Constraint multi-target vehicle scheduling method based on dynamic constraint and evolutionary multitask

Abstract

The invention discloses a constrained multi-target vehicle scheduling method based on dynamic constraint and evolutionary multitask, and relates to the technical field of constrained multi-target vehicle scheduling, and the method comprises the following steps: obtaining a constrained multi-target vehicle scheduling problem, and decomposing the problem into three tasks; respectively initializing populations and parameters of the three tasks; if the current iteration stage is in the early stage, executing an early evolution operation, and if the current iteration stage is in the later stage, executing a later evolution operation; and iteration is carried out until the maximum number of iterations is reached, and the main task population at the moment is output as a final feasible non-dominated solution set for vehicle scheduling. According to the method, the multi-task structure is set, each task corresponds to different constraint strategies, and the effectiveness and the accuracy of constraint multi-target vehicle scheduling are improved in cooperation with the two-stage evolution operation.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of constrained multi-objective vehicle scheduling, and particularly relates to a constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking. BACKGROUND

[0002] A vehicle scheduling problem not only involves meeting various constraint conditions, but also involves multi-objective optimization. Such a problem can be uniformly modeled as a constrained multi-objective vehicle scheduling problem, which is a problem of optimizing multiple conflicting objectives under complex constraint conditions. The dual challenges of ensuring objective trade-off and constraint satisfaction make the constrained multi-objective vehicle scheduling problem more difficult to solve than the unconstrained problem. Therefore, research on the constrained multi-objective vehicle scheduling method is needed.

[0003] In the prior art, a multi-AGV path planning method based on constrained multi-objective optimization is disclosed in Chinese Patent CN119290011A. The entire population is dynamically divided into three mutually exclusive subsets: FNDS, FNDS dominant subset and non-FNDS dominant subset. According to the proposed division of labor, there is no need to balance convergence and constraint satisfaction in each subset.

[0004] However, the above prior art lacks a targeted collaboration mechanism, making it difficult to balance constraint satisfaction and objective optimization in scheduling, and the effectiveness and accuracy of the constrained multi-objective vehicle scheduling are poor. SUMMARY

[0005] The application provides a constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking, to solve the problem that the prior art lacks a targeted collaboration mechanism, making it difficult to balance constraint satisfaction and objective optimization in scheduling, and the effectiveness and accuracy of the constrained multi-objective vehicle scheduling are poor.

[0006] In one aspect, the application provides a constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking, comprising the following steps: Step one, obtain a constrained multi-objective vehicle scheduling problem and decompose it into three tasks, including a main task, a first auxiliary task and a second auxiliary task.

[0007] The main task uses a constrained multi-objective evolutionary algorithm based on dynamic constraint processing as an optimizer.

[0008] The first auxiliary task uses a constrained multi-objective evolutionary algorithm based on dynamic changes in constraint boundaries as an optimizer.

[0009] The second auxiliary task uses a multi-objective evolutionary algorithm based on ignoring constraints as an optimizer.

[0010] Step two, initialize the population and parameters of the three tasks respectively.

[0011] Step three, judging whether the current iteration stage is in an early stage or a later stage based on the evaluation number and the stage transition parameter.

[0012] Step four, if the current iteration stage is in the early stage, performing an early evolution operation, and if the current iteration stage is in the later stage, performing a later evolution operation.

[0013] In the early evolution operation, three temporary populations of the three tasks are respectively constructed, the corresponding optimizers are used to perform environmental selection on the three temporary populations, and the populations of the three tasks are updated.

[0014] In the later evolution operation, three initial temporary populations of the three tasks are respectively constructed, three transmission populations are determined, three final temporary populations fused with the transmission populations and the original populations are constructed, the corresponding optimizers are used to perform environmental selection on the three final temporary populations, and the populations of the three tasks are updated.

[0015] Step five, returning to step three for iteration until the maximum iteration number is reached, and outputting the main task population at this time as the final feasible non-dominated solution set of vehicle scheduling.

[0016] In a possible implementation, in step three, when the evaluation number is less than the product of the stage transition parameter and the maximum evaluation number, it is judged that the current iteration stage is in the early stage, and when the evaluation number is greater than or equal to the product of the stage transition parameter and the maximum evaluation number, it is judged that the current iteration stage is in the later stage.

