the path with high transportation efficiency is retained first; the third step is secondary verification and set determination: the full constraint verification is performed again on the repaired solution individuals to ensure that no violations are missed; all solution individuals that pass the verification are summarized to form the final initial feasible solution set; if the number of qualified individuals after repair is less than the set size, new solution individuals are generated, and the strategy of steps 4.2 to 4.3 is used to complete the verification to ensure that the initial feasible solution set meets both the size requirement and all constraints, providing a high-quality initial population for subsequent algorithm iteration and optimization.

[0057] In a preferred embodiment of the present invention, step 5 above may include: Step 5.1: Using the initial feasible solution set as the initial population, calculate the fitness value of each solution individual according to the single-objective comprehensive utility minimization problem. Specifically, this includes: using the initial feasible solution set generated in step 4.4 as the initial population, each solution individual is represented by a three-dimensional distribution matrix. and 3D shared matrix The composition has been validated and the constraints have been verified; the fitness value calculation strictly follows the single-objective comprehensive utility function. The specific process is as follows: First, calculate the total transportation time for the individual. Substituting into the formula for the first objective function: ; Substitute each element of the matrix with its corresponding unit transportation time, ensuring no element is omitted during the summation; then calculate the overall psychological satisfaction level. Substitute into the formula for the second objective function ,in , according to Calculate the positive and negative cases. + Then respectively , Normalize, , Substitute the determined reference boundary values; finally, compare the normalized result with the preset weights. w t , w s Substituting into the comprehensive utility formula, we obtain the fitness value of this individual. U The smaller the value, the better the overall optimization effect. After all individuals have been calculated, a list of fitness values ​​with serial numbers is formed, which corresponds one-to-one with the solution individuals.

[0058] Step 5.2: Based on fitness values, a tournament selection strategy is used to select parent individuals from the current population for genetic operations, resulting in a set of parent individuals. Specifically, this includes: selecting parent individuals based on a fitness value list using a tournament selection strategy, the core of which is balancing the preservation of superior genes with population diversity; first, determining the tournament size. k When the population size is 50 to 100 k =3, from 100 to 150 k =4, above 150 k =5, the larger the scale k The larger the value, the greater the selection pressure; the selection process strictly follows the logic of sampling without replacement, competition, and retention: random sampling without replacement is performed from the current population. k Individual solutions are grouped into temporary competitive groups; the fitness values ​​of individuals within each group are compared one by one. U Select U The individual with the smallest value is selected as the parent; this parent is temporarily removed from the original population to avoid duplicate selection, while a new randomly sampled individual is added to the original population to maintain the sampling pool size; this process is repeated until a parent set equal to the initial population size is selected, forming the parent set; if multiple... U If the best individuals have the same value, one of them is randomly selected to ensure the randomness and fairness of the selection process. In the end, the parent set contains both individuals with top fitness and a certain proportion of individuals with medium fitness, providing a rich gene pool for subsequent crossover and mutation.

[0059] Step 5.3 involves performing a uniform crossover operation along the resource dimension on the individuals in the parent set to generate new offspring individuals, resulting in a candidate population after crossover. Specifically, this includes performing a uniform crossover operation along the resource dimension on the parent set according to a random pairing and resource-by-resource crossover principle, with the crossover probability... Dynamically set according to problem size: Small scenarios medium-sized scene Large-scale scenes The larger the scale, the higher the crossover probability, promoting population iteration; the specific process is as follows: First, pair the parent generation sets in random order to form several pairing groups, and retain unpaired individuals directly as offspring; for each pairing group, parent generation 1 and parent generation 2, for each resource type... k Independently generate binary mask matrix M k Matrix Dimensions and Delivery Matrix X Consistent m × n Each element is randomly selected as either 0 or 1, with a probability of 0.5 for both. Furthermore, the mask matrices for different resources within the same pairing group are completely independent; the offspring delivery matrix... According to the formula as follows: ; This indicates that the matrix elements are multiplied correspondingly, meaning that when the mask is 1, the matrix inherits 1 from the parent. When the value is 0, it inherits 2 from the parent. Verify immediately after crossover. Supply capacity constraints, if a certain supply area i resources k Total delivery volume Exceeding existing stock Then reduce each proportionally The reduction factor is Ensure that the sum after reduction equals After the repair is complete, recalculate the shared matrix according to the logic in step 4.3. First, calculate the net surplus or deficit of each disaster-stricken area, then allocate shared resources in ascending order of transportation time. After all pairing groups have been processed, a crossover candidate population with the same size as the parent generation is formed.

[0060] Step 5.4 involves performing a targeted resource reallocation mutation operation on individuals in the candidate population after crossover to enhance local search capabilities and obtain the mutated population. Specifically, this includes performing a targeted resource reallocation mutation operation on individuals in the candidate population after crossover. This operation focuses on the optimal allocation of scarce resources, avoiding excessive mutation that could destroy high-quality genes, while also enhancing the algorithm's local search capabilities and increasing the mutation probability. p m The quantity is dynamically adjusted according to resource type; when there are 2 to 3 types of resources... p m =0.08, when there are 4 or more types p m =0.05, p m This represents the probability that an individual will be selected to undergo a mutation operation; a lower value reduces the damage to desirable genes. The specific process is as follows: First, determine the individuals to be mutated, and then... p m Iterate through all individuals in the crossover candidate population, randomly determining whether each individual is a candidate for mutation. If an individual is selected, proceed to the subsequent mutation process; unselected individuals are directly retained in the mutated population. Next, select the most scarce resource, and for the selected candidates, calculate the resource requirements for each resource. k scarcity score ;in Characterization resources k The degree of scarcity is indicated by a value; a higher value indicates a more scarce resource. For resources k The global supply probability; Assign importance weights to resource k; select scores The highest resource is recorded as , The number represents the most scarce resource; subsequent mutations only apply to... Execution ensures that mutations focus on core needs.

[0061] Then randomly select a supply area. i Supply area collection I ={1 , 2 , … ,m}, statistics on the supply area to Distribution of goods: Identify the supply area's distribution to The disaster-stricken area with the largest allocation is denoted as The number of the affected area that requires a reduction in delivery volume is indicated; then, the supply area's coverage area is calculated for all affected areas. Demand satisfaction rate ; Characterizing the disaster-stricken area j For the most scarce resources The degree of demand satisfaction is determined by a value closer to 1, indicating a higher satisfaction rate. Then, the following is found... The lowest-affected area is denoted as The disaster area number indicates where increased delivery volume is needed; begin calculating available resources, starting from... Towards The amount of resources mobilized Δ , Δ The resource mobilization amount represents a single mutation, a non-negative real number. We then define two intermediate variables to simplify the calculation: yes right The remaining amount after the safety requirements are met is calculated using the following formula: ; yes right The safety demand gap is calculated using the following formula: ; The amount of resources that can be mobilized is simplified to: ,in express In meeting safety requirements The maximum amount of resources that can be mobilized after the mobilization is ensured. right The demand satisfaction rate is no less than the safety demand coefficient. θ ; express To achieve the maximum amount of resources required to meet security needs, ensure that after mobilization... right The demand satisfaction rate should not exceed 1, to avoid wasting resources; minThe function takes the smaller of the two values ​​to ensure that the mobilization amount meets the model constraints.

[0062] Finally, resource allocation and constraint repair are performed. If the calculated Δ > 0, adjustments are made to the corresponding elements in the delivery matrix. , If Δ≤0, it means there are no available resources to allocate, and the mutation operation for that individual is abandoned directly. After the resource allocation is completed, re-verify whether the individual meets all model constraints such as supply capacity and demand satisfaction range. If there are violations, reduce or supplement the corresponding resource amount proportionally. After the constraint repair is completed, recalculate the shared matrix according to the calculation logic of net surplus and net deficit in step 4.3. Y First, ensure that the sharing scheme is adapted to the adjusted delivery matrix. Then, summarize all unselected individuals, individuals that have completed mutation and repair, and individuals that have given up mutation operations to ensure that the population size is consistent with the candidate population after crossover, and finally obtain the mutated population.

[0063] Step 5.5: Implement an elite retention strategy on the mutated population, directly retaining the individuals with the highest fitness values ​​from the previous generation into the next generation. After elite retention, monitor population diversity to trigger a diversity injection operation when the population diversity falls below a set threshold. This includes implementing a combined elite retention and diversity maintenance strategy on the mutated population to ensure both algorithm convergence speed and solution quality. First, perform elite retention: extract the fitness values ​​from the previous generation population. U The smallest 0.5% of individuals are designated as elite individuals. If the calculated number is less than one, one is retained; otherwise, the integer value is rounded up. For example, one elite individual is retained for a population size of 200, and two are retained for a population size of 400. These elite individuals are then directly added to the current offspring population, replacing an equal number of individuals with the highest (or worst) fitness values ​​in the offspring. This ensures the stable inheritance of superior genes and avoids the loss of high-quality solutions during iteration. Next, diversity monitoring is performed: the variance of all fitness values ​​of the current population including elite individuals is calculated. ,in N For population size, The mean of the fitness values ​​of all individuals is used; a variance threshold is set: 0.001 for small-scale scenarios, 0.0008 for medium-scale scenarios, and 0.0005 for large-scale scenarios. The larger the scale, the lower the threshold, indicating a higher requirement for diversity. If the calculated variance is less than the corresponding threshold, it indicates that the population similarity is too high, and there is a risk of premature convergence, triggering a diversity injection operation: retain the elite individuals in the population, and replace the remaining 50% of the individuals with newly generated random solutions. The new solutions are generated according to the strategies in steps 4.2 to 4.3, with each of the three allocation strategies accounting for 1 / 3. Then, the shared matrix is ​​calculated to ensure that the injected new solutions satisfy all constraints, injecting new genes into the population and breaking the local optimum.

[0064] Step 5.6: Determine if the current population meets the preset iteration termination condition. If not, treat the current population as a new population to be optimized and restart the iteration optimization process. This includes recalculating the fitness value based on the new population and sequentially performing selection, crossover, mutation, elite retention, and diversity maintenance operations. If the condition is met, determine the current population as the convergent optimal solution population. Specifically, this includes: setting dual iteration termination conditions to ensure efficient algorithm convergence and stable solution quality: 1) a maximum number of iterations: 250 for small scenarios, 350 for medium scenarios, and 450 for large scenarios, dynamically adjusted according to the problem size; 2) a continuous convergence condition: the change in the optimal fitness value of the population over 20 consecutive generations is less than a threshold of 1. e -5, that is ,in For the first t The optimal fitness value of each generation is determined as follows: First, check if the maximum number of iterations has been reached. If it has, the iteration is terminated directly. If not, calculate the change in the optimal fitness value over the last 20 generations. If the change is less than the threshold, it indicates that the population has converged, and the iteration is terminated early. If neither condition is met, the current population (including elite individuals, crossover and mutation individuals, and newly injected solutions) is taken as the new population to be optimized. Return to step 5.1 to recalculate the fitness value of each individual, and perform selection, crossover, mutation, elite retention, and diversity maintenance operations in sequence to enter the next iteration. After the iteration terminates, the current population is determined as the converged optimal solution population. The population contains multiple high-quality solutions that balance transportation efficiency and psychological satisfaction, and all solutions satisfy the model constraints, providing sufficient choices for subsequent selection of the optimal solution.

[0065] In a preferred embodiment of the present invention, step 6 above may include: Step 6.1: From the converged population of optimized solutions, select the highest-ranked solution based on its fitness value. This specifically includes: accurately selecting high-quality solutions from the converged population of optimized solutions, with the core criterion being the calculated fitness value. U The smaller the value, the better the overall optimization effect. The specific implementation process is as follows: First, the fitness values ​​of the entire population are sorted in ascending order, that is, the individual with the smallest fitness value is ranked first. If there are multiple individuals with the same fitness value, the tie is broken by calculating the balance score between the total transportation time and the overall psychological satisfaction of the individual (the better the balance, the higher the ranking), so as to avoid the omission of high-quality solutions due to random sorting. After sorting, the number of selections is determined based on the actual alternative needs of the rescue decision. The selection criteria are the top 5%, with no less than 3 and no more than 10. The core logic of setting the number is: too few will limit the decision selection space, and too many will increase the subsequent decoding and review costs; for example, 10 are selected when the population size is 200, and 3 are selected when the population size is 50.

[0066] Subsequently, a secondary constraint check is performed on the top-ranked candidate individuals, covering all core constraints: supply capacity constraint (verifying whether the delivery volume of each supply area does not exceed the inventory), demand satisfaction range constraint (confirming that the demand satisfaction rate of each disaster area is between θ and 1), shared resource constraint (checking that the shared volume does not exceed the net surplus), and prohibition of self-sharing constraint (all diagonal elements of the sharing matrix are 0). If minor violations are found due to the accumulation of values ​​during the iteration process, such as the delivery volume exceeding the inventory by less than 0.1%, they are corrected by proportional fine-tuning, such as reducing the excess portion according to the allocation ratio of each disaster area, and then re-checked. If the violation degree exceeds 0.5%, the individual is directly removed and replaced by individuals from the subsequent ranking. Finally, a high-quality solution candidate set is formed. Each individual in the candidate set is accompanied by three core indicators: fitness value, total transportation time, and overall psychological satisfaction, providing a clear basis for comparison for subsequent decoding and decision-making.

[0067] Step 6.2 involves decoding the selected top-ranked solution to convert the joint matrix encoding into specific delivery and sharing quantities, resulting in an executable material allocation detail. This includes performing refined decoding on each solution in the high-quality candidate set. The core objective is to transform the abstract three-dimensional delivery matrix... X +3D shared matrix Y The combined coding structure is transformed into a material allocation detail that fits the actual business scenario and can be directly verified. The specific process is as follows: First, the correspondence between matrix dimensions and business entities is broken down, and a unique business identifier is matched for each matrix dimension, resulting in a three-dimensional distribution matrix. X The supply area dimension corresponds to the name and code of the actual reserve warehouse or distribution center; the disaster area dimension corresponds to the name and geographical coordinates of the disaster-stricken township or village; and the resource type dimension corresponds to the standard name and specifications of the materials; 3D shared matrix Y The originating or receiving area dimension also matches the name and code of the disaster-stricken area to ensure complete consistency with the business identifier of the delivery matrix.

[0068] Next, matrix element extraction and filtering are performed, extracting each element of the delivery matrix. x ijk For the specific numerical values, invalid items with a value of 0 are removed, indicating no delivery activity. All non-zero items are retained and labeled with their corresponding supply area, disaster area, and resource type combination. For the shared matrix, only non-zero and non-self-shared values ​​are extracted. y ljkThe data is labeled with the shared initiating area, shared receiving area, and resource type combination, while automatically filtering out self-shared zero-value items on the diagonal. The extracted data is then processed for precision, with the retention precision set according to the material type: solid materials retain one decimal place, liquid or bulk materials retain two decimal places, and integer materials are rounded down to avoid operational ambiguity due to excessive decimal places. Finally, the data is categorized and organized according to resource type, transportation direction (direct delivery or mutual sharing), and originating area to form a structured material allocation detail. The detail fields include: serial number, material type and specifications, transportation direction, originating area name (supply area or shared initiating area), originating code, destination name (disaster area or shared receiving area), destination code, specific quantity, and precision description, ensuring that every material flow is traceable, verifiable, and free of any ambiguous information.

[0069] Step 6.3: Based on the executable material allocation details, generate and output the final relief material distribution plan and resource sharing plan. Specifically, this includes: generating highly operable final relief material distribution and resource sharing plans in modules and throughout the entire process, based on the structured material allocation details, ensuring the plans can directly guide relief dispatch and execution. The specific implementation process is as follows: First, break down the core modules of the plan, confirm the division of labor between the distribution plan module and the sharing plan module, and add a summary statistics module and an operation guidance module to form a complete plan system; the distribution plan module summarizes detailed information for each supply area, with each supply area corresponding to an independent sub-module, including: basic information of the supply area (name, code, contact person, contact information); responsible distribution scope (list of all disaster-stricken areas covered); material distribution list for each disaster-stricken area (including material type, specifications, and quantity); and estimated transportation time (based on unit transportation time). t ij And calculation of vehicle speed; transportation route planning, matching unit transportation time. t ij The corresponding actual road or emergency access names are provided, along with key nodes such as bridges and tunnels. Transportation vehicle matching suggestions are provided based on the characteristics and quantity of the supplies: refrigerated trucks for medical supplies and vans for bulk food items. Delivery priorities are also assigned according to resource importance: high-priority supplies such as emergency medicines and blood plasma are marked as first-level priority, requiring delivery in the shortest possible time; medium-priority supplies such as drinking water and convenience foods are marked as second-level priority; and ordinary daily necessities are marked as third-level priority, thus determining the dispatch order.

[0070] The sharing scheme module summarizes information by initiating area, with each initiating area corresponding to an independent sub-module. The content includes: basic information of the initiating area; a summary of shareable resources, i.e., the surplus quantity of various materials; a sharing list for each receiving area, including material type, specifications, quantity, and estimated transportation time; sharing route planning, marking emergency channels between disaster-stricken areas; a material handover process description, identifying the responsible persons, handover points, and acceptance standards between the initiating and receiving areas; and supplementing the core basis for sharing, briefly explaining the logic of the initiating area's sharing capabilities and the existence of a demand gap in the receiving area, enhancing the persuasiveness of the scheme. The summary and statistics module integrates all scheme data, forming three types of summary tables: first, a total flow table by material type, including total distribution volume, total sharing volume, and the number of areas involved; second, a demand satisfaction table by disaster-stricken area, including the satisfaction rate of various materials and whether the safety demand threshold has been reached. θ Third, a summary table of the transportation efficiency of the entire plan, including average transportation time and longest / shortest transportation time; the operation guidance module supplements key precautions for plan execution, including: material loading and unloading specifications, safety protection requirements for the transportation of fragile or perishable materials, emergency response procedures (such as alternative routes when roads are interrupted), and feedback mechanisms after plan execution (such as requiring feedback within 2 hours after each delivery or shared task is completed); finally, all modules are integrated according to a standardized document format to form a complete output document including a cover, table of contents, core plan details, summary table, operation guidance, and attachments (such as transportation route maps and material handover form templates). The document uses clear hierarchical headings and diagrams to ensure that rescue dispatchers can quickly locate key information and directly execute various tasks according to the plan.

[0071] Figure 3 This is a schematic diagram of the distribution matrix X, containing two supply zones (i=1,2), three disaster-stricken zones (j =1,2,3), and two types of relief supplies (k=1,2). Each element... This indicates the quantity of a certain type of relief supplies delivered from a supply area to a disaster-stricken area. For example: X[0,0,0]=3 indicates that supply area 1 delivered 3 units of type 1 relief supplies to disaster-stricken area 1; (X[1,2,1]=3) indicates that supply area 2 delivered 3 units of type 2 relief supplies to demand area 3.

[0072] Figure 4 This is a schematic diagram of the crossover operation of the distribution matrix X, illustrating the process of two parent individuals undergoing element-wise crossover under the control of a mask matrix to generate child individuals. The crossover operation is performed separately for each type of relief material, that is, independently on the resource dimension k. Specifically, it is assumed that parent individual 1 and parent individual 2 are both three-dimensional distribution matrices. and For resource type 1, a Boolean mask matrix with the same dimension as its two-dimensional distribution matrix (supply area × disaster area) is first generated. When the mask position is "true", the offspring inherits the corresponding element of parent individual 1 at that position; when the mask position is "false", it inherits the corresponding element of parent individual 2. Resource type 2 follows the same principle, using another set of mask matrices to independently complete the cross-transfer. For example, in the cross-transfer process of type 1 relief supplies, the mask matrix at position... If the value at position 1 is "true", then the offspring inherits the delivery quantity of the parent individual 1 at that position, that is, retains its value of 3; at position 2... If the value at a location is "false", then the offspring inherits the delivery quantity of individual 2 from the parent at that location, i.e., retains its value 3. For example, in the cross-processing of Category 2 relief supplies, the mask matrix at the location... If the value at position 1 is "true", then the offspring inherits the delivery quantity of the parent individual 1 at that position, that is, retains its value of 1; at position 2... If a position is "false", then the corresponding quantity of the parent individual 2 is inherited, that is, its value of 2 is retained. After judging and replacing each position one by one, a new offspring delivery matrix is ​​finally formed.

[0073] Figure 5 This diagram illustrates the mutation operation of the distribution matrix X, demonstrating the process of local resource reallocation for individual distribution plans under the mutation mechanism. First, based on the resource shortage situation in each disaster-stricken area, the resource type with the most severe constraints is identified as the target resource for this mutation. Then, a targeted adjustment is performed in the corresponding two-dimensional distribution matrix (supply area × disaster-stricken area). For example, assuming that type 2 relief supplies are the most scarce resource type, the algorithm randomly selects supply area 1 from the supply area set as the operation target. In the allocation of type 2 relief supplies in this supply area, disaster-stricken area 3, which receives the largest allocation, is identified and designated as the "reduction target area"; simultaneously, based on the demand satisfaction rate calculation, disaster-stricken area 2, with the lowest demand satisfaction rate, is selected as the "increase target area". The mutation adjustment amount is then calculated, and finally, one unit of type 2 relief supplies is reduced from disaster-stricken area 3, and one unit of the corresponding relief supplies is added to disaster-stricken area 2.

[0074] like Figure 6 As shown in the figure, the data comes from the calculation results of six specific verification scenarios generated, illustrating the trend of the range of target values ​​that the method of this invention can handle as the problem size increases. In practical applications, this boundary can be obtained through sampling or problem characteristic analysis.

[0075] like Figure 7 As shown, the data indicates that in scenarios of different scales, when the weights of two objectives are similar (such as...), A value of 0.5 often yields relatively better overall results, and this trend is consistent and can be used as a reference for decision-making.

[0076] like Figure 8 As shown, the data indicates that as the weights shift towards transportation time ( Increasing the variance usually improves the stability of the solution (decreases the variance), which provides information for decision-makers to weigh the trade-off between efficiency and stability.

[0077] like Figure 9 and Figure 10 As shown, the baseline parameter values ​​are: =0.88, =0.88, =1, =2.25, =0.61; relative sensitivity is a qualitative judgment based on the magnitude of data change; analysis shows that in two different medium-sized scenarios, the gain-related parameter ( , The impact of ) on the results was most significant, while the loss-related parameters ( , The impact of gain-related parameters is relatively small, and this conclusion is consistent. In practical parameter calibration, priority should be given to gain-related parameters.

[0078] To verify the effectiveness of the method of the present invention and to illustrate its technical effects, a specific verification embodiment of the simulation rule-generated data is provided below.

[0079] Verification scenario settings: The embodiments construct six test scenarios of different scales to verify the universality of the method of the present invention: Small-scale scenarios (S1, S2): 3-4 supply areas, 5-7 disaster points, 2-3 types of resources; Medium-scale scenarios (M1, M2): 8-10 supply areas, 12-15 disaster points, 3-4 types of resources; Large-scale scenarios (L1, L2): 10-12 supply areas, 20-25 disaster points, 3-4 types of resources.

[0080] When applying the method of this invention, it is necessary to normalize the multiple targets. Figure 6 The study demonstrates the range of objective function values ​​obtained through preliminary analysis under the six sets of verification scenarios. This range is used for subsequent normalization calculations. The results show that the method of this invention can adapt to problems of varying scales, from small to large; decision-makers can adjust the weights of transportation time and psychological satisfaction according to actual rescue needs. Figure 7 and Figure 8 The system displays the level of the comprehensive utility value U calculated under different weight combinations in all six verification scenarios, which comprehensively illustrates the influence trend of weights on the final solution and the consistency of the method of the present invention in different scenarios.

[0081] The prospect theory parameters introduced in this invention can be set according to the general psychological characteristics of disaster-affected populations. Figure 9 and Figure 10 The system demonstrates the relative impact of minor fluctuations in a set of typical parameter values ​​on the optimization results of medium-sized scenarios (M1, M2), comprehensively illustrating the sensitivity of each parameter and its consistency across different problem instances. The optimal or preferred solution obtained by the algorithm is decoded to clarify the specific material delivery volume from each supply point to each disaster-stricken area. ) and the amount of supplies shared among the various disaster-stricken areas ( It can be combined with a Geographic Information System (GIS) to visualize the material distribution routes and allocation plans; decision-makers can adjust the model weights based on the actual progress of disaster relief, resource arrival status, or other unforeseen factors. , The algorithm can be rerun after setting parameters to achieve dynamic decision support.

[0082] like Figure 2 As shown, embodiments of the present invention also provide an optimized relief supplies distribution system that takes into account the psychological factors of disaster victims, including: The basic data processing module is used to process the basic data acquired in the disaster relief scenario to obtain a basic dataset containing supply points, disaster-stricken points, types of materials, inventory, demand, and transportation time. The model building module is used to construct a multi-objective optimization model that integrates prospect theory based on the basic dataset. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. The aggregation and transformation module is used to perform normalization and weighted aggregation processing on the multi-objective optimization model, so as to transform the two objective functions, the first objective function and the second objective function, into a single-objective comprehensive utility minimization problem; The coding and strategy coordination module is used to generate an initial population by employing joint matrix coding and hybrid strategies for the single-objective comprehensive utility minimization problem of transformation, thereby obtaining an initial feasible solution set that satisfies all constraints. The iterative optimization module is used to run an improved genetic algorithm to iteratively optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a convergent population of optimized solutions is finally obtained. The matching output module is used to select the individual with the smallest comprehensive utility function value from the converged optimization solution population for decoding, and output the final relief material distribution plan and resource sharing plan.

[0083] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, characterized in that, The method includes: The basic data obtained from the disaster relief scenario are processed to obtain a basic dataset containing supply points, disaster-stricken areas, types of materials, inventory, demand, and transportation time. Based on the basic dataset, a multi-objective optimization model integrating prospect theory is constructed. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. The multi-objective optimization model is normalized and weighted aggregation to transform the first objective function and the second objective function into a single-objective comprehensive utility minimization problem. To address the single-objective comprehensive utility minimization problem of transformation, a joint matrix encoding and hybrid strategy are used to generate an initial population, resulting in an initial feasible solution set that satisfies all constraints. An improved genetic algorithm is run iteratively to optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a convergent population of optimized solutions is finally obtained. From the converged population of optimized solutions, select the individual with the smallest comprehensive utility function value for decoding, and output the final relief material distribution plan and resource sharing plan.

2. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 1, is characterized in that... The acquired basic data from disaster relief scenarios is processed to obtain a basic dataset containing supply points, disaster-stricken areas, types of materials, inventory, demand, and transportation time, including: Raw disaster relief data from different data sources are collected and aggregated to obtain a raw data set; the raw data includes geographic location information, inventory reports, demand assessment reports, and road network status information. The original dataset is validated and cleaned to remove outliers and missing items, resulting in cleaned and normalized data. Standardization and quantification processes are performed on the cleaned and normalized data to convert non-numerical information into numerical parameters in a uniform format, resulting in a standardized set of parameters. Based on a pre-defined data structure template, standardized parameter sets are integrated and correlated to ultimately generate a structured basic dataset.

3. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 2, is characterized in that... Based on a basic dataset, a multi-objective optimization model incorporating prospect theory is constructed. This model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes overall psychological satisfaction based on a prospect value function and a probability weight function. Based on the aforementioned basic dataset, the sets and parameters required for the model are extracted and defined to obtain the model parameter set; the required sets include the supply point set, the disaster point set, and the material type set, and the required parameters include transportation time, material inventory, demand, material weight, and safety requirement coefficient. Based on the model parameter set, a mathematical expression is established with the goal of minimizing the total transportation time, resulting in the first objective function; Based on the model parameter set and the preset foreground theoretical parameters, the core parameters used to characterize psychological perception are calculated; the core parameters include the subjective perception probability obtained based on the probability weight function, and the psychological perception value obtained based on the foreground value function. By comprehensively considering the weight of materials, the probability of subjective perception, and the value of psychological perception, a mathematical expression is constructed with the goal of maximizing overall psychological satisfaction, thus obtaining the second objective function; Define the decision variables of the model, and set constraints on resource supply, regional sharing, and demand satisfaction range based on the model parameter set; By integrating the first objective function, the second objective function, decision variables, and constraints, a multi-objective optimization model incorporating prospect theory is formed.

4. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 3, is characterized in that... The multi-objective optimization model is normalized and weighted to transform the first and second objective functions into a single-objective comprehensive utility minimization problem, including: Determine the boundaries of the value intervals for the first objective function and the second objective function, and obtain the reference maximum and reference minimum values ​​for each objective function; Based on the reference maximum and reference minimum values ​​of each objective function, the output values ​​of the first objective function and the second objective function are normalized to obtain the normalized transportation time index and psychological satisfaction index. By setting the relative importance weights of transportation time and psychological satisfaction based on decision-making needs, a set of weighting coefficients is obtained; The normalized transportation time index and the psychological satisfaction index are linearly weighted and combined using the aforementioned weighting coefficients to form a single-objective comprehensive utility function. The optimization objective is defined as minimizing the single-objective comprehensive utility function, thus transforming the multi-objective optimization model into a single-objective comprehensive utility minimization problem.

5. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 4, is characterized in that... To address the single-objective comprehensive utility minimization problem of transformation, a joint matrix encoding and hybrid strategy are employed to generate the initial population, resulting in an initial feasible solution set that satisfies all constraints, including: Based on the supply points, disaster-stricken points, and material types defined in the multi-objective optimization model, a joint matrix coding structure is designed to obtain a coding framework for representing individual complete solutions. The coding framework includes a three-dimensional delivery matrix representing the direct delivery volume and a three-dimensional sharing matrix representing the resource sharing volume between regions. Based on the three-dimensional delivery matrix in the coding framework, multiple sets of different direct delivery schemes are generated using various allocation strategies to obtain a set of delivery schemes. Among them, the various allocation strategies include random allocation based on demand ratio, heuristic allocation based on spatiotemporal efficiency, and completely random allocation. For each direct delivery scheme in the set of delivery schemes, the corresponding sharing matrix is ​​calculated and filled according to the material inventory, demand and transportation time constraints to obtain the corresponding resource sharing scheme, thus forming a complete solution. All the individual solutions formed are collected and verified to ensure that each individual meets all the constraints set by the multi-objective optimization model of the fusion prospect theory, and finally constitute an initial feasible solution set that meets all constraints.

6. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 5, is characterized in that... An improved genetic algorithm is iteratively optimized by running on the initial feasible solution set. Through selection, crossover, mutation, elite retention, and diversity maintenance operations, a convergent population of optimized solutions is finally obtained, including: Using the initial set of feasible solutions as the initial population, the fitness value of each individual solution is calculated based on the single-objective comprehensive utility minimization problem; Based on fitness values, a tournament selection strategy is used to select parent individuals from the current population to be genetically manipulated, resulting in a set of parent individuals. Perform a uniform crossover operation based on resource dimensions on the individuals in the parent set to generate new offspring individuals, thus obtaining the candidate population after crossover. Perform targeted resource reallocation mutation operations on individuals in the candidate population after crossover to enhance local search capabilities and obtain the mutated population; An elite retention strategy is implemented on the mutated population, directly retaining the individuals with the highest fitness values ​​from the previous generation into the next generation; diversity is monitored on the population after elite retention is implemented, and a diversity injection operation is triggered when the population diversity falls below a set threshold. Determine whether the current population meets the preset iteration termination condition. If the condition is not met, the current population is taken as the new population to be optimized and the iteration optimization process is restarted. This includes recalculating the fitness value based on the new population to be optimized and performing selection, crossover, mutation, elite retention and diversity maintenance operations in sequence. If the condition is met, the current population is determined as the converged optimal solution population.

7. The method for optimizing the distribution of relief supplies while taking into account the psychological factors of disaster victims, as described in claim 6, is characterized in that... From the converged population of optimal solutions, the individual with the smallest comprehensive utility function value is selected for decoding, and the final relief supplies distribution plan and resource sharing plan are output, including: From the converged population of optimized solutions, select the highest-ranking solution based on its fitness value. The top-ranked solution is decoded to convert the joint matrix code into specific delivery and sharing values, resulting in an executable material allocation detail. Based on the executable material allocation details, generate and output the final relief material distribution plan and resource sharing plan.

8. A relief supplies distribution optimization system that takes into account the psychological factors of disaster victims, the system implementing the method as described in any one of claims 1 to 7, characterized in that, include: The basic data processing module is used to process the basic data acquired in the disaster relief scenario to obtain a basic dataset containing supply points, disaster-stricken points, types of materials, inventory, demand, and transportation time. The model building module is used to construct a multi-objective optimization model that integrates prospect theory based on the basic dataset. The multi-objective optimization model includes a first objective function that minimizes the total transportation time, and a second objective function that maximizes the overall psychological satisfaction based on the prospect value function and the probability weight function. The aggregation and transformation module is used to perform normalization and weighted aggregation processing on the multi-objective optimization model, so as to transform the two objective functions, the first objective function and the second objective function, into a single-objective comprehensive utility minimization problem; The coding and strategy coordination module is used to generate an initial population by employing joint matrix coding and hybrid strategies for the single-objective comprehensive utility minimization problem of transformation, thereby obtaining an initial feasible solution set that satisfies all constraints. The iterative optimization module is used to run an improved genetic algorithm to iteratively optimize the initial feasible solution set. Through selection, crossover, mutation, elite retention and diversity maintenance operations, a convergent population of optimized solutions is finally obtained. The matching output module is used to select the individual with the smallest comprehensive utility function value from the converged optimization solution population for decoding, and output the final relief material distribution plan and resource sharing plan.

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