Multi-objective optimization service facility site selection method under uncertain scene

Abstract

The invention discloses a multi-objective optimization service facility site selection method under an uncertain scene, and the method comprises the steps: firstly, building a worker distribution mechanism under the constraint that the number of workers is limited to a small value; secondly, uncertainty analysis is carried out on an application scene by researching the characteristics of environmental parameters, and the probability of future accidents is converted into probability distribution by introducing a disturbance coefficient and an asymmetric perturbation mechanism; and finally, based on a worker distribution mechanism and uncertainty analysis, obtaining a target function of multi-target interval optimization, and determining the most suitable facility site selection through an interval optimization algorithm. According to the method, the workstation layout is effectively optimized, and meanwhile, the requirements of improving the emergency response efficiency, minimizing the response time and reducing the cost are met. By effectively distributing limited resources, the safety and response capability of the city are enhanced.

Description

Technical Field

[0001] The present invention relates to the field of geographic information technology, and in particular to a method for multi-objective optimization of service facility site selection under uncertain scenarios. Background Art

[0002] Facility location problems are crucial in logistics and urban management, where optimization decisions significantly impact resource efficiency, system performance, and service accessibility. These problems often involve multiple conflicting objectives, such as maximizing service coverage and responsiveness while minimizing facility construction and operating costs. However, real-world facility location decisions are subject to various uncertainties, including demand fluctuations, resource availability, and unpredictable events, which can affect long-term planning and system stability.

[0003] As long-term and irreversible investments, facility location impacts resource allocation and routing, often involving multiple conflicting objectives. Typical objective functions aim to maximize demand coverage and minimize construction and transportation costs, while common constraints include the number of facilities and facility capacity. These problems arise in a variety of real-world scenarios, including schools, fire stations, and hospitals, where decisions may involve selecting, relocating, or expanding facilities while considering constraints such as facility capacity and coverage distance.

[0004] And in reality, due to noise and the precision limitations of data acquisition equipment, it is almost impossible to obtain reliable and deterministic estimates of key model parameters. In addition, because site selection decisions are long-term strategies, they often lack sensitivity to environmental changes and downstream tasks. Traditional research on emergency location problems often assumes deterministic parameters, which means that event locations and frequencies are considered fixed. While this assumption provides useful insights based on historical data, it cannot accurately predict future environmental changes, resulting in location strategies that may not adapt to dynamic real-world environments. Pursuing optimal solutions under deterministic assumptions often leads to inadequate decisions in practical applications and lacks robustness to interference.

[0005] Specifically, early research focused on relatively simple problems, such as single-facility location and those without capacity constraints. However, as demand increased, researchers began to tackle more complex problems, including those involving multiple facility locations and capacity constraints. Facility location problems are currently generally categorized into three types: continuous, discrete, and network-based, based on the location space. They can also be categorized based on the number of objectives, the planning horizon, and the solution method. The number of objectives can be single or multi-objective, affecting the model complexity and solution approach. Furthermore, the planning horizon plays a crucial role, and the model can be static or dynamic; dynamic models need to consider multiple time periods. Finally, regarding solution methods, exact and heuristic methods are commonly used. Exact methods are applicable to small-scale problems and guarantee optimal solutions, while heuristic methods are more commonly used for large-scale problems and provide approximate solutions. These categories have helped researchers systematically explore the p-median, p-center, and set-covering problems, and develop optimization models for facility location problems.

[0006] Meanwhile, early research focused on deterministic environments, in which all parameters, such as demand and transportation costs, were assumed to be known with certainty. However, as researchers began to tackle more complex real-world scenarios, the limitations of deterministic modeling became apparent, particularly in its inability to account for unpredictable variations in demand. In recent years, researchers have expanded the scope of facility location research under uncertainty.

[0007] Of course, modeling methods are also evolving, including robust optimization models and interval optimization models. These models consider both facility spatial characteristics and regional risk assessment, improving their practical applicability. Some methods also define the cost of reducing interval uncertainty as an additional objective function to obtain optimal solutions for varying interval uncertainties.

[0008] Despite significant progress in facility location selection under uncertainty, several challenges remain: current research primarily uses probabilistic models or scenario-based analysis, but rarely considers asymmetric interference and multiscale uncertainty. Furthermore, most studies focus on single-objective optimization (e.g., minimizing cost or maximizing coverage), while real-world applications often require trade-offs between cost, response time, environmental impact, and other conflicting objectives. Finally, computational complexity remains a challenge when solving large-scale facility location problems in real time. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide a method for multi-objective optimization of service facility site selection under uncertain scenarios, effectively optimizing workstation layout and worker allocation to improve emergency response efficiency, minimize response time and reduce costs, and enhance the city's safety and responsiveness by effectively allocating limited resources.

[0010] In order to solve the above technical problems, the present invention provides a method for multi-objective optimization of service facility location selection under uncertain scenarios, comprising the following steps:

[0011] Establish a worker allocation mechanism under the constraint that the number of workers is limited to a small value;

[0012] Through the characteristics of environmental parameters, uncertainty analysis of application scenarios is carried out. The probability of future accidents is converted into probability distribution by introducing disturbance coefficients and asymmetric perturbation mechanisms.

[0013] Based on the worker allocation mechanism and uncertainty analysis, the objective function of multi-objective interval optimization is obtained, and then the most appropriate facility location is determined through the interval optimization algorithm.

[0014] Furthermore, when establishing the worker allocation mechanism, a greedy algorithm is introduced and a greedy metric is defined. The greedy value C of the greedy metric reflects the current system's preference for adding new workers. When the number of workers approaches the upper limit, the greedy value C gradually increases, indicating that the greediness is rising and the opportunity to add new workers needs to be reduced. When the greedy value C = 0, it represents a completely greedy strategy, ignoring the limit on the number of workers and giving priority to the addition of new workers to achieve the shortest processing time. When the greedy value C = 1, it represents a completely conservative strategy, not allowing new workers to join.

[0015] The greedy value C is defined as:

[0016] Where P j is the number of workers at all current workstations, P max is the upper limit of the number of workers, is a parameter that controls the growth rate.

[0017] Furthermore, the evaluation function for determining whether to add a new worker is:

[0018] Evaluation = T saved -C.Cost new_worker ;

[0019] Where T saved Cost represents the time saved by comparing the benefits of adding new workers and scheduling existing workers. new worker is the cost of adding a new worker. If Evaluation>0, a new worker is added to the workstation, otherwise, an existing worker is used.

[0020] The evaluation function for adding new workers is dynamically adjusted according to the greed value C of the current situation to achieve a balance between adding new workers and pursuing distance minimization.

[0021] Furthermore, in the uncertainty analysis, the environmental parameters include travel time fluctuation T′, accident resolution time Solvetime′, and the probability of future accidents η′;

[0022] Travel time fluctuation T′ represents the range of influence of time fluctuation on workers’ travel time and is calculated as follows:

[0023] Among them, T′ is the value caused by traffic conditions, T and are the lower and upper limits of fluctuation respectively, that is, T represents the smoothest road condition, Indicates the most congested conditions on the road;

[0024] Solvetime′ represents the time fluctuation range of workers' accident handling time and is calculated as follows:

[0025]

[0026] Among them, μ Solvetime is the average time to handle an accident, σ Solvetime is the standard deviation of the different resolution times for handling incidents, μ Solvetime and σ Solvetime Obtained by calculating the resolution time of all incidents in historical data;

[0027] Since the probability η′ of future accidents is obviously uncertain, we first perform a clustering operation, using the distance from the accident site to the workstation and the number of occurrences as criteria. Then, we determine the number of clusters by calculating the coefficient CV, which is equal to σ / μ. The larger the value of the coefficient CV, the more dispersed the data points are. By minimizing the value of the coefficient CV, we obtain several categories and ensure that each category is highly similar, thus completing the clustering.

[0028] After the clustering process is completed, the mean and variance of the historical accident occurrence time in each region are obtained to reflect the regional attributes and reduce the impact of individual randomness on the individual occurrence probability;

[0029] The probability of a historical accident occurring at the i-th accident location is expressed as:

[0030]

[0031] Where, Counts i represents the number of accidents that occurred at the i-th accident location in previous years, Σ i∈N Counts i Indicates the total number of accidents that occurred at all accident locations in previous years;

[0032] The probability η′ of a future accident occurring at the i-th accident location is calculated as follows:

[0033]

[0034] in or i and are the lower and upper limits of fluctuation, μ η It is the average value of the probability of an accident occurring at each accident location calculated using historical data. It represents the average value of the probability of an accident occurring at all accident locations in a region and is used to provide a central trend of accidents. η is the standard deviation of the probability of an accident at each accident location, which represents the average deviation from the mean and is used to quantify the fluctuation and uncertainty range of the probability of an accident, ξ η is the disturbance coefficient.

[0035] Furthermore, when the probability of an accident in the surrounding area is close to the probability of an accident at each accident location, the interference coefficient remains stable and the disturbance coefficient ξ η is a fixed value;

[0036] On the contrary, by introducing an asymmetric perturbation mechanism and controlling the perturbation coefficient to produce different effects on the upper and lower bounds of the environmental parameters, the probability of future accidents occurring after the change η′ at the i-th accident location is calculated as follows:

[0037]

[0038] in, is the lower threshold, is the upper threshold.

[0039] Further, confirm and The process is as follows:

[0040] First, set a preset threshold that is three times the standard deviation of the mean. Then, when adjusting the perturbation coefficient, consider the following guidelines:

[0041] If the probability of an accident at a certain location exceeds the upper threshold, it means that the location itself is prone to risk.

[0042] The probability of future risk occurrence must increase, then the interference coefficient Increase accordingly, reduce;

[0043]

[0044] On the contrary, if the probability of the accident location is less than the lower threshold, then Reduce, Increase;

[0045]

[0046] Among them, kk is the adjustment coefficient that controls the degree to which each position is affected by the surrounding positions. The larger the value of kk is, the deeper the degree to which each position is affected by the surrounding positions is. i is the set of accident sites surrounding the i-th accident site, θ∈Neighbor i η θ is the summary of the historical accident probability of all locations in the set, is the base perturbation coefficient. The formula shows that the perturbation coefficient tends to the overall characteristics of the region from a fixed base value.

[0047] Furthermore, constraints are set on the objective function, including constraining the number of workers in each selected workstation, constraining the working hours of workers, constraining the number of workers assigned to accident handling, constraining the rest interval between completing a task and starting a task, and constraining the minimum number of accident locations handled by each workstation.

[0048] Furthermore, in the interval optimization algorithm, calculations are performed through interval transformation and knee joint solution identification;

[0049] In interval transformation, the interval of target values ​​obtained in the multi-interval optimization process is transformed into its center value, and the length of the target value interval is retained.

[0050] Furthermore, in the process of knee joint solution identification, the achievement scaling function (ASF-SD) is used to segment the dominance of each solution and calculate the dominance degree of each solution. In the stage of finalizing the knee joint solution, the length of the interval is introduced and the consistency is compared. The solution with the shortest length is selected as the final knee joint solution.

[0051] Beneficial effects of the present invention:

[0052] To address the uncertainty caused by environmental parameter fluctuations, interval optimization is introduced. This approach uses interval discussion to model environmental parameters to better capture uncertainty. In real-world scenarios, environmental disturbances can cause variations in input parameters under different conditions. Interval descriptions not only capture the range of parameter fluctuations but also identify optimal solutions that adapt to different scenarios by considering upper and lower bounds.

[0053] Interval-based models enable us to extract general patterns from historical data while simulating future scenarios with potential fluctuations, making localization strategies more applicable to real-world conditions. Therefore, interval optimization provides an effective way to handle uncertainty and offers more flexible and robust solutions to localization problems.

[0054] The problem-solving approach considered multiple objectives, such as minimizing the number of workers, minimizing the weighted distance between the incident and the nearest workstation, and minimizing emergency response time. By balancing these objectives and using interval modeling of environmental parameters, the solution's adaptability to future scenarios is enhanced. This not only helps to better protect public safety and reduce losses caused by emergencies, but also provides theoretical support and practical guidance for building a modern emergency management system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of the site selection method of the present invention;

[0056] Figure 2 It is the initial selection diagram of the knee joint solution of the present invention;

[0057] Figure 3 This is a confirmation diagram of the knee joint solution finally determined by the present invention. DETAILED DESCRIPTION

[0058] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0059] Reference Figure 1 As shown, an embodiment of the method for multi-objective optimization of service facility site selection under uncertain scenarios of the present invention mainly proposes an uncertain greedy allocation algorithm, which enables the allocation strategy to be dynamically adjusted according to constraints during the allocation process. The application scenario is also analyzed for uncertainty by exploring the characteristics of environmental parameters. It extracts general patterns from historical data while introducing reasonable micro-perturbations. The environmental parameters are modeled as interval values, and an asymmetric perturbation mechanism is proposed to simulate potential changes, so that the scenario is more in line with future real-world conditions. Finally, in the context of emergency management, a multi-objective optimization method under uncertain scenarios is explored. By considering the interval fluctuations of the objective function, the proposed optimization method achieves a balance between robustness and optimality, and the solution provided not only provides optimal performance but also ensures stability under different environmental conditions.

[0060] Specifically, the site selection method includes: establishing a worker allocation mechanism under the constraint that the number of workers is limited to a small value; at the same time, conducting uncertainty analysis on the application scenario through the characteristics of environmental parameters, wherein the probability of future accidents is converted into a probability distribution by introducing a disturbance coefficient and an asymmetric perturbation mechanism; finally, based on the worker allocation mechanism and uncertainty analysis, parameter perturbation and multi-interval optimization are introduced to obtain the objective function of multi-objective interval optimization, and the facility site is determined according to the objective function.

[0061] The worker allocation mechanism specifically includes the following methods:

[0062] The worker allocation mechanism is described below. Initially, no workers are assigned because no actual accidents have occurred. When the first accident occurs, a worker is dispatched from the nearest workstation to handle it. Thereafter, each time a new accident occurs, the distances between idle workers at other accident locations and the workers at the nearest workstation are compared, and the worker closest to the accident is selected to handle it. Throughout this process, the number of workers cannot exceed an upper limit.

[0063] An innovative enhancement to this mechanism is that workers no longer need to return to their workstation after handling an incident before moving on to the next one. Instead, they can travel directly from one incident location to another, reducing unnecessary travel time and improving efficiency. This adjustment helps optimize the worker allocation process by minimizing total travel distance, streamlining the overall workflow.

[0064] This worker allocation mechanism is a series of decision-making processes that gradually builds a solution. At each step, it selects the optimal option relevant to the current situation. Similar to a greedy algorithm, this process accumulates local optimal solutions in the hope of reaching a global optimal solution. However, conventional greedy algorithms only determine the local optimal solution based on the current minimum processing distance, without considering the relationship between the current number of assigned workers and the upper bound of the constraint. This leads to a rigid worker allocation mechanism and the risk of exceeding the upper bound.

[0065] To overcome this shortcoming, this application proposes an improved method, which is to define a greedy metric C. The greedy metric value of C reflects the current system's preference for adding new workers, which is determined by the difference between the number of existing workers in each choice and the upper limit. When the number of workers approaches the upper limit, the value of C gradually increases, indicating that the greediness increases, thereby reducing the chance of adding new workers. For example, if adding a new worker can only save a small amount of time but pushes the number of workers close to the upper limit, the algorithm will choose not to add new workers. When C = 0, it represents a completely greedy approach, ignoring the limit on the number of workers, and always giving priority to the addition of new workers to achieve the shortest processing time. When C = 1, it represents a completely conservative strategy, and no new workers are allowed to join. The greedy value is defined as:

[0066]

[0067] Where P j is the number of workers at all current workstations, P max is the upper limit of the number of workers. Therefore, as P j As the value of C increases, the value of C gradually increases. is a parameter that controls the growth rate. The larger the value of becomes, the faster the value of C grows.

[0068] To summarize, the evaluation function for determining whether to add a new worker is:

[0069] Evaluation = T saved -C.Cost new_worker

[0070] Where T saved Cost represents the time saved by comparing the benefits of adding workers and scheduling existing workers. new worker is the cost of adding a new worker, which includes both the cost of hiring the worker and the cost of violating the constraint that the number of workers is limited to a small value. If Evaluation > 0, then a new worker is added to the workstation. Otherwise, an existing worker is used.

[0071] Compared to existing methods that have a fixed greediness in each case, our greediness is dynamically adjusted according to the changing greediness value based on the current situation. Therefore, the improved worker allocation mechanism is more suitable for dynamic demand and achieves a balance between adding new workers and pursuing distance minimization.

[0072] The uncertainty analysis method of the application scenario is as follows:

[0073] The characterization of uncertainty mainly focuses on three environmental parameters, including travel time fluctuation T′, accident resolution time Solvetime′, and the probability of future accidents η′, which together determine the perturbation degree of the problem.

[0074] First, T′ represents the impact of time fluctuations on workers' travel time, which is calculated as follows:

[0075]

[0076] Among them, T′ is the value caused by traffic conditions, T and are the lower and upper limits of fluctuation respectively. T Indicates the smoothest road conditions. Indicates the most congested road conditions.

[0077] Second, Solvetime′ represents the time fluctuation range of workers’ accident handling time, which is calculated as follows:

[0078]

[0079] Among them, due to the differences in the difficulty, time and time of accident resolution, μ Solvetime is the average time to handle an accident, σ Solvetimeis the standard deviation of the different resolution times for handling incidents, and both are calculated based on the resolution times of all incidents in the historical data.

[0080] The probability η′ of a future accident is obviously uncertain. However, traditional practices do not take this into account. They assume that an accident or event must occur at a given location and time, and its frequency corresponds to the historical frequency, thus taking the historical frequency as the probability of a future accident

[37] . However, the historical frequency does not directly reflect the situation regarding the occurrence of future accidents. In this paper, the occurrence of accidents themselves is uncertain, and the number of accidents is no longer assumed to be fixed. Historical accident distribution information can help to explore the range of future accident probability. In summary, this parameter not only takes into account the features extracted from historical data, but also the uncertainty of the accident itself.

[0081] To achieve this, clustering is first performed. Clustering is performed based on the distance between the accident site and the workstation and the number of accidents. Accident sites should be as close together as possible, and the number of accidents should be as similar as possible. The number of clusters is then determined by calculating the coefficient of variation (CV). This coefficient, which is equal to σ / μ, is commonly used in probability theory and statistics to compare the degree of dispersion between multiple data sets. A larger CV value indicates greater dispersion of the data points. By minimizing the CV value, we can achieve an appropriate number of clusters while ensuring a high degree of similarity within each cluster.

[0082] After the clustering process is complete, the mean and variance of historical accident occurrence times for each region are obtained. These values ​​reflect regional attributes, reduce the impact of individual randomness on individual occurrence probabilities, and are more suitable for predicting future accidents. Although the probability of individual future accidents remains highly uncertain and difficult to accurately predict, shifting the focus to the entire region rather than each accident site allows for a more stable analysis. By focusing on the entire region, the differences between individual accident sites are mitigated, providing a more consistent and reliable probability assessment. Importantly, through comprehensive probability analysis at the regional scale, the inherent uncertainty of individual events can be mitigated, resulting in a clearer understanding of accident trends.

[0083] The probability of a historical accident occurring η at the i-th accident location can be expressed as:

[0084]

[0085] Where Counts i represents the number of accidents that occurred at the i-th accident location in previous years, ∑ i∈N Counts i Represents the total number of accidents that occurred at all accident locations in previous years.

[0086] The uncertainty of accident occurrence can be converted into a probability range to better characterize the randomness and uncertainty of reality. The probability of a future accident occurring at the i-th accident location is calculated as follows:

[0087]

[0088] in or i and are the lower and upper limits of fluctuation respectively. η It is the average value of the probability of an accident occurring at each accident location calculated using historical data. It represents the average value of the probability of an accident occurring at all accident locations in a region and provides a central trend of accidents. η is the standard deviation of the accident probability at each accident location, which represents the average deviation from the mean and is used to quantify the fluctuation and uncertainty range of the accident probability. η The value of the disturbance coefficient directly affects the fluctuation range of the accident probability, which in turn affects the prediction of accidents in the entire region. Therefore, it is important to learn how to determine a reasonable disturbance coefficient based on historical data. First, when the standard deviation of the historical probability is large, it indicates that the accident occurrence varies greatly at each accident location, and therefore the influence of the surrounding environment on each accident location is limited. Therefore, the disturbance coefficient ξ η will decrease, and vice versa. Ideally, if the probability of an accident in the surrounding area is close to the probability of an accident at each accident location, the interference coefficient can remain stable, indicating that the probability of an accident at each location is roughly the same. In this case, ξ η is a fixed value.

[0089] On the other hand, setting equal upper and lower bounds based on the mean value does not conform to the actual situation of the environmental parameters. Therefore, this paper proposes an asymmetric perturbation mechanism that has different effects on the upper and lower bounds of the environmental parameters by controlling the perturbation coefficient.

[0090]

[0091] in is the lower threshold, Is the upper threshold. and The process is as follows:

[0092] First, a preset threshold is set, which is the average value (μ η ±3σ η ), then the following guidelines should be considered when adjusting the perturbation coefficients:

[0093] If the probability of an accident location exceeds the upper threshold (μ η +3σ η), indicating that the location itself is prone to risk and the probability of risk occurring in the future must increase, then the interference coefficient Increase accordingly, reduce;

[0094] On the contrary, if the probability of the accident location is less than the lower limit threshold (μ η -3σ η ),but Reduce, Increase;

[0095]

[0096] Among them, kk is the adjustment coefficient that controls the degree to which each position is affected by the surrounding positions. The larger the value of kk is, the deeper the degree to which each position is affected by the surrounding positions is. i is the set of accident sites surrounding the i-th accident site, θ∈Neighbor i η θ is the summary of the historical accident probability of all locations in the set, is the base perturbation coefficient. The formula shows that the perturbation coefficient tends to the overall characteristics of the region from a fixed base value.

[0097] Multi-interval optimization problem:

[0098] From the above discussion, we can see that the environmental parameter,Solvetime,η,T,is distributed within a certain range. Considering the complexity of the actual situation and the implicit relationship between historical occurrences and future occurrences, in each objective function, each environmental parameter has an upper and lower limit of the perturbation interval.

[0099] f1 is used to represent the weighted sum of the distances from the accident site to the nearest workstation:

[0100]

[0101] Where a is the number of workstations and b is the number of accident sites. ij is the distance from the i-th accident site to the j-th workstation, α ij is a label that identifies whether the i-th accident site is processed by the j-th workstation. i ′ is the probability of a future accident occurring at the i-th accident location, which is a uniformly distributed probability interval.

[0102] f2 represents the total number of workers at all workstations:

[0103]

[0104] Where a is the number of workstations, Pj is the number of workers at workstation j, and f2 is related to the solution time. Since the solution time is uniformly distributed, Pj is also uniformly distributed, and f2 is the probability interval of the uniform distribution.

[0105] f3 represents the accident emergency response time:

[0106]

[0107] Where k j is the worker index number of workstation j, l j The index number of the accident handled by workstation j. j is the number of incidents handled by workstation j, and is the number of incidents handled by workstation j. For workstation j, the kth j A worker on l j Response time to incidents, represents the kth j Is a worker currently processing this workstation? j The label of the accident. The perturbations in are reflected by T'. Although individual travel times fluctuate due to factors such as road conditions, the average travel time across all individuals tends to be stable. These fluctuations cancel each other out, and the overall distribution of travel times can be approximated as uniform.

[0108] Therefore, the form of the multi-interval optimization problem can be expressed as (i.e., the objective function):

[0109] minimize F(x)=(f1(x,c′),f2(x,c′),f3(x,c′)) T (twenty two)

[0110] with x=(x1,...,x n ) T (twenty three)

[0111]

[0112]

[0113] Where each decision variable xj = (X1j, X2j), represents the location of workstation j, X1j and X2j represent the latitude and longitude coordinates respectively.

[0114] In this problem, several constraints must be satisfied. Constraint (29) means that the number of workers is constrained to be between 1 and 20 workers at each workstation. Constraint (30) reflects the worker's working time constraint, that is, the workers' working hours cannot exceed 8 hours per day. Constraint (31) represents the accident handling allocation constraint, each accident is handled by only one worker from one workstation. Constraint (32) requires that there is at least a 10-minute break interval between completing a task and starting a new task. In constraint (33), workers must return to their original workstations for a half-hour break after working for 4 hours continuously. Constraint (34) requires that each workstation handle at least 10 accident locations.

[0115] The interval optimization algorithm is as follows:

[0116] KI-MOEA (Knee-based and Interval-based MOEA) is used to solve this multi-objective optimization problem. The steps of interval transformation and knee joint solution identification are given:

[0117] Regarding interval transformation, since the perturbation interval of the environmental variables yields the target value interval, the center of the interval is used instead of the upper and lower bounds for multi-objective optimization. Furthermore, the length of the target value interval is retained as a measure of solution robustness and contributes to the judgment of solution superiority. In summary, the target and interval lengths for the problem are as follows:

[0118]

[0119] Regarding knee solution identification, we use the Achievement Scaling Function-Dominance Segmentation (ASF-SD) to calculate the dominance of each solution. This plays two roles: first, environmental selection indicates the dominance of each solution in the population, helping to retain the better population. Second, in each generation, it selects knee solutions that are as evenly distributed as possible, providing more appropriate choices for the decision maker.

[0120] The purpose of segmentation is to obtain evenly distributed knee joint solutions. Assuming that k knee joint solutions are needed, the solution set is first divided into k equal parts according to the dimension of interest. Then, for each subset, the subset that best meets the requirements is selected to form the final output. Figure 2 As shown in Figure 1, assume that the solution set P = {x1, x2, x3, x4, x5, x6} requires two knee joint solutions. Then, the solution set is split into two subsets C1 = {x1, x2, x3, x4} and C2 = {x5, x6} according to the second objective function. C1 and C2 are each considered as independent solution sets, and the optimal knee joint solution is selected from each.

[0121] The Achievement scalising function serves the selection process by converting multiple objective values ​​into a single scalar. fi* represents the maximum value (reference point) of the i-th objective function in a subset. The ASF of the decision variable x in this subset is then calculated as:

[0122]

[0123] Where M is the number of objective functions, f i (x) is the value of the i-th objective function. W i is the weight of each objective, indicating the relative importance of each objective to the final optimization. Therefore, ASF(x) reflects the degree of deviation from the reference point. The larger its value, the better the performance of x. Then for each solution, the cumulative difference between its neighbors reflects its local performance, which can be calculated as:

[0124]

[0125] Where N is the number of neighboring solutions. They are selected by computing their respective objective function value weight vectors and then sorting them by the cosine of their angles with xi.

[0126] Finally, we can calculate the control range of each solution. The control range reflects the size of the range in which a solution can maintain the best optimization performance. For a solution x i , find other solutions (x i ). Among these solutions, the one with the smallest angle is the dominant range. In each subset, the solution with the largest dominant range is the knee solution.

[0127] Regarding the interval optimization strategy, to account for the impact of interval robustness, the interval length is introduced during the final determination of the knee solution. When a knee solution is initially obtained, all solutions within a certain range of its neighborhood are considered candidate solutions. Their interval lengths are then consistently compared, and the solution with the shortest length is selected as the final knee solution. This improves robustness at the expense of slightly reduced performance.

[0128] like Figure 3 As shown in the figure, when x2 and x5 are selected, their candidate neighborhoods are selected using threshold b (threshold b is a predefined hyperparameter representing the range of the neighborhood and is automatically set at runtime). Assume that the candidate solutions for x2 consist of x1 and x3, while the candidate solutions for x5 consist of x6. Compare the target value interval lengths to obtain the final output.

[0129] To address the challenges of facility site selection under uncertain conditions, this application proposes a multi-objective interval optimization method, including model construction and optimization. The model construction is based on real-world emergency management scenarios, including the design of interval estimation methods for environmental parameters such as accident frequency and response time, the construction of a dynamic decision-making mechanism based on the actual performance of facility site selection schemes under variable conditions by minimizing worker allocation costs, minimizing weighted distances to accident sites, and minimizing emergency response times. In order to solve the model and assist decision makers in making robust facility site selection decisions without relying on precise parameter estimates, a multi-objective interval optimization evolutionary algorithm was developed. The algorithm obtains robust solutions under different risk scenarios through the proposed asymmetric perturbation strategy; and enhances the adaptability of the solution through the proposed interval optimization algorithm. The superiority of the model and algorithm is demonstrated through empirical analysis of benchmark datasets.

[0130] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or modification made by those skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for service facility location selection under uncertain scenarios, characterized by: The following steps are involved: Establish a worker allocation mechanism under the constraint that the number of workers is limited to a small value; Through the characteristics of environmental parameters, uncertainty analysis of application scenarios is carried out. The probability of future accidents is converted into probability distribution by introducing disturbance coefficients and asymmetric perturbation mechanisms. Based on the worker allocation mechanism and uncertainty analysis, the objective function of multi-objective interval optimization is obtained, and then the most appropriate facility location is determined through the interval optimization algorithm.

2. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 1, characterized in that: When establishing the worker allocation mechanism, a greedy algorithm is introduced and a greedy metric is defined. The greedy value C of the greedy metric reflects the current system's preference for adding new workers. When the number of workers approaches the upper limit, the greedy value C gradually increases, indicating that the greediness is rising and the opportunity to add new workers needs to be reduced. When the greedy value C = 0, it represents a completely greedy strategy, ignoring the limit on the number of workers and giving priority to the addition of new workers to achieve the shortest processing time. When the greedy value C = 1, it represents a completely conservative strategy, and no new workers are allowed to join. The greedy value C is defined as: Where P j is the number of workers at all current workstations, P max is the upper limit of the number of workers, is a parameter that controls the growth rate.

3. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 2, characterized in that: The evaluation function to determine whether to add a new worker is: Evalution=T saved -C·Cost new_worker ; Where T saved Cost represents the time saved by comparing the benefits of adding new workers and scheduling existing workers. new worker is the cost of adding a new worker. If Evaluation>0, a new worker is added to the workstation, otherwise, an existing worker is used. The evaluation function for adding new workers is dynamically adjusted according to the greed value C of the current situation to achieve a balance between adding new workers and pursuing distance minimization.

4. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 1, characterized in that: In uncertainty analysis, environmental parameters include travel time fluctuation T′, accident resolution time Solvetime′, and probability of future accidents η′; Travel time fluctuation T′ represents the range of influence of time fluctuation on workers’ travel time and is calculated as follows: Among them, T′ is the value caused by traffic conditions, T and are the lower and upper limits of fluctuation respectively, that is, T Indicates the smoothest road conditions. Indicates the most congested conditions on the road; Solvetime′ represents the time fluctuation range of workers' accident handling time and is calculated as follows: Among them, μ Solvetime is the average time to handle an accident, σ Solvetime is the standard deviation of the different resolution times for handling incidents, μ Solvetime and σ Solvetime Obtained by calculating the resolution time of all incidents in historical data; Since the probability η′ of future accidents is obviously uncertain, we first perform a clustering operation, using the distance from the accident site to the workstation and the number of occurrences as criteria. Then, we determine the number of clusters by calculating the coefficient CV, which is equal to σ / μ. The larger the value of the coefficient CV, the more dispersed the data points are. By minimizing the value of the coefficient CV, we obtain several categories and ensure that each category is highly similar, thus completing the clustering. After the clustering process is completed, the mean and variance of the historical accident occurrence time in each region are obtained to reflect the regional attributes and reduce the impact of individual randomness on the individual occurrence probability; The probability of a historical accident occurring at the i-th accident location is expressed as: Where, Counts i represents the number of accidents that occurred at the i-th accident location in previous years, ∑ i∈N Counts i Indicates the total number of accidents that occurred at all accident locations in previous years; The probability η′ of a future accident occurring at the i-th accident location is calculated as follows: in or i and are the lower and upper limits of fluctuation, μ η It is the average value of the probability of an accident occurring at each accident location calculated using historical data. It represents the average value of the probability of an accident occurring at all accident locations in a region and is used to provide a central trend of accidents. η is the standard deviation of the probability of an accident at each accident location, which represents the average deviation from the mean and is used to quantify the fluctuation and uncertainty range of the probability of an accident, ξ η is the disturbance coefficient.

5. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 4, characterized in that: When the probability of an accident in the surrounding area is close to the probability of an accident at each accident location, the interference coefficient remains stable and the disturbance coefficient ξ η is a fixed value; On the contrary, by introducing an asymmetric perturbation mechanism and controlling the perturbation coefficient to produce different effects on the upper and lower bounds of the environmental parameters, the probability of future accidents occurring after the change η′ at the i-th accident location is calculated as follows: in, is the lower threshold, is the upper threshold.

6. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 5, characterized in that: Sure and The process is as follows: First, set a preset threshold that is three times the standard deviation of the mean. Then, when adjusting the perturbation coefficient, consider the following guidelines: If the probability of an accident at a certain location exceeds the upper threshold, it means that the location itself is prone to risk and the probability of risk occurring in the future must increase. Increase accordingly, reduce; On the contrary, if the probability of the accident location is less than the lower threshold, then Reduce, Increase; Among them, kk is the adjustment coefficient that controls the degree to which each position is affected by the surrounding positions. The larger the value of kk is, the deeper the degree to which each position is affected by the surrounding positions is. i is the set of accident sites surrounding the i-th accident site, θ∈Neighbor i η θ is the summary of the historical accident probability of all locations in the set, is the base perturbation coefficient. The formula shows that the perturbation coefficient tends to the overall characteristics of the region from a fixed base value.

7. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 1, characterized in that: Constraints are set on the objective function, including constraining the number of workers in each selected workstation, constraining the working hours of workers, constraining the number of workers assigned to accident handling, constraining the rest interval between completing a task and starting a task, and constraining the minimum number of accident locations handled by each workstation.

8. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 1, characterized in that: In the interval optimization algorithm, calculations are performed through interval transformation and knee joint solution identification; In the interval transformation, the interval center of the target value obtained in the multi-interval optimization process is used for multi-objective optimization, and the length of the target value interval is retained.

9. The method for multi-objective optimization of service facility location selection under uncertain scenarios according to claim 8, characterized in that: During the knee joint solution identification process, the achievement scaling function (ASF-SD) is used to calculate the dominance degree of each solution. In the stage of finalizing the knee joint solution, the length of the interval is introduced, and the consistency is compared. The solution with the shortest length is selected as the final knee joint solution.

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