[0017] In step four, the evaluation number is updated at the end of each iteration.

[0018] In a possible implementation, in the early evolution operation, before the three temporary populations of the three tasks are constructed, a preset number of individuals are randomly selected from the main task population as main task pairing parents, and a preset number of individuals are selected from the first auxiliary task population and the second auxiliary task population as first auxiliary task pairing parents and second auxiliary task pairing parents by using binary tournament selection.

[0019] The main task offspring population, the first auxiliary task offspring population and the second auxiliary task offspring population are respectively generated based on the main task pairing parents, the first auxiliary task pairing parents and the second auxiliary task pairing parents.

[0020] In a possible implementation, the temporary population of the main task is constructed by fusing the main task population and the main task offspring population, the first auxiliary task offspring population and the second auxiliary task offspring population.

[0021] The temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the first auxiliary task offspring population and the second auxiliary task offspring population.

[0022] The temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the first auxiliary task offspring population, the second auxiliary task offspring population.

[0023] In a possible implementation, the constraint multi-objective evolutionary algorithm based on dynamic change of constraint boundary comprises: The constraint boundary of the current generation is calculated, and the constraint boundary of each generation is gradually reduced.

[0024] The temporary population of the first auxiliary task is divided into two individual sets according to the constraint boundary.

[0025] The first auxiliary task population is updated by environmental selection according to the state of the two individual sets.

[0026] In a possible implementation, the first auxiliary task population is updated by environmental selection according to the state of the two individual sets, comprising: The individuals in the temporary population of the first auxiliary task, whose total constraint violation level is less than or equal to the constraint boundary, are merged into the first individual set, and the individuals whose total constraint violation level is greater than the constraint boundary are merged into the second individual set.

[0027] When the first individual set is empty, the second individual set is selected by environmental selection, and the first auxiliary task population is updated.

[0028] When the first individual set is not empty and less than or equal to the population size, the entire first individual set and part of the second individual set are selected by environmental selection, and the first auxiliary task population is updated.

[0029] When the first individual set is greater than the population size, the first individual set is selected by environmental selection, and the first auxiliary task population is updated.

[0030] In a possible implementation, in the late evolutionary operation, before constructing the initial temporary populations of the three tasks, a binary tournament selection method is used to select a preset number of individuals from the main task population, the first auxiliary task population and the second auxiliary task population as main task pairing parents, first auxiliary task pairing parents and second auxiliary task pairing parents.

[0031] The main task offspring population, the first auxiliary task offspring population and the second auxiliary task offspring population are generated based on the main task pairing parents, the first auxiliary task pairing parents and the second auxiliary task pairing parents respectively.

[0032] In a possible implementation, the initial temporary population of the main task is constructed by fusing the main task population and the main task offspring population.

[0033] The initial temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the first auxiliary task offspring population.

[0034] The initial temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the second auxiliary task offspring population.

[0035] In a possible implementation, in the later evolution operation, the success rates of the three mating parents and the corresponding offspring populations are calculated respectively, and the three transmission populations are determined based on the success rates.

[0036] The final temporary population of the main task is constructed by fusing the main task population and the first auxiliary task transmission population and the second auxiliary task transmission population.

[0037] The final temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the second auxiliary task offspring population.

[0038] The final temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the first auxiliary task offspring population.

[0039] The constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-task in the application has the following advantages: By setting a multi-task structure, each task corresponds to a different constraint strategy, and independent development promotes mutual support to improve search efficiency. The main task adopts a constraint multi-objective evolutionary algorithm based on dynamic constraint processing as an optimizer, the first auxiliary task adopts a constraint multi-objective evolutionary algorithm based on dynamic changes of constraint boundaries as an optimizer, and the second auxiliary task adopts a multi-objective evolutionary algorithm based on ignoring constraints as an optimizer. In combination with a two-stage evolution operation, in the early evolution operation, temporary populations of the three tasks are constructed respectively, the corresponding optimizers are used for environmental selection of the three temporary populations, and the populations of the three tasks are updated. In the later evolution operation, initial temporary populations of the three tasks are constructed respectively, three transmission populations are determined, three final temporary populations fused with the transmission populations and the original populations are constructed, the corresponding optimizers are used for environmental selection of the three final temporary populations, and the populations of the three tasks are updated. In summary, the effectiveness and accuracy of the constraint multi-objective vehicle scheduling are improved.

[0040] In the early evolution operation, before constructing the temporary populations of the three tasks, a preset number of individuals are randomly selected from the main task population as main task mating parents, a preset number of individuals are selected from the first auxiliary task population and the second auxiliary task population as first auxiliary task mating parents and second auxiliary task mating parents respectively by using a binary tournament selection method, and the convergence of the population is improved.

[0041] The constraint boundary of the current generation is calculated, the constraint boundary of each generation is gradually reduced, the temporary population of the first auxiliary task is divided into two individual sets according to the constraint boundary, the environment selection is performed according to the state of the two individual sets, and the population of the first auxiliary task is updated, thereby establishing a high degree of correlation with the main task.

[0042] In the late evolution operation, before constructing the initial temporary populations of the three tasks, a binary tournament selection method is used to select a preset number of individuals from the main task population, the first auxiliary task population and the second auxiliary task population as the main task mating parent, the first auxiliary task mating parent and the second auxiliary task mating parent, thereby improving the convergence of the population.

[0043] In the late evolution operation, the success rates of the three mating parents and the corresponding offspring populations are calculated respectively, the three transmission populations are determined based on the success rates, the final temporary population of the main task is constructed by fusing the main task population and the first auxiliary task transmission population and the second auxiliary task transmission population, the final temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the second auxiliary task offspring population, and the final temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the first auxiliary task offspring population, thereby guiding the migration of high-quality individuals across tasks, achieving effective knowledge transfer and enhancing the optimization ability of the main task. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0045] Figure 1 A flowchart of a constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking provided by the embodiments of the present application is shown. Figure 2 A framework diagram of a constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking provided by the embodiments of the present application is shown. Figure 3 A knowledge transfer diagram of an early evolution operation provided by the embodiments of the present application is shown. Figure 4 A knowledge transfer diagram of a late evolution operation provided by the embodiments of the present application is shown. DETAILED DESCRIPTION

[0046] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0047] Specifically, the constrained multi-objective vehicle scheduling problem is usually defined as optimizing multiple objective functions under a set of constraints, which can be expressed as: .

[0048] Subject to: .

[0049] The violation degree of each constraint is calculated using the following formula: .

[0050] x The total constraint violation level (denoted by the value of G ) can be calculated as: .

[0051] In the formula, x =( x 1, x 2,⋯ x D )∈ S denotes a solution with D dimensions; S ≤ R ^ D is the decision space; f : S → R ^ M denotes M objective functions; G j ( x ) and m denote the JTH inequality constraint and the number of inequality constraints, respectively; h j ( x ) and ( n - m ) denote the ( j - m ) equality constraints and the number of equality constraints, respectively. When a solution satisfies all the constraints, it is defined as a feasible solution; otherwise, it is infeasible. The purpose of constrained multi-objective optimization is to find a set of feasible non-dominated solutions.

[0052] AsFigure 1 and Figure 2 As shown in the figure, the embodiment of the present application provides a constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking, including the following steps: Step one, obtain the constraint multi-objective vehicle scheduling problem and decompose it into three tasks, including the main task, the first auxiliary task and the second auxiliary task.

[0053] The main task adopts a constraint multi-objective evolutionary algorithm based on dynamic constraint processing as an optimizer.

[0054] The first auxiliary task adopts a constraint multi-objective evolutionary algorithm based on dynamic changes of constraint boundaries as an optimizer.

[0055] The second auxiliary task adopts a multi-objective evolutionary algorithm based on ignoring constraints as an optimizer.

[0056] Step two, initialize the population and parameters of the three tasks respectively.

[0057] Step three, judge whether the current iteration stage is in the early stage or the late stage based on the evaluation number and the stage conversion parameter.

[0058] Step four, if the current iteration stage is in the early stage, perform early evolution operation, and if the current iteration stage is in the late stage, perform late evolution operation.

[0059] In the early evolution operation, temporary populations of the three tasks are constructed respectively, the corresponding optimizers are used for environmental selection on the three temporary populations, and the populations of the three tasks are updated.

[0060] In the late evolution operation, initial temporary populations of the three tasks are constructed, three transmission populations are determined, three final temporary populations fused with the transmission populations and the original populations are constructed, the corresponding optimizers are used for environmental selection on the three final temporary populations, and the populations of the three tasks are updated.

[0061] Step five, return to step three for iteration until the maximum iteration number is reached, and output the main task population at this time as the final feasible non-dominated solution set of vehicle scheduling.

[0062] Specifically, in the embodiment, the main task, the first auxiliary task and the second auxiliary task are denoted as T 1, T 2, T 3 respectively, the generated main task population, the first auxiliary task population and the second auxiliary task population are denoted as P 1, P 2, P 3 respectively, the initial value of the evaluation number FES is 0, and the stage conversion parameter βThe value range is from 0 to 1, and can be set by the user.

[0063] For example, in step three, when the number of evaluations is less than the product of the stage transition parameter and the maximum number of evaluations, the current iteration stage is determined to be in the early stage; when the number of evaluations is greater than or equal to the product of the stage transition parameter and the maximum number of evaluations, the current iteration stage is determined to be in the late stage.

[0064] In step four, the number of evaluations is updated at the end of each iteration.

[0065] Specifically, in this embodiment, when the initialization in step two ends, the following steps are taken: Number of assessments FES Perform an update. In step four, at the end of each iteration, use... The number of assessments has been updated. NP Indicates population size.

[0066] like Figure 3 As shown, exemplarily, in the early evolutionary operation, before constructing temporary populations for the three tasks, a preset number of individuals are randomly selected from the main task population as main task pairing parents, and a preset number of individuals are selected from the first auxiliary task population and the second auxiliary task population respectively as first auxiliary task pairing parents and second auxiliary task pairing parents using a binary competition selection method.

[0067] The main task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population are generated based on the main task paired parent, the first auxiliary task paired parent, and the second auxiliary task paired parent, respectively.

[0068] Specifically, in this embodiment, from the main task population P Random selection from 1 NP Individuals of 2 / 3 were used as primary task parents, and a binary competitive selection method was used to select from the first auxiliary task population. P 2. Second auxiliary task population P Choose from 3 NP Individuals of 2 / 2 were used as the first auxiliary task pairing parents and the second auxiliary task pairing parents.

[0069] For example, the temporary population of the main task is constructed by merging the main task population with the main task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population.

[0070] The temporary population of the first auxiliary task is constructed by merging the population of the first auxiliary task, the offspring population of the first auxiliary task, and the offspring population of the second auxiliary task.

[0071] The temporary population of the second auxiliary task is constructed by merging the population of the second auxiliary task with the offspring population of the first auxiliary task and the offspring population of the second auxiliary task.

[0072] Specifically, in this embodiment, the temporary population of the main task The temporary population for the first auxiliary task The temporary population for the second auxiliary task ,in, , , These represent the primary task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population, respectively.

[0073] Evaluate , Performance evaluation on constrained multi-objective evolutionary algorithms Performance on multi-objective evolutionary algorithms.

[0074] right Environment selection is performed using a constrained multi-objective evolutionary algorithm based on dynamic constraint processing. NP Individuals, update the main task population ;right An environment selection is performed using a constrained multi-objective evolutionary algorithm based on dynamically changing constraint boundaries. NP Individuals, updating the first auxiliary task population. ;right Environment selection is performed using a multi-objective evolutionary algorithm that ignores constraints. NP Individuals, update the second auxiliary task population .

[0075] For example, the constrained multi-objective evolutionary algorithm based on dynamically changing constraint boundaries includes: Calculate the constraint boundary of the current generation, and the constraint boundary gradually decreases with each generation.

[0076] Based on the constraint boundary, the temporary population of the first auxiliary task is divided into two sets of individuals.

[0077] Environmental selection is performed based on the state of the two types of individual sets, and the first auxiliary task population is updated.

[0078] For example, the step of selecting the environment based on the states of the two types of individual sets and updating the first auxiliary task population includes: In the temporary population of the first auxiliary task, individuals with a total constraint violation level less than or equal to the constraint boundary are merged into the first population set, and individuals with a total constraint violation level greater than the constraint boundary are merged into the second population set.

[0079] When the first set of individuals is empty, environmental selection is performed on the second set of individuals to update the first auxiliary task population.

[0080] When the first set of individuals is not empty and is less than or equal to the population size, environmental selection is performed on the entire first set of individuals and part of the second set of individuals to update the first auxiliary task population.

[0081] When the first set of individuals is larger than the population size, environmental selection is performed on the first set of individuals to update the first auxiliary task population.

[0082] Specifically, in this embodiment, the objective functions of both auxiliary tasks are consistent with those of the main task. The difference lies in that the constraint function of the first auxiliary task is dynamically changing. The objective function, dynamic constraints, and constraint boundaries of the first auxiliary task are shown in the following three equations: , , .

[0083] in T For the current generation, NP T For the first T The constraint boundary of the generation. Max T It is the largest algebra. ε To control pp T The parameter for the rate of descent is set to 0.5. ε 0 represents the initial constraint violation value, which is equal to the total constraint violation level of the initial primary task population, the first auxiliary task population, and the second auxiliary task population. G The maximum value. Constraint boundaries are calculated in each generation. ε T And gradually decrease. Based on ε T ,Will G Value less than or equal to ε T The individuals are merged into the first set of individuals. M 1. The remaining individuals are merged into a second set of individuals. M 2.

[0084] When the first body set M When 1 is empty, for the second set of volumes M2, the solutions in 2 are sorted, and the original ε top .

[0085] When the first individual set M 1 is not empty and M 1 is less than or equal to the population size NP , environmental selection is performed on the entire first individual set M 1 and part of the second individual set M 2 (a constraint multi-objective evolutionary algorithm based on dynamic constraint processing is used to sort the two individual sets, and then, from the top M 1 individuals in the entire first individual set M 1 and the sorted second individual set NP 2, top M 1 individuals are selected), and the first auxiliary task population NP .

[0086] When the first individual set M 1 is greater than the population size NP , environmental selection is performed on the first individual set M 1 (a non-dominated sorting method is used to sort the first individual set M 1, and the constraint violation degree is taken as an additional objective. Then, the top M 1 individuals in the sorted first individual set NP 1 are reserved), and the first auxiliary task population .

[0087] As shown in FIG. 3, in the late evolutionary operation, a binary tournament selection method is used to select a preset number of individuals from the main task population , the first auxiliary task population and the second auxiliary task population as main task pairing parents, first auxiliary task pairing parents and second auxiliary task pairing parents, respectively, before the initial temporary populations of the three tasks are constructed.

[0088] The main task offspring population, the first auxiliary task offspring population and the second auxiliary task offspring population are generated based on the main task pairing parents, the first auxiliary task pairing parents and the second auxiliary task pairing parents, respectively.

[0089] Specifically, in this embodiment, a binary tournament selection method is used to select a preset number of individuals from the main task population , the first auxiliary task population and the second auxiliary task population as main task pairing parents, first auxiliary task pairing parents and second auxiliary task pairing parents, respectively, before the initial temporary populations of the three tasks are constructed.​ and a second auxiliary task population is selected Figure 4 / 2 individuals as the main task mating parent, the first auxiliary task mating parent and the second auxiliary task mating parent.

[0090] Exemplarily, the initial temporary population of the main task is constructed by fusing the main task population and the main task offspring population.

[0091] The initial temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the first auxiliary task offspring population.

[0092] The initial temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the second auxiliary task offspring population.

[0093] Specifically, in the embodiment, the initial temporary population of the main task is , the initial temporary population of the first auxiliary task is , and the initial temporary population of the second auxiliary task is .

[0094] Exemplarily, in the later evolution operation, the success rates of the three mating parents and the corresponding offspring populations are respectively calculated, and the three transmission populations are determined based on the success rates.

[0095] The final temporary population of the main task is constructed by fusing the main task population and the first auxiliary task transmission population and the second auxiliary task transmission population.

[0096] The final temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the second auxiliary task offspring population.

[0097] The final temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the first auxiliary task offspring population.

[0098] Specifically, in the embodiment, the success rates of the three mating parents and the corresponding offspring populations are respectively calculated, wherein the success rate of the mating parent is as follows: .

[0099] The success rate of the offspring population is as follows: .

[0100] Wherein, The range of p is [0, 1], The range of p is [0, 1], respectively representing the success rates of the mating parent P j and the offspring population NP j In T2 / j (This indicates that when one of the tasks is represented as) T j ( j When =1 or 2), the other corresponding task is represented as T 2 / j The success rate on ) ; num_ P j and num_ OP j The best OP The number of parental individuals and the number of offspring individuals in an individual. When < At that time, it indicates the offspring population NP j More suitable for T 2 / j Based on the formulas for the degree of violation of each constraint and the total level of constraint violations, the transmission population can be determined. OP j (No. j (a total of transport populations), including the main task transport population. TrP 1. First auxiliary task: Transfer population TrP 2. Second auxiliary task: Transfer population TrP 3. The final temporary population of the main quest. The final temporary population of the first auxiliary task The final temporary population for the second auxiliary task .

[0101] Evaluate , Performance evaluation on constrained multi-objective evolutionary algorithms Performance on multi-objective evolutionary algorithms.

[0102] right Environment selection is performed using a constrained multi-objective evolutionary algorithm based on dynamic constraint processing. TrP Individuals, update the main task population ;right An environment selection is performed using a constrained multi-objective evolutionary algorithm based on dynamically changing constraint boundaries. NP Individuals, updating the first auxiliary task population. ;right Environment selection is performed using a multi-objective evolutionary algorithm that ignores constraints. NP Individuals, update the second auxiliary task population .

[0103] The time complexity of the constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking of the present application is mainly dominated by the population environment selection and the non-dominated sorting process. In the early stage and the late stage, the merging and selection of the three populations (P1, P2 and P3) P 1、 P 2and P 3) require repeated non-dominated sorting and truncation operations. Assuming the population size is N , the size of the merged population is O ( N ), and each environment selection step adopts a truncation strategy similar to SPEA2, the computational complexity is O ( N ^3). In addition, the worst-case complexity of the abundance-dominated sorting is related to the number of objective functions, which is O ( M ·〖(2.5 N )〗^2)≈ O ( NP ^2). However, since the complexity of the truncation strategy O ( N ^3) is significantly higher than that of other operations (such as population merging O ( N ) and evolutionary operations O ( N )), the overall time complexity of the algorithm is dominated by the environment selection part. Therefore, the overall time complexity of the constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking is O ( N ^3), which is mainly consumed in the truncation strategy and non-dominated sorting process of the environment selection.

[0104] In a possible embodiment, in order to verify the effectiveness of the constraint multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking of the present application, it is compared with five existing algorithms (including: BiCo algorithm, CCMO algorithm, CTAEA algorithm, CMOEAMS algorithm, EMCMO algorithm) proposed in recent years, wherein the BiCo algorithm is a two-way collaborative evolution of a double-population algorithm; the CCMO algorithm and the CTAEA algorithm are based on a double-population constraint multi-objective evolutionary algorithm, which uses a constraint multi-objective evolutionary algorithm based on dynamic constraint processing to process constraints; the CMOEAMS algorithm is based on a two-stage constraint multi-objective evolutionary algorithm, which uses an adaptive state switching stage to balance the objectives and constraints; the EMCMO algorithm uses a multitasking optimization method, introduces a partial constraint pruning task, and promotes the adaptive migration of knowledge between tasks. All experiments are carried out using the PlatEMO open source platform.

[0105] Benchmark suite: The evaluation is performed on the CF test suite and two feasible domain complexity CMOP test suites (DASCMOP test suite and LIRCMOP test suite). The LIRCMOP test suite and DASCMOP test suite pose a significant challenge to most existing constrained multi-objective evolutionary algorithms. Most of the boundaries appear as small feasible domains or disjoint combinations of sparse points, and some of the boundaries even form curves. Some of the test problems contain a large number of infeasible domains between the unconstrained boundaries and the feasible region. On the other hand, the CF test suite covers a variety of features such as continuous and discontinuous feasible regions, which pose a challenge to the solution capability of constrained multi-objective evolutionary algorithms.

[0106] Performance metrics and parameter settings: In order to measure the performance difference between various algorithms, the Inverse Generational Distance (IGD) and Hypervolume (HV) are used as performance metrics. In addition, in order to determine whether the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking has a significant performance difference compared with each comparative algorithm, a Wilcoxon rank-sum test with a significance level of 0.05 is used for comparative analysis.

[0107] Inverse Generational Distance IGD represents the average distance from each reference point on the true Pareto front (PF) to the nearest solution. Let S* be a set of points uniformly distributed on the PF, S be a set of solutions, then the calculation formula of IGD is as follows: .

[0108] d nn x , S be the Euclidean distance between the point S and its nearest neