A post-disaster unmanned aerial vehicle path planning method and system based on double-population constraint multi-objective optimization

Abstract

The application relates to the technical field of post-disaster path planning, in particular to a post-disaster unmanned aerial vehicle path planning method and system based on double-population constraint multi-objective optimization. The method comprises the following steps: based on a post-disaster task scene model, establishing an unmanned aerial vehicle voyage multi-objective cooperative optimization objective function and constraint conditions, including constructing a multi-objective function system, setting system constraint conditions and establishing a constraint violation degree evaluation mechanism; utilizing a double-population constraint multi-objective evolution algorithm to perform path optimization, including establishing a multi-unmanned aerial vehicle path coding mechanism and initializing a double-population architecture, implementing double-population cooperative genetic breeding operation, determining a double-stage constraint processing strategy; and implementing environment selection based on elite perception sorting; the multi-objective cooperative optimization model and the accurate risk quantification mechanism constructed by the application effectively solve the key problems of single target and rough risk processing of the existing method.

Description

Technical Field

[0001] This invention relates to the field of post-disaster path planning technology, and in particular to a post-disaster UAV path planning method and system based on dual-population constraint multi-objective optimization. Background Technology

[0002] As an important supplement to emergency material delivery, drones have gradually become an effective means of disaster relief due to their advantages such as rapid deployment and flexibility. With the rapid development of drone technology and the increasing demand for multi-drone collaborative operations, multi-drone path planning has become a key technology for improving rescue efficiency and reducing rescue costs.

[0003] However, post-disaster emergency rescue environments are highly complex and uncertain, and existing multi-UAV cooperative path planning technologies have several shortcomings in application. First, existing methods lack comprehensive modeling and collaborative optimization considerations for multiple objectives such as task coverage, response time, safety risks, load balancing, and energy consumption. They often use single-objective optimization or simple weighted combinations to handle multi-objective problems, failing to fully reflect the complexity and multidimensional needs of post-disaster rescue missions. Simultaneously, for the numerous risk areas in the post-disaster environment, such as building collapse zones and severe weather zones, many methods simply treat these risk areas as no-fly zones, lacking precise quantitative analysis of the path hazard exposure degree and failing to fully utilize limited airspace resources while ensuring flight safety. Second, existing multi-objective algorithms mainly rank individuals based on dominance relationships, resulting in coarse hierarchical division. When dealing with post-disaster path planning problems with intense multi-objective conflicts, they cannot accurately identify high-quality solutions, resulting in insufficient selection pressure and affecting algorithm convergence efficiency. Finally, existing methods typically only output Pareto solutions or a single optimal solution, lacking intelligent decision support mechanisms for different emergency scenarios (emergency rescue, safety priority, resource constraints, etc.). When faced with numerous technical options, rescue commanders often struggle to quickly select the most suitable execution plan based on the specific characteristics of the current rescue environment. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a post-disaster UAV path planning method and system based on dual-population constrained multi-objective optimization. Efficient and intelligent post-disaster UAV path planning is achieved through constructing a multi-objective collaborative optimization model and continuous risk field modeling, employing an elite-perception ranking and dual-stage constraint processing dual-population multi-objective evolutionary algorithm, and establishing a preference-oriented decision-making scheme generation mechanism based on prioritizing the primary objective while balancing other objectives.

[0005] In a first aspect, the present invention provides a post-disaster UAV path planning method based on dual-population constrained multi-objective optimization, which adopts the following technical solution:

[0006] A disaster recovery UAV path planning method based on dual-population constrained multi-objective optimization includes:

[0007] Based on post-disaster image data, a post-disaster mission scenario model is constructed, including establishing a two-dimensional coordinate system, determining mission points and UAV configurations and defining UAV flight paths, and constructing a risk field model.

[0008] Based on the post-disaster mission scenario model, we establish a multi-objective collaborative optimization objective function and constraints for UAV range, including constructing a multi-objective function system, setting system constraints, and establishing a constraint violation evaluation mechanism.

[0009] Path optimization is performed using a dual-population constrained multi-objective evolutionary algorithm, including establishing a multi-UAV path coding mechanism and initializing a dual-population architecture, implementing dual-population cooperative genetic reproduction operations, determining a two-stage constraint processing strategy, and implementing environment selection based on elite perception ranking.

[0010] Generate preference-oriented decision-making solutions, including building and normalizing a solution library, configuring multi-scenario preference strategies, and performing TOPSIS comprehensive evaluation;

[0011] Output the optimized path solution.

[0012] In summary, the present invention has the following beneficial technical effects:

[0013] The multi-objective collaborative optimization model and precise risk quantification mechanism constructed in this invention effectively solve the key problems of existing methods, such as single objectives and coarse risk treatment. By establishing a comprehensive objective system covering task coverage, response time, risk control, load balancing, and energy consumption optimization, it achieves a coordinated balance between rescue efficiency and safety. It innovatively establishes differentiated modeling methods for point-like and regional risk sources, extending the traditional no-fly zone handling method to a continuous risk field quantitative assessment, effectively expanding the available flight path space while ensuring flight safety. Experimental results show that compared with traditional methods, this invention improves task coverage by 5.7 percentage points, shortens response time by 10.1%, and reduces risk exposure by 17.8%, while maintaining good load balancing and energy efficiency, providing more scientific and reliable technical support for post-disaster relief decision-making.

[0014] The proposed dual-population constrained multi-objective evolutionary algorithm significantly improves solution quality and convergence efficiency under complex constraints. It achieves refined individual evaluation through an elite-aware ranking mechanism, and the dual-stage constraint processing strategy balances exploration breadth and convergence accuracy. Experimental results show that the algorithm reaches stable convergence on average around 1200 generations, an improvement of approximately 40% compared to NSGA-II. In terms of solution set quality, the HV index reaches 0.789±0.015, a 7.3% improvement compared to the best-performing comparison algorithm CCMO. Load balancing is improved by 23.8%, and total system energy consumption is reduced by 10.3%. This algorithm maintains stable performance advantages under different scale scenarios, providing an efficient and reliable optimization tool for large-scale disaster relief mission planning.

[0015] The preference-oriented decision support mechanism established in this invention effectively solves the practical problem of rescue commanders quickly selecting the optimal solution from a complex set of solutions. Through multi-scenario preference configuration and TOPSIS comprehensive evaluation, it can automatically select the most suitable execution plan according to the specific needs of the current rescue environment, significantly improving the efficiency and accuracy of emergency decision-making. This mechanism not only transforms abstract mathematical optimization results into specific executable flight commands and task arrangements, but also provides comprehensive performance indicators, including task coverage, response time, risk assessment, load distribution, and energy consumption analysis, providing a quantitative basis for real-time monitoring and dynamic adjustment of the rescue process. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall process of a post-disaster UAV path planning method based on dual-population constraint multi-objective optimization according to Embodiment 1 of the present invention.

[0017] Figure 2 This is a flowchart of the dual-population constrained multi-objective evolutionary algorithm in a post-disaster UAV path planning method based on dual-population constrained multi-objective optimization according to Embodiment 1 of the present invention.

[0018] Figure 3 This is a schematic diagram of the elite perception ranking mechanism in a post-disaster UAV path planning method based on dual-population constraint multi-objective optimization according to Embodiment 1 of the present invention.

[0019] Figure 4 This is a schematic diagram of multi-UAV flight paths using traditional path planning methods.

[0020] Figure 5 This is a schematic diagram of the multi-UAV route of the path planning method in Embodiment 1 of the present invention.

[0021] Figure 6 This is a schematic diagram comparing the convergence performance of various multi-objective evolutionary algorithms in Embodiment 1 of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the accompanying drawings.

[0023] Example 1

[0024] Reference Figure 1 This embodiment of a post-disaster UAV path planning method based on dual-population constrained multi-objective optimization includes:

[0025] S1. Constructing a post-disaster mission scenario model

[0026] S1.1 Establishing a two-dimensional coordinate system

[0027] In the complex post-disaster environment, accurate spatial positioning is fundamental to route planning. Based on multi-source data acquired through post-disaster satellite imagery or UAV surveys, the geographic coordinates of the disaster area are determined, and a two-dimensional coordinate system is established. The purpose of this step is to abstract the real geographic environment into a mathematical model, providing a standardized coordinate reference for subsequent algorithmic calculations.

[0028] Specifically, the space for post-disaster mission scenarios should be determined based on the actual extent of the disaster area. Boundary range ,in , These represent the minimum and maximum x-coordinates of the working area, respectively. , These represent the minimum and maximum ordinates, respectively. This method standardizes the irregular disaster area into a rectangular region, facilitating algorithm processing and calculation. A Cartesian coordinate system is established with the disaster area's centroid as the origin, ensuring that the center of the coordinate system represents the centroid of the entire disaster area, providing a reasonable reference point for subsequent distance calculations and path optimization.

[0029] S1.2 Determine the mission location and drone configuration

[0030] Based on the established standard coordinate system, it is necessary to transform actual relief needs into mathematical objects that can be processed by the algorithm. By utilizing post-disaster communication and other information, all locations requiring material delivery should be identified, including key relief points such as hospitals, shelters, schools, and residential areas. Based on this, a task point set should be established. ,in Total number of task points. Each task point... Using two-dimensional coordinates This method simplifies complex geographic location information into numerical coordinates that computers can directly process. It also helps determine drone base locations. coordinates Establish a drone ensemble ,in This represents the total number of drones.

[0031] S1.3 Define the UAV flight path

[0032] Based on the set of task points and UAV configuration determined in S1.2, it is necessary to further establish a mathematical representation of the UAV flight path to provide a foundation for subsequent distance calculation, time estimation, and risk assessment.

[0033] Each drone All need to comply with the base Departure and return To complete a closed-loop constraint condition for one flight, this is a necessary requirement based on the limited endurance of UAVs and considerations of mission safety. Specifically, when the first... drones After being assigned a set of mission points, its complete flight path includes the base departure point, the mission points visited in sequence, and the final base return point. To support subsequent path length calculation and risk exposure integral calculation, these key locations are uniformly defined as flight points. Let's assume the UAV... The flight route includes Each waypoint (including the starting and ending bases) is recorded in the order of visit:

[0034] ,

[0035] in Indicates drone The Two-dimensional coordinates of each waypoint. To be allocated to drones The number of task points.

[0036] To calculate flight distance, time, and risk exposure, a path segment between adjacent waypoints is defined. To connect waypoints and line segments, path segments The geometric length is:

[0037] ,

[0038] Path segment This can be expressed by parametric equations as follows:

[0039] ,

[0040] ,

[0041] Where parameters Indicates the path segment starting from the origin. To the finish line The distance. This parameterized representation allows the risk density value to be calculated at any point on the path segment, thus obtaining the risk exposure of the entire path segment through integration.

[0042] S1.4 Constructing a risk field model

[0043] Traditional path planning methods often simply mark dangerous areas as no-fly zones and adopt a complete avoidance strategy. While this approach is simple, it has significant shortcomings: firstly, it cannot quantify the degree of risk; secondly, it significantly reduces available flight path space, potentially leading to infeasible solutions or forcing drones to take detours in complex post-disaster environments, thus reducing rescue efficiency. In reality, many dangerous areas (such as building collapse zones and severe weather zones), while posing risks, can be traversed cautiously in emergency situations. The key is to quantify the degree of risk exposure and make reasonable trade-offs in path optimization. To more accurately describe the complex risk distribution in post-disaster environments and support flexible path planning under the premise of controllable risks, this invention establishes a continuous risk field model based on a risk density function.

[0044] First, The restricted areas within are divided into two categories ( Differentiated treatment will be implemented for no-fly zones. This includes completely inaccessible areas such as military control zones and areas where high-voltage power grids have collapsed; these areas remain strictly prohibited. Risk areas... This indicates areas that pose certain risks but are passable in emergencies, such as areas prone to building collapses or areas affected by severe weather.

[0045] Based on risk areas Medium-risk sources Different types, for each type of risk source Establish the risk density function. For point-source risk sources (such as collapsed buildings, hazardous chemical spills, etc.), a Gaussian decay model is used to represent it as follows:

[0046] ,

[0047] in As a source of risk The center coordinates, The risk intensity coefficient reflects the degree of danger of a risk source. To control the decay rate of risk impact, a parameter representing the range of influence is used. The Gaussian model, with its continuous differentiability, well-defined peak and decay characteristics, can accurately reflect the impact of point-like risk sources. The calculated risk density value... Directly reflects the coordinate point Risk source The level of threat provides a quantitative basis for subsequent path risk assessment.

[0048] For large-area regional risk sources (such as flood-prone areas, debris flow-affected areas, etc.), the risk distribution within them is relatively uniform, but there are gradient transitions at the boundaries. To accurately model these risk sources, a piecewise constant model is adopted:

[0049] ,

[0050] in This is the core hazardous area of ​​the risk source, and the risk value within this area remains constant. , For point The shortest distance to the boundary of the core area. The risk impact radius is used to define the transition zone where the risk decreases from the core area outwards.

[0051] Post-disaster environments often involve multiple risk sources acting simultaneously. To obtain a complete risk distribution map, the impacts of all risk sources need to be superimposed and integrated. The comprehensive risk density is obtained by superimposing the impacts of various risk sources.

[0052] ,

[0053] in The total number of point-like risk sources, This represents the total number of regional risk sources. This linear superposition method is based on the assumption of risk independence, meaning that the impacts of different risk sources can accumulate. The resulting comprehensive risk density is... It provides continuous risk assessment for the entire work area, and the risk level at any spatial location can be obtained directly through this function.

[0054] The ultimate goal of establishing a risk field model is to quantify the risk exposure of a drone flying along a specific path. Based on the comprehensive risk density function, the drone... Along the path segment Risk exposure is calculated using path integrals:

[0055] ,

[0056] The physical meaning of this integral formula is: to parameterize the path segment from 0 to... parameters Calculate the cumulative risk density along the entire path, where the integral result This represents the total risk exposure experienced by the drone during its flight along this path segment; a higher value indicates a higher flight risk. This quantitative result will serve as the foundational data for the risk control objective function in multi-objective optimization. and They represent drones In the path segment Upper Discretized points and The coordinates, this quantification result, will serve as the basic data for the risk control objective function in multi-objective optimization.

[0057] S2. Establish the objective function and constraints for multi-objective collaborative optimization of UAV range.

[0058] S2.1 Constructing a multi-objective function system

[0059] Based on the post-disaster mission scenario model constructed using S1, a multi-objective collaborative optimization objective function for UAV range is established. This objective function comprehensively considers multiple dimensions such as mission coverage, response time, risk control, load balancing, and energy consumption optimization, and is expressed as follows:

[0060] ,

[0061] In the formula This represents a solution for planning paths for multiple drones. Represented as The objective function vector represents the formalization of the complex multi-objective problem into a mathematical optimization problem, laying the foundation for subsequent algorithms. Specifically, the five objective functions are:

[0062] (1) Weighted task coverage objective function ,

[0063] In disaster relief, different task sites have varying levels of importance; critical facilities such as hospitals and shelters should be prioritized for rescue efforts over sparsely populated areas. To reflect this priority difference and maximize the service quality of high-priority task sites, a weighted task coverage objective function is designed. :

[0064] ,

[0065] in This represents the set of task points that have been visited and successfully served. For the task point priority weight The total number of task points. The design logic of this function is as follows: the numerator represents the sum of the weights of the task points that have completed services, and the denominator represents the sum of the weights of all task points. The ratio between the two reflects the weighted coverage rate. Subtracting this ratio from 1 yields the objective function value that needs to be minimized; that is, the higher the coverage rate, the smaller the objective function value. This design ensures that the algorithm will prioritize solutions that cover high-weight task points, thereby improving the rationality of rescue resource allocation.

[0066] (2) Priority response time objective function ,

[0067] The timeliness of rescue missions is crucial, especially for emergency missions such as medical rescue. Furthermore, many rescue missions are subject to time windows; arriving too early or too late will negatively impact the effectiveness of the rescue. To comprehensively consider time window violations and priority differences, a priority response time objective function is designed. :

[0068] ,

[0069] in For the task point Completion time, For the start of service, and These are the latest completion time and the earliest start time, respectively. Early arrival penalty coefficient. When completion time... Exceeding the latest permitted time When this occurs, a positive penalty is applied, and the severity of the penalty is proportional to the task priority. Proportional. When the service starts. Earlier than the earliest permitted time This incurs additional waiting costs. The coefficient can adjust the different tolerance levels for early arrival and late arrival; generally, the penalty for early arrival should be less than the penalty for late arrival.

[0070] (3) Comprehensive risk exposure objective function ,

[0071] Based on the risk density function established in S1.4, a comprehensive assessment of the safety risks during UAV mission execution is required. Risk exposure stems not only from the flight path but also from risks encountered during hovering operations at the mission point. A comprehensive risk exposure objective function is needed. It includes these two parts:

[0072] ,

[0073] The first term in the formula Indicates drone The total risk exposure along the flight path, of which Path integral calculation from S1.4, For drones Number of waypoints visited. (Second item) Indicates drone Risk exposure during hovering operations at the mission point, among which For drones The set of service task points For the task point The required service duration, Risk density at the mission point location.

[0074] (4) Load balancing objective function ,

[0075] In multi-drone collaborative operations, load imbalance can lead to some drones being overused while others remain idle, reducing overall operational efficiency and potentially causing equipment damage. Traditional methods often only consider load balancing from a single dimension. This invention designs a load balancing objective function that simultaneously considers payload weight, flight time, and the number of tasks. :

[0076] ,

[0077] In the formula For drones Total load capacity, For flight duration, For the number of service task points, These are the corresponding average values. These are the weighting coefficients. This function quantifies the load distribution of each dimension using the standard deviation; a smaller standard deviation indicates a more balanced load. The three terms control weight balance, time balance, and task quantity balance, respectively, and the importance of different balance dimensions can be adjusted through the weighting coefficients.

[0078] (5) System energy consumption objective function ,

[0079] Energy efficiency optimization not only affects the endurance of drones but also directly impacts the sustainability of rescue missions. To accurately calculate the total energy consumption of a drone, the energy consumption characteristics of different operations such as flight, turning, and deployment need to be considered. (Drone) The total energy consumption is expressed as:

[0080] ,

[0081] In the formula drones Energy consumption weights for flight, turning, and deployment. For drones Flight duration, For drones Turning time For drones The number of deployments. Based on the energy consumption calculation of a single drone, the objective function for the total system energy consumption is expressed as: :

[0082] ,

[0083] Minimizing this objective function will drive the algorithm to select a more energy-efficient path, thereby extending the drone's operating time and improving the sustainability of rescue missions.

[0084] S2.2 Setting system constraints

[0085] After establishing a multi-objective optimization function system, it is also necessary to consider the various constraints imposed on UAV path planning by the real physical world. As a physical system, UAVs have hard upper limits on their payload capacity, battery capacity, and flight time, and their flight paths must avoid no-fly zones to ensure safety. These constraints must be strictly satisfied to ensure the practical feasibility of the solution; otherwise, even with optimal objective function values, implementation is impossible. Therefore, a unified constraint function system is established:

[0086] ,

[0087] In the formula express The constraint function vector. The solution satisfies all constraints when all constraint function values ​​are less than or equal to 0.

[0088] Specifically, the four constraint functions are as follows:

[0089] (1) Load constraint function ,

[0090] The payload capacity of a drone is a hard limit; overloading can lead to problems such as inability to take off. (Payload constraint function) Represented as:

[0091] ,

[0092] In the formula For the task point The demand for supplies, For drones The maximum load, For drones The set of service task points. The design logic of this constraint is as follows: For each drone, calculate the difference between the total material demand of all task points it undertakes and its maximum load, and take the largest difference among all drones as the constraint function value. When all drones are not overloaded, the constraint function value is less than or equal to 0, thus satisfying the constraint condition.

[0093] (2) Energy Constraint Function ,

[0094] The battery capacity of drones limits their flight time, and energy consumption constraints ensure that each drone can complete its assigned task. Energy consumption constraint function. Represented as:

[0095] ,

[0096] In the formula For drones Total energy consumption For drones The maximum energy consumption limit. Similar to the load constraint, this function calculates the extent to which each drone's energy consumption exceeds the limit, ensuring that no drone is unable to complete its mission due to insufficient battery capacity.

[0097] (3) Endurance time constraint function ,

[0098] Besides energy consumption limitations, drones are also limited by their maximum flight time. (Endurance constraint function) Represented as:

[0099] ,

[0100] In the formula For drones Total task time, For drones The maximum flight time. This constraint ensures that the total mission time of each drone does not exceed its flight endurance.

[0101] (4) No-fly zone constraint function ,

[0102] To ensure flight safety, drones must strictly avoid no-fly zones. No-fly zone constraint function. Represented as:

[0103] ,

[0104] In the formula Path segment No-fly zone The length of overlap. This function calculates the degree of overlap between all path segments and the no-fly zone; the constraint function value is 0 when the no-fly zone is completely avoided.

[0105] S2.3 Establish a constraint violation assessment mechanism

[0106] In practical optimization, there may be intermediate solutions that temporarily violate constraints. To quantify the degree of such violations and guide the algorithm to converge to feasible solutions, a constraint violation evaluation function is established:

[0107] ,

[0108] in For the first The penalty weight coefficient for each constraint violation is used to quantify the degree to which the solution violates the constraints. The function is designed by weighting and summing the positive values ​​(i.e., the degree of violation) of each constraint function. When... At that time, the plan All constraints are fully satisfied; when A value of 0 indicates a constraint violation, with larger values ​​indicating more severe violations. This quantitative indicator will be used to guide individual selection and population evolution in subsequent evolutionary algorithms.

[0109] S3. Path optimization is performed using a dual-population constrained multi-objective evolutionary algorithm.

[0110] S3.1 Establish a multi-UAV path coding mechanism

[0111] Before designing an evolutionary algorithm, a suitable encoding mechanism is needed to represent the solution space of the multi-UAV path planning problem. The encoding mechanism serves as a bridge between the problem domain and the algorithm domain, directly affecting the algorithm's search efficiency and the expressive power of its solutions. Analysis of the multi-UAV path planning problem reveals that its essence lies in solving two core decision problems: task allocation (which task points are assigned to which UAV) and access order (the order in which each UAV accesses its assigned task points). Other parameters, such as service time and payload allocation, are derived from these two core decisions and are automatically determined.

[0112] Each individual The complete multi-UAV path planning scheme is represented by a task sequence encoding structure:

[0113] ,

[0114] in Indicates drone Task access sequence:

[0115] ,

[0116] in For drones Visiting in sequence One task point, To be allocated to drones The number of task points. This encoding simultaneously expresses two core pieces of information: task allocation and access order: task allocation is achieved through... The set of task points contained therein is represented by the order of access, which is reflected by the arrangement of the task points in the sequence.

[0117] S3.2 Initialize the dual-population architecture

[0118] Traditional single-population multi-objective optimization algorithms often face a trade-off between convergence and diversity when dealing with constrained problems: overly strict constraints can lead to a small feasible solution space, affecting the algorithm's exploration ability; overly lenient constraints may cause the algorithm to linger in infeasible regions for a long time, affecting convergence efficiency. To effectively solve this problem, this invention designs a dual-population collaborative optimization architecture.

[0119] Based on the multi-objective collaborative optimization objective function and constraints established by S2, a dual-population constrained multi-objective evolutionary algorithm is used to solve for the UAV's range and obtain the globally optimal solution set. For example... Figure 2 As shown, the algorithm balances the needs of exploration and convergence by maintaining two complementary populations: the main population focuses on finding high-quality solutions in the feasible solution space, ensuring that the final output solution fully satisfies the constraints; the auxiliary population explores in a larger search space, providing the main population with potential high-quality gene fragments.

[0120] Specifically, setting the main population and auxiliary population The scale is Construct a set of reference vectors. The reference vector, used to guide the search direction, is designed based on the decomposition concept, breaking down the multi-objective problem into multiple single-objective sub-problems to improve the algorithm's convergence and the uniformity of solution distribution. Crossover probabilities are set. and basic mutation probability This is used to control the frequency and intensity of perturbation in genetic operations. It also sets the maximum number of generations. As a termination condition for the algorithm.

[0121] Initial solution individuals are then generated randomly, with each individual representing a complete multi-UAV path planning scheme according to the encoding mechanism established in S3.1. During the generation process, the main population... All initial individuals are required to satisfy the basic constraints, while the auxiliary population... This allows individuals to violate the constraints.

[0122] S3.3, Implementing dual-population collaborative genetic reproduction operations

[0123] Based on the aforementioned dual-population architecture, in each generation of evolution, the dominant population... and auxiliary population Offspring populations are generated through genetic operations including selection, crossover, and mutation. These three genetic operations are performed sequentially: first, selection selects individuals with superior fitness from the current population to serve as parents; then, crossover is performed on the selected parents to generate initial offspring through gene recombination; finally, mutation is performed on the crossover offspring to introduce random perturbations and enhance population diversity. Through this complete reproductive process, each population reaches a size of [missing information]. The offspring population.

[0124] S3.3.1, Perform the selection operation

[0125] A binary tournament selection strategy is used to select parent individuals from the current population for subsequent crossover operations. Specifically, individuals are randomly selected from the population. and The individuals are compared, and those with better performance are selected as parents to participate in subsequent crossover and mutation operations. The selection criteria are based on the objective function value and the degree of constraint violation.

[0126] ,

[0127] in This is the balance coefficient. Represents the objective function vector The Euclidean norm is calculated using the following formula:

[0128] ,

[0129] Used to comprehensively evaluate an individual's performance across multiple objectives.

[0130] S3.3.2, Perform crossover operation

[0131] Crossover is the primary method for generating new individuals, and it operates on the parent individuals selected in S3.3.1. For multi-UAV path planning problems, it is necessary to ensure that the crossed individuals still represent valid path planning schemes. Based on the characteristics of the hierarchical coding structure, a two-layer crossover strategy is designed.

[0132] The two-layer crossover strategy comprises two phases: task allocation layer crossover and access order layer crossover. At the task allocation layer, an improved split-crossover operation ensures that all task points are fully allocated and not duplicated: firstly, crossover points are randomly selected to assign parent individuals... and The process is divided into two parts. The task allocation for the first part remains unchanged, while the conflicting task points for the second part are reassigned using a nearest neighbor heuristic. This approach preserves the parent generation's genetic information while ensuring the feasibility of solutions for the offspring.

[0133] At the access order layer, the task access order within each drone is performed using a sequential interleaving operation: the parent is randomly selected. A subsequence is copied from the parent generation to the corresponding position in the child generation, and then from the parent generation... The remaining task points are then filled in sequentially. This operation maintains the relative order of task visits, which helps preserve locally optimal path segments.

[0134] Crossover operations with probability Execution is performed; this probability was set during the initialization phase.

[0135] S3.3.3, Perform mutation operation

[0136] Mutation operations further enhance population diversity by perturbing the offspring individuals generated by the S3.3.2 crossover operation. Considering the characteristics of the multi-UAV path planning problem, targeted mutation strategies are needed based on the different deficiencies of individuals. Therefore, an adaptive mutation mechanism is designed, capable of identifying the main problems of individuals and selecting corresponding improvement methods.

[0137] Specifically, based on the constraint violations and objective function performance of the offspring individuals, one of the following two mutation strategies is adaptively selected according to individual characteristics:

[0138] 1. For individuals with uneven loads, identify the drones with the heaviest and lightest loads. ,Will Some tasks were transferred to At the same time, it meets the load constraints.

[0139] 2. For individuals with path redundancy, perform a 2-opt local search operation on the mission sequence of a single UAV to reduce flight distance and time by adjusting the access order.

[0140] Mutation probability Dynamically adjusted based on the degree of individual constraint violation:

[0141] ,

[0142] in Based on the probability of mutation, The maximum constraint violation rate for the current population. This is a numerically stable term to prevent the denominator from being zero. The principle behind this adaptive mechanism is that individuals with a higher degree of constraint violation require stronger mutation perturbations to escape infeasible regions, thus they are given a higher mutation probability.

[0143] S3.3.4, Generate candidate population

[0144] Through the above selection, crossover, and mutation operations, the main population... and auxiliary population Each generates a scale of offspring main population and offspring auxiliary population To fully leverage the synergistic advantages of two populations and avoid the loss of synergistic effects due to independent evolution, it is necessary to design candidate population generation strategies that promote inter-population interaction. Specifically, this involves merging the offspring of the two populations, ensuring that each population benefits from the superior individuals of the other during environmental selection, thus achieving true co-evolution.

[0145] main population With offspring candidate population The merger resulted in a scale of Parental candidate main population Similarly, the auxiliary population will be... With offspring candidate population The merger resulted in a scale of Parental candidate auxiliary population This merging strategy ensures that both populations can receive offspring from each other, achieving co-evolution.

[0146] After the candidate population is generated, high-quality individuals need to be selected to form the next generation population; this process is called environment selection. Environment selection is a crucial step in evolutionary algorithms, directly determining the convergence direction and the quality of the solution. In constrained multi-objective optimization problems, environment selection not only needs to consider the merits of the objective function but also must handle constraint violations. How to handle constraints during environment selection is a core issue affecting algorithm performance. This invention employs a two-stage constraint handling strategy, using different constraint handling methods at different evolutionary stages of the algorithm, and combines this with an elite-aware ranking mechanism to achieve efficient environment selection.

[0147] S3.4 Determine the two-stage constraint handling strategy

[0148] Constraint handling is a core challenge in constrained optimization algorithms. Overly strict constraints limit the algorithm's exploration capabilities, while overly lenient constraints negatively impact convergence quality. This invention designs a two-stage constraint handling strategy, employing different constraint handling methods at different stages of the algorithm to balance the needs of exploration and convergence. Based on the aforementioned dual-population architecture, the two-stage constraint handling strategy is implemented to effectively handle multiple types of constraints.

[0149] In the first stage, the parental candidate dominant population A strict constraint approach is adopted, meaning only those conditions that are fully satisfied are accepted. Individuals, through an elite-perception ranking environment selection strategy, select the next dominant population. .

[0150] Meanwhile, the parental candidate auxiliary population The first phase adopts an unconstrained approach, that is, accepting all individuals ( The population is maintained by selecting the next generation of auxiliary population through an elite perception-ranking environmental selection strategy. .

[0151] When the algorithm enters the second phase, the parent candidate leader population Keep the strategy unchanged, parent generation candidate auxiliary population Switch to a constraint relaxation approach, meaning accept that the degree of constraint violation is less than the tolerance threshold. (Individuals). Among them, the degree of constraint tolerance. Based on the current evolutionary generation Dynamic adjustment, represented as:

[0152] ,

[0153] in As the initial tolerance level, The attenuation coefficient controls the rate at which the degree of constraint relaxation tightens as the evolutionary process progresses. For the current generation, This represents the maximum number of generations. The formula implements a gradual constraint process, from lenient to strict: initially, the tolerance is high, gradually tightening as evolution progresses, eventually tending towards strict constraints. This dynamic adjustment mechanism ensures both the early exploration capabilities of the auxiliary population and the final convergence quality.

[0154] To accurately control the timing of stage transitions in the constraint handling strategy, an adaptive transition mechanism based on the rate of change of the ideal point and the worst point is adopted. This invention monitors the auxiliary population in real time during algorithm execution. Ideal point in the target space and worst The changes in the ideal point. The The components are:

[0155] ,

[0156] Indicates the auxiliary population in the first The current best value and worst value for each objective. The The components are:

[0157] ,

[0158] Indicates the first The current worst value on each target.

[0159] To quantify the evolutionary state of a population and calculate the ideal point rate of change:

[0160] ,

[0161] And calculate the worst point rate of change:

[0162] ,

[0163] in, To evaluate the algebraic interval of the rate of change, the overall rate of change is obtained:

[0164] ,

[0165] When the comprehensive rate of change satisfies Time (of which) The threshold is used to determine if the population convergence has stabilized, triggering the transition from the first stage to the second stage. The principle behind this mechanism is that when the changes in the population's ideal point and worst point are very small, it indicates that the population has fully explored the current search area, and this is the optimal time to enter the convergence stage.

[0166] S3.5 Implementing environment selection based on elite-perceived ranking

[0167] Based on the two-stage constraint processing strategy determined in S3.4, this section elaborates on the specific implementation process of environment selection. Environment selection needs to complete two core tasks: first, to rank the individuals in the candidate population according to their merits; and second, to select the next generation of the population based on the ranking results and the constraint processing strategy. To achieve accurate individual evaluation, this invention designs an elite-perceived ranking mechanism; to achieve flexible individual selection, a scoring function system adapted to the constraint processing stage is designed.

[0168] S3.5.1, Execute elite perception ranking

[0169] Traditional multi-objective optimization algorithms typically employ only a single ranking mechanism (such as non-dominated ranking). When dealing with complex multi-objective problems, the hierarchical division is often too coarse, making it difficult to accurately identify the superiority or inferiority relationships between individuals. To achieve more accurate individual evaluation and selection, this invention designs an elite-aware ranking mechanism, which refines the individual hierarchy by integrating multiple ranking strategies.

[0170] First, for candidate populations All individuals are subjected to a non-dominated sort. For any individual and Its non-dominant relationship is defined as:

[0171] ,

[0172] This relationship table Not inferior to in all objectives And superior to at least one objective Through non-dominated ordering, each individual Obtaining a non-dominated level ,in This represents the maximum number of levels, and individuals within the same level do not dominate each other.

[0173] The limitation of non-dominated ranking is that individuals within the same level cannot be further differentiated in terms of merit, especially in high-dimensional objective spaces (multi-objective problems with more than 3 objective functions are called high-dimensional multi-objective optimization problems). A large number of individuals may cluster in the same non-dominated level, leading to an overly coarse level division. To further differentiate the merit of individuals within the same level, a θ-dominated ranking based on decomposition is needed as a supplementary evaluation mechanism. This ranking method divides the objective space into different search directions using a reference vector, independently evaluating the merit of individuals in each direction. The innovation of this invention lies in not simply replacing non-dominated ranking with θ-dominated ranking, but rather organically integrating the evaluation results of both non-dominated and θ-dominated rankings through an elite-perceived ranking mechanism. This comprehensively considers the performance of individuals in both ranking systems, thereby achieving a more refined level division than a single ranking method.

[0174] Specifically, firstly, each individual The reference vector with the smallest angle in the target space Link:

[0175] ,

[0176] in Represents an individual With reference vector The included angle:

[0177] ,

[0178] in For individuals Relative to the ideal point offset vector, For individuals in the target space To the ideal point The Euclidean distance. The association process assigns individuals to different search directions, laying the foundation for decomposition-based ranking.

[0179] Then, calculate the individual's angular penalty distance:

[0180] ,

[0181] in The penalty intensity coefficient, For the maximum permissible angle, This is a penalty index. This distance index comprehensively considers the individual's distance from the ideal point and the angle of deviation from the reference direction; the smaller the distance, the higher the individual's quality. Individuals are ranked based on the angle penalty distance. Assigned theta-dominant hierarchy ,in The maximum number of levels for the θ-dominant sort.

[0182] Finally, the elite perception ranking level for each individual is calculated:

[0183] ,

[0184] ,

[0185] ,

[0186] In the formula Represents an individual The better hierarchy in the two sorting methods =1 indicates an individual Individuals whose ranking is consistent in both sorting methods are considered elite. This ranking mechanism establishes a final elite perception hierarchy. Its advantage lies in the following: when an individual performs consistently in both rankings, they are considered elite and their ranking is elevated; when their performance is inconsistent, neutrality is maintained, ensuring fairness in the ranking.

[0187] S3.5.2, Implementation Environment Selection Operation

[0188] Based on a two-population, two-stage framework and elite-perceived ranking results, a hierarchical inoculation environmental selection strategy is employed to select the next generation of the population. The goal of environmental selection is to choose the optimal population from the candidate populations. Individuals form the next generation of the population, and it is necessary to ensure both the quality of the solutions and the diversity of the population.

[0189] Initialize the next generation population For an empty set, from the parent generation candidate population Individuals are selected using a tiered filling method. Specifically, the elite perception levels are first sorted. All individuals were placed into the next generation population. In this context, these individuals represent the optimal solution in the current population. If the population... The size is smaller than the preset population size. Then continue Individuals are placed in, and so on.

[0190] When the number of individuals at a certain level exceeds that of the next generation population When the remaining capacity is exhausted, a truncation operation needs to be performed on the individuals within that level to determine the final selected individual. At this point, based on the current constraint processing stage and strategy of the population, the individuals within that level are evaluated and ranked using the corresponding scoring function, and the individual with the best score is selected to fill the population.

[0191] For the main population Due to the use of strict constraint processing, a constraint scoring function is employed:

[0192] ,

[0193] The scoring function uses constraint violation rate Individuals that do not meet the constraints are severely penalized to ensure that selected individuals prioritize meeting all constraints. Represents an individual The degree of crowding is used to maintain the diversity of solution distribution. Equal to Associated with the same reference vector The total number of individuals, i.e. ,in This is the current candidate population. This is the balance coefficient.

[0194] For auxiliary populations In the first stage, an unconstrained approach is adopted, using an unconstrained scoring function:

[0195] ,

[0196] This scoring function ignores constraint violations and only penalizes the distance based on the angle. Conduct assessments and encourage comprehensive exploration within the target space.

[0197] For auxiliary populations In the second stage, the approach shifts to constraint relaxation, using a constraint relaxation scoring function:

[0198] ,

[0199] The scoring function applies to cases where the constraint violation is less than the tolerance threshold. Individuals who perform poorly are given lighter penalties, while those who seriously violate the constraints are severely punished, achieving a smooth transition from exploration to convergence. This is a numerically stable term to prevent the denominator from being 0.

[0200] The fitness score of each individual within the same level is calculated using the scoring function described above, and individuals are selected for the next generation of the population in descending order of their scores. until the population size reaches Complete the environment selection operation.

[0201] Thus, through the environment selection operation of S3.5, the parent candidate primary population was selected. Select a new dominant population From the parental candidate auxiliary population Select a new auxiliary population This completes one generation of evolution. A complete generation of evolution includes: generating offspring through genetic reproduction (S3.3), merging to form candidate populations, determining individual acceptance criteria based on a two-stage constraint treatment strategy (S3.4), and obtaining a new generation of population through environmental selection via elite perception ranking (S3.5).

[0202] Evolutionary algebra Increase by 1, that is Then, with the newly generated main population and auxiliary population As the current population, the evolutionary operations from S3.3 to S3.5 are repeated, continuously iterating and optimizing until the algorithm's termination condition is met.

[0203] S3.6 Terminate the algorithm and output the result.

[0204] When evolutionary generations Reaching the maximum number of generations The algorithm terminates when the time is right. Output the main population. The set of Pareto optimal solutions is formed by considering all non-dominated individuals that satisfy the constraints. The main population was chosen as the output source because it undergoes strict constraints throughout the evolutionary process, ensuring that the output solution fully satisfies all constraints and is practically feasible. The Pareto optimal solution set provides diverse, high-quality choices for subsequent decision analysis.

[0205] S4. Generate preference-oriented decision-making schemes

[0206] S4.1 Build and normalize the solution library

[0207] Pareto optimal solution set output by the S3 dual-population constrained multi-objective evolutionary algorithm Build a candidate solution library Although Pareto solutions are mathematically optimal, in practical applications, rescue commanders need to choose the most suitable execution plan based on the specific circumstances.

[0208] Because the objective functions have different numerical ranges and units (e.g., time is measured in minutes, distance in kilometers, and risk is a dimensionless value), directly comparing multiple objectives can lead to the objective with the larger value dominating, affecting the fairness of the decision-making process. To ensure the fairness of multi-objective evaluation, for each objective function... Perform normalization processing.

[0209] Specifically, for the first Each objective function is evaluated by iterating through all solutions in the solution library and calculating their ideal values. and worst value The formula for calculating the ideal value is:

[0210] ,

[0211] This value represents the first The objective function is in the candidate solution library The minimum value among all solutions. Since all objective functions are minimization problems, the ideal value reflects the best performance level that the objective can achieve in the current solution set, that is, the best result that can be obtained if only the objective is optimized without considering other objectives, providing a lower bound benchmark for normalization.

[0212] The formula for calculating the worst value is:

[0213] ,

[0214] This value represents the first The objective function is in the candidate solution library The maximum value among all solutions reflects the worst performance of the objective in the current solution set. The worst value usually corresponds to the result of sacrificing the objective in order to optimize other objectives in a multi-objective trade-off, that is, the worst level to which the objective may degenerate, providing an upper bound benchmark for normalization.

[0215] Based on the above ideal and worst values, the first... The actual range of values ​​of the objective function in the current solution set Based on this range, the objective function value is normalized:

[0216] ,

[0217] in This is a numerically stable term used to avoid cases where the denominator is zero. Through normalization, all objective function values ​​are mapped to the interval [0,1], eliminating the influence of dimensions and numerical range, and creating a fair basis for subsequent comprehensive evaluation. After normalization, This indicates that the scheme is in the... To achieve the ideal level for each goal, This indicates that the worst level has been reached.

[0218] S4.2 Configuring Multi-Scenario Preference Strategies

[0219] Post-disaster relief scenarios are highly diverse and uncertain, and different emergency situations have different requirements for route planning solutions. For example, during the golden rescue time, response speed may be more important; under severe weather conditions, safety may be more important; and when resources are scarce, energy efficiency may be more important. Although S3 outputs a solution library... While providing diverse options for decision-making, rescue commanders still need to quickly determine the most suitable execution plan based on the specific scenario. To support this scenario-based decision-making need, a solution selection and evaluation mechanism that incorporates decision-making preferences needs to be established.

[0220] Based on factors such as the urgency of the rescue mission, resource constraints, and environmental conditions, the primary preferred objective is determined. ∈ {coverage, response speed, security, load balancing, energy efficiency}. The determination of the primary preference objective should be based on the most critical needs of the current rescue scenario, which will become the dominant factor in solution selection and evaluation.

[0221] Considering only the primary objective may lead to a severe degradation in the performance of other objectives, affecting the overall feasibility of the solution. Therefore, while optimizing the primary objective, it is necessary to ensure that other objectives are also maintained at an acceptable level. To this end, acceptable thresholds are set for non-primary objectives. The threshold setting is based on the "satisfactory decision" theory: while ensuring the optimization of the primary objective, other objectives must reach an acceptable level. For the... For each non-primary preference objective, the threshold is defined as:

[0222] ,

[0223] In the formula For the first The acceptability coefficient for each objective ranges from [0,1]. When the ideal value is required, The worst-case scenario is accepted. The median value represents the tolerance level for the objective; the smaller the value, the stricter the requirements.

[0224] Based on the primary preference objective and threshold constraints, a set of preference schemes that meet the conditions is selected:

[0225] ,

[0226] This screening process ensures that the selected solutions reach an acceptable level in non-primary objectives, thus providing a guarantee for the optimization of the primary objective.

[0227] S4.3 Implementation of TOPSIS Comprehensive Evaluation

[0228] Through the preference strategy configuration in S4.2, a set of preference schemes that satisfy the threshold constraint has been selected from the Pareto optimal solution set. However, this set usually still contains multiple candidate solutions, requiring further selection of the optimal solution as the final recommendation. To achieve scientific quantitative evaluation, this invention employs an improved TOPSIS method to comprehensively evaluate candidate solutions. TOPSIS is a classic multi-attribute decision-making method whose basic idea is to select the solution that is closest to the ideal solution and furthest from the negative ideal solution, comprehensively considering the trade-offs between multiple objectives.

[0229] For each candidate solution Calculate its degree of optimization on the main preference objective:

[0230] ,

[0231] This metric reflects the position of the candidate solution relative to the optimal and worst solutions in terms of the main preference objective. A larger value indicates a higher degree of optimization. A value of 1 indicates that the optimal level of the objective has been achieved, while a value of 0 indicates that the solution is at the worst level.

[0232] Then, calculate the degree of balance of the candidate solutions on non-primary preference objectives:

[0233] ,

[0234] in This represents the total number of objective functions. This indicator reflects the degree of balance between the proposed solution and non-primary objectives; a higher value indicates a better degree of satisfaction. The indicator value is 1 when all non-primary objectives reach the ideal level, and 0 when the threshold requirement is just met.

[0235] The comprehensive preference score can be obtained based on the degree of optimization of the primary preference objective and the degree of balance between non-primary preference objectives.

[0236] ,

[0237] in The weighting coefficients for primary objective optimization and objective balancing are used to adjust the relative importance of the two in the overall score.

[0238] Based on the comprehensive preference rating results, the option with the highest rating is selected as the final recommended option:

[0239] ,

[0240] If multiple solutions have the same highest score, a lexicographical comparison method is used: first, compare the main preference objective values ​​and select the solution with the better performance in the main preference objective; if the main preference objective values ​​are still the same, then compare other objective function values ​​in turn until a unique optimal solution is determined.

[0241] Output the optimal solution The system provides detailed performance metrics, including five objective function values, constraint violations, and a comprehensive score, to inform subsequent path execution decisions.

[0242] S5, Output optimized path scheme

[0243] Through the preference-oriented decision-making process of S4, the optimal solution that best meets the needs of the current rescue scenario has been selected from the Pareto optimal solution set. However, this scheme currently exists as an abstract task sequence encoding and cannot be directly used for actual UAV execution. In order to transform the optimization results into actionable flight commands, a decoding process is needed to convert the encoding scheme into a complete execution scheme containing detailed coordinates, time, payload, and other information.

[0244] S5.1, Execution Scheme Decoding Process

[0245] The optimal solution Optimized task sequence for each UAV The following decoding process converts it into a complete execution plan.

[0246] (1) Constructing the flight path

[0247] Based on task sequence encoding, construct a detailed flight path for each UAV:

[0248] ,

[0249] This path clearly defines the complete flight trajectory of the drone, starting from the base, visiting assigned task points in an optimized order, and finally returning to the base. Each waypoint contains precise two-dimensional coordinates. .

[0250] (2) Calculate load distribution

[0251] Based on the assigned task sequence, automatically calculate the payload allocation scheme for each drone:

[0252] ,

[0253] in For the first The calculation determines the material requirements for each task point. This calculation ensures the rationality of load allocation and the satisfaction of load constraints.

[0254] (3) Determine the schedule

[0255] Based on the flight path and parameters, calculate the detailed time schedule for mission execution. Mission point arrival time calculation:

[0256] ,

[0257] in Indicates the initial time of departure from the base. The distance traveled from the previous mileage point to the current mission point. For drones Flight speed. This formula calculates the arrival time at each mission point by summing up the flight times of each segment.

[0258] The task start time needs to take into account time window constraints:

[0259] ,

[0260] in This represents the earliest start time of the mission. The formula indicates that if the drone arrives earlier than the earliest start time, service must wait until that time to begin; if the drone arrives later than the earliest start time, service begins immediately.

[0261] The task completion time is obtained by adding the service duration after the service starts:

[0262] ,

[0263] in The service duration required for the task point.

[0264] S5.2, Generate Execution Instructions

[0265] The decoded execution plan is converted into a specific flight command sequence for each drone. The implementation plan includes:

[0266] (1) Detailed flight path instructions

[0267] It includes precise coordinates, heading angle, and flight speed settings for each waypoint, ensuring that the drone can accurately execute the planned path.

[0268] (2) Task execution schedule

[0269] ,

[0270] The schedule includes the task number, start time, and completion time for each task point, providing a time baseline for task execution and monitoring.

[0271] (3) Load configuration list

[0272] List the quantity and weight of supplies that each drone needs to carry, ensuring that the requirements of all mission points are met and that the load constraints are satisfied.

[0273] S5.3, Output System Performance Indicators

[0274] It also outputs overall system performance indicators, including task coverage performance, time efficiency indicators, security risk assessment, resource utilization efficiency, and energy consumption analysis report.

[0275] Experimental verification

[0276] To verify the effectiveness and superiority of the proposed dual-population constrained multi-objective evolutionary algorithm in post-disaster UAV path planning, an experiment was conducted based on a simulation system, setting up three post-disaster relief scenarios of different complexities: small-scale (20km×20km area, 30 task points, 4 UAVs), medium-scale (30km×30km area, 50 task points, 6 UAVs), and large-scale (40km×40km area, 80 task points, 8 UAVs). Each test scenario included 3-5 point-like risk sources and 2-4 regional risk sources, with risk intensity coefficients randomly distributed between 0.3 and 0.8. The maximum payload of the UAVs was set to 30kg, the maximum flight time to 90 minutes, and the average flight speed to 60km / h.

[0277] The experiment selected three classic multi-objective optimization algorithms—NSGA-II, CCMO, and MOEA / D—as benchmarks for comparison. NSGA-II is a classic multi-objective genetic algorithm based on fast non-dominated sorting; CCMO is a constrained collaborative optimization algorithm specifically designed for constrained multi-objective problems; and MOEA / D decomposes multi-objective problems using weight vector decomposition. All algorithms used the same encoding method, crossover and mutation operators, and parameter settings to ensure fairness in the comparison. Each algorithm was run independently 30 times, with 5000 generations of evolution each time.

[0278] As shown in Table 1, the algorithm compared with the method of this invention was comprehensively evaluated in three simulated post-disaster relief scenarios using key performance indicators such as task coverage, average response time, risk exposure, load balancing, and total energy consumption, as well as the HV convergence index. Experimental results show that:

[0279] Table 1

[0280] algorithm Task coverage (%) Average response time (min) Risk Exposure Load balancing Total energy consumption (kWh) HV NSGA-II 87.3±2.1 45.2±3.8 12.6±1.4 0.23±0.03 28.5±2.2 0.712±0.023 CCMO 89.1±1.8 42.7±3.2 11.8±1.1 0.21±0.02 27.1±1.9 0.735±0.019 MOEA / D 88.6±2.3 44.1±4.1 12.2±1.6 0.24±0.04 28.8±2.5 0.728±0.025 Algorithm of this invention 94.2±1.3 38.4±2.5 9.7±0.8 0.16±0.02 24.3±1.6 0.789±0.015

[0281] The algorithm of this invention achieves a task coverage rate of 94.2%, which is 5.7 percentage points higher than the best comparison algorithm CCMO's 89.1%. In terms of response time, it achieves an average response time of 38.4 minutes, a 10.1% reduction compared to CCMO's 42.7 minutes. Regarding risk exposure control, it reduces the score to 9.7, a 17.8% decrease compared to CCMO's 11.8. In terms of load balancing, it achieves a score of 0.16, a 23.8% improvement compared to CCMO's 0.21. In terms of total energy consumption, it achieves 24.3 kWh, a 10.3% saving compared to CCMO's 27.1 kWh. The performance differences described above are all statistically significant (p < 0.001), as verified by the Wilcoxon signed-rank test.

[0282] like Figure 6 As shown, from a convergence perspective, the algorithm of this invention achieves stable convergence on average around 1200 generations, with a convergence speed approximately 40% faster than NSGA-II. Regarding solution set quality, the HV index reaches 0.789±0.015, a 7.3% improvement compared to CCMO's 0.735±0.019, indicating that the algorithm of this invention can obtain a superior Pareto front distribution.

[0283] In scalability tests across different scales, the algorithm maintained a relatively stable performance advantage as the number of task points increased from 30 to 80. The most significant improvements were observed in small-scale scenarios, with a 6.8% increase in coverage, a 12.3% reduction in response time, and a 19.2% reduction in risk. While the improvement narrowed somewhat in medium- to large-scale scenarios, the algorithm still maintained its advantage, demonstrating its scalability.

[0284] To verify the robustness of the algorithm, tests were conducted under perturbation conditions of risk source location shift of ±2km and intensity change of ±30%. The coefficient of variation of the task coverage of the algorithm of this invention was only 1.4%, which is lower than the average fluctuation level of 2.8% of the comparative algorithms; the coefficient of variation of risk exposure was 8.2%, which is better than the average performance of 15.6% of the comparative algorithms, demonstrating the stability and adaptability of the algorithm of this invention in complex dynamic environments.

[0285] A computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned disaster-relief UAV path planning method based on dual-population constraint multi-objective optimization.

[0286] A terminal device includes a processor and a computer-readable storage medium, the processor being used to implement various instructions; the computer-readable storage medium being used to store multiple instructions, the instructions being adapted to be loaded and executed by the processor to provide a disaster-resistant UAV path planning method based on dual-population constraint multi-objective optimization.

[0287] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for post-disaster UAV path planning based on double-population constrained multi-objective optimization, characterized in that, Comprise: According to post-disaster image data, a post-disaster task scene model is constructed, including establishing a two-dimensional coordinate system, determining task points and unmanned aerial vehicle configurations, defining unmanned aerial vehicle flight paths, and constructing a risk field model; Based on the post-disaster task scene model, an unmanned aerial vehicle flight multi-objective collaborative optimization objective function and constraint conditions are established, including constructing a multi-objective function system, setting system constraint conditions, and establishing a constraint violation degree evaluation mechanism; Path optimization is performed using a double-population constrained multi-objective evolutionary algorithm, including establishing a multi-unmanned aerial vehicle path encoding mechanism and initializing a double-population architecture, implementing double-population collaborative genetic reproduction operations, and determining a double-stage constraint processing strategy; And implementing environment selection based on elite perception ordering; A preference-oriented decision scheme is generated, including constructing and normalizing a scheme library, configuring multi-scenario preference strategies, and performing TOPSIS comprehensive evaluation; An optimized path scheme is output.

2. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 1, characterized in that, The establishing of the two-dimensional coordinate system, the determining of the task point and the unmanned aerial vehicle configuration and the defining of the unmanned aerial vehicle flight path comprise determining the boundary range of the post-disaster task scene space according to the disaster area range, standardizing the irregular disaster area range into a rectangular region, establishing a rectangular coordinate system with the disaster area centroid as the origin, and ensuring that the central position of the coordinate system can represent the center of gravity of the entire disaster area to provide a reference point for distance calculation and path optimization. The establishing of the two-dimensional coordinate system, the determining of the task point and the unmanned aerial vehicle configuration and the defining of the unmanned aerial vehicle flight path comprise determining the boundary range of the post-disaster task scene space according to the disaster area range, standardizing the irregular disaster area range into a rectangular region, establishing a rectangular coordinate system with the disaster area centroid as the origin, and ensuring that the central position of the coordinate system can represent the center of gravity of the entire disaster area to provide a reference point for distance calculation and path optimization. Based on the established coordinate system, the actual rescue demand is converted into a mathematical object that can be processed by the algorithm, all positions that need to be supplied with materials are identified through post-disaster communication information, and then a task point set is established Each task point is represented by a two-dimensional coordinate , and the coordinate position of the unmanned aerial vehicle base is determined , and a set of unmanned aerial vehicles is established , where is the total number of unmanned aerial vehicles, and a mathematical representation of the unmanned aerial vehicle flight path is further established, each unmanned aerial vehicle obeys the closed-loop constraint condition of starting from the base and returning to complete a flight, when the first unmanned aerial vehicle is assigned a set of task points, its complete flight includes the base departure point, each task point visited in turn, and the final base return point, and the flight of the unmanned aerial vehicle contains flight points, which are recorded in the order of visit as: ， wherein represents a drone second waypoint of the drone, is the number of task points assigned to the drone for calculating the flight distance, time and risk exposure, defining a path segment between adjacent waypoints is a line segment connecting waypoints and the geometric length of the path segment is​ ， Path segment By parametric equation: ， ， where the parameters denote the distance along the path segment from the start to the end point.

3. The method according to claim 2, wherein, The construction of the risk field model includes establishing a continuous risk field model based on the risk density function to accurately describe the complex risk distribution in the post-disaster environment. First, the post-disaster mission scenario space is... The restricted areas within the area are divided into two categories and treated differently, based on risk areas. Medium-risk sources Different types, for each type of risk source The risk density function is established, and for point-like risk sources, it is expressed using a Gaussian decay model as follows: ， wherein is the central coordinate of the risk source is the risk intensity coefficient is the influence range parameter is the calculated risk density value directly reflects the threat degree of the coordinate point to the risk source For a large-area regional risk source, a segmented constant model is used, which is expressed as: ， wherein is the core danger zone of the risk source, in which the risk value is constant , is the point to the shortest distance to the boundary of the core zone, is the risk influence radius, and by superimposing the influences of all risk sources to obtain a complete risk distribution map, the comprehensive risk density is obtained by superimposing the influences of various risk sources: ， wherein is the total number of point-like risk sources, is the total number of regional risk sources, based on the integrated risk density function, the UAV The risk exposure along a path segment is calculated by path integration: ， where the path segment is parameterized from 0 to the parameter the integral result represents the total risk exposure the drone is subjected to during the flight of the path segment.

4. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 3, characterized in that, The multi-objective function system is constructed, including establishing a multi-objective cooperative optimization objective function of the flight range of the unmanned aerial vehicle based on the constructed post-disaster task scene model, the objective function comprehensively considering multiple dimensions of task coverage, response time, risk control, load balancing and energy consumption optimization, and being expressed as: , in the formula indicates a solution of the planned path of the multi-unmanned aerial vehicle, is expressed as a target function vector, wherein the weighted task coverage objective function is expressed as: ， wherein represents a set of task points that have been visited and successfully served, is a task point priority weight is a total number of task points; priority response time objective function is represented as: ， in For the task point Completion time, For the start of service, and These are the latest completion time and the earliest start time, respectively. Early arrival penalty coefficient; Comprehensive risk exposure objective function Represented as: ， where the first term represents a drone the sum of risk exposure along the flight path, where is calculated from the path integral, is a drone the number of en-route waypoints visited, the second term represents a drone the risk exposure during hovering operations at task points, where is a drone the set of task points served, is the required service duration at task point , is the risk density at the task point location; the load balancing objective function is represented as: ， In the formula For drones Total load capacity, For flight duration, For the number of service task points, These are the corresponding average values. These are the weighting coefficients.

5. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 4, characterized in that, The setting system constraint condition comprises establishing a unified constraint function system In the formula Indicates The constraint function vector of wherein the load constraint function is represented as: ， In the formula the material demand quantity of the task point , the maximum load of the UAV , the task point set served by the UAV energy consumption constraint function is represented as: ， wherein total energy consumption of the UAV, maximum energy consumption limit of the UAV; endurance time constraint function total mission time of the UAV, maximum endurance time of the UAV; no-fly zone constraint function is expressed as: wherein total mission time of the UAV, total energy consumption of the UAV, maximum endurance time of the UAV; no-fly zone constraint function maximum energy consumption limit of the UAV; endurance time constraint function is expressed as: ， In the formula For path segment No-fly zone The length of the overlap.

6. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 5, characterized in that, The establishment of a multi-UAV path coding mechanism and the initialization of a dual-population architecture include establishing a coding mechanism to represent the solution space of the multi-UAV path planning problem, where each individual... The complete multi-UAV path planning scheme is represented by a task sequence encoding structure: in Indicates drone Task access sequence: in For drones Visiting in sequence One task point, To be allocated to drones The number of task points, task allocation through The set of task points included is represented, and the access order is represented by the arrangement order of the task points in the sequence; based on the established multi-objective collaborative optimization objective function and constraints, a dual-population constrained multi-objective evolutionary algorithm is used to solve the UAV range and obtain the global optimal solution set, in which a principal population is set. and auxiliary population The scale is Construct a set of reference vectors The reference vector, used to guide the search direction, is designed based on the decomposition concept, breaking down a multi-objective problem into multiple single-objective sub-problems and setting crossover probabilities. and basic mutation probability It is used to control the frequency and intensity of new individuals generated in genetic operations, while also setting the maximum number of generations. As a termination condition for the algorithm, initial solution individuals are then generated randomly. Each individual represents a complete multi-UAV path planning scheme according to the established encoding mechanism. During the generation process, the main population is... All initial individuals are required to satisfy the basic constraints, while the auxiliary population... This allows individuals to violate the constraints.

7. The method according to claim 6, wherein, The implementation of the dual-population co-evolutionary genetic breeding operation includes, based on the dual-population architecture, in each generation of evolution, the main population and the auxiliary population generate a child population through genetic operations of selection, crossover and mutation, respectively, wherein, first, a binary tournament selection strategy is adopted to select parent individuals from the current population for subsequent crossover operations, individuals are randomly selected from the population and are compared, and individuals with better performance are selected as parents to participate in subsequent crossover and mutation operations, and the selection criteria are based on the objective function value and the constraint violation degree: ， wherein is a balancing coefficient, denotes the Euclidean norm of the objective function vector ; then a crossover operation is performed on the selected parent individuals to generate preliminary offspring individuals, and at the task assignment level, an improved partition crossover operation is used to ensure complete and non-repeated assignment of all task points: first, a crossover point is randomly selected to divide the parent individuals and into two segments, then the task assignment of the former segment is kept unchanged, and the latter segment is re-assigned using a nearest neighbor heuristic to conflict task points; finally, a mutation operation is performed on the crossed offspring individuals to introduce random perturbations to enhance population diversity, and based on the constraint violation and objective function performance of the offspring individuals, a mutation strategy is adaptively selected according to the individual characteristics, and the mutation probability is dynamically adjusted according to the constraint violation degree of the individual: ， wherein is the base mutation probability, is the maximum constraint violation of the current population, is the numerical stability term; through selection, crossover, mutation operations, the main population and the auxiliary population generate a child main population and a child auxiliary population of size respectively, a candidate population generation strategy is designed to promote the communication between the two populations, the main population is merged with the child candidate population to form a parent candidate main population of size , similarly, the auxiliary population is merged with the child candidate population to form a parent candidate auxiliary population of size , through the merging strategy, both populations receive offspring individuals from the other, achieving co-evolution.

8. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 7, characterized in that, The determining the two-stage constraint processing strategy comprises: in the first stage, the parent candidate main population is selected based on the two-stage constraint processing strategy In the strict constraint processing mode, only the individual completely satisfying the constraint condition is accepted, and the next generation main population is selected by the elite perception ordering environment selection strategy ; meanwhile, the parent candidate auxiliary population In the first stage, the unconstrained processing mode is adopted, that is, all individuals are accepted, and the next generation auxiliary population is selected by the elite perception ordering environment selection strategy ; When the algorithm enters the second phase, the parent candidate primary population The strategy remains unchanged, the parent candidate secondary population Switches to a constraint relaxation processing mode, that is, accepts individuals with a constraint tolerance degree less than a tolerance threshold, wherein the constraint tolerance degree According to the current evolution generation Is dynamically adjusted, expressed as: ， wherein is the initial tolerance level, is the decay coefficient, is the current evolution generation, is the maximum evolution generation; to accurately control the phase transition opportunity of the constraint processing strategy, an adaptive transition mechanism based on ideal point and worst point change rate is adopted, and the auxiliary population of ideal points in the target space and the change of the worst point , wherein the first component of the ideal point is: ​ ， represents the current optimum value of the auxiliary population on the jth objective, the worst point of the jth component is: ​​ ， represents the current worst value on the target; to quantify the evolutionary state of the population, the rate of change of the ideal point is calculated: ， and calculate the rate of change of the worst point of the worst point: ， wherein To evaluate the algebraic interval of the rate of change, the integrated rate of change is thus obtained: .

9. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 8, characterized in that, The implementation is based on the environment selection of elite-aware ranking, including the merit ranking of individuals in the candidate population based on the determined two-stage constraint handling strategy, and selecting the next generation population according to the ranking result and the constraint handling strategy; based on the elite-aware ranking mechanism, the individual hierarchy is refined by fusing multiple ranking strategies; first, the non-dominated sorting is performed on all individuals in the candidate population For any individual And , through non-dominated sorting, each individual Obtains the non-dominated level , wherein is the maximum level number, then each individual Is associated with the reference vector With the smallest angle in the target space ， wherein represents the angle of the individual with the reference vector and calculates the angle penalty distance of the individual: ， wherein is a penalty intensity coefficient, is a maximum allowed angle, is a penalty index, based on the angle penalty distance, each individual is assigned a θ-dominance rank wherein is the maximum number of θ-dominance ranks, the final elite-aware rank of each individual is calculated; Based on the double-population double-stage framework and the elitist-aware ranking results, an environment selection strategy of hierarchical filling is adopted to select the next generation population, wherein when the number of individuals in a certain level exceeds the remaining capacity of the next generation population , the individuals in the level need to be truncated to determine the finally selected individuals, and the individuals in the level are evaluated and ranked by using a corresponding scoring function, and the individuals with the optimal score are selected to fill the population. For the main population , since the strict constraint processing method is adopted, the constraint scoring function is used: ， For the auxiliary population In the first stage, the unconstrained processing mode is adopted, and the unconstrained scoring function is used In the second stage, the constrained relaxation processing mode is adopted, and the constrained relaxation scoring function is used to calculate the fitness scores of each individual in the same level, and the individuals are selected in turn according to the scoring from good to bad to put into the next generation population , until the population size reaches , the environmental selection operation is realized, and the new main population is selected from the parent candidate main population , and the new auxiliary population is selected from the parent candidate auxiliary population , the one-generation evolution process is completed, and when the evolution generation number reaches the maximum evolution generation number , all the non-dominated individuals in the main population that meet the constraint conditions are output, forming the Pareto optimal solution set .

10. The post-disaster UAV path planning method based on double-population constrained multi-objective optimization according to claim 9, characterized in that, The construction and normalization scheme library, configuration multi-scenario preference strategy and execution of TOPSIS comprehensive evaluation, including based on the Pareto optimal solution set of double population constraint multi-objective evolutionary algorithm output , construct candidate scheme library , in order to ensure the fairness of multi-objective evaluation, for each objective function Perform normalization processing, after normalization, Indicates that the scheme reaches the ideal level on the th objective, Indicates that the worst level is reached, and then the optimization of the main objective is set while the acceptable threshold for the non-main preference objective is set , based on the main preference objective and threshold constraint, the preference scheme set that meets the condition is screened out; finally, the improved TOPSIS method is used to comprehensively evaluate the candidate schemes, and for each candidate scheme , calculate the optimization degree on the main preference objective: ， Then, the balance degree of the candidate scheme on the non-main preference target is calculated: ， wherein is the total number of objectives and the overall preference score is obtained according to the degree of optimization of the main preference objective and the degree of balance on the non-main preference objectives: ， wherein are weight coefficients for the main objective optimization and the target balancing, respectively, for adjusting the relative importance of both in the overall score; based on the overall preference score result, the solution with the highest score is selected as the final recommended solution: ， Output optimal solution and its corresponding detailed performance indicators.

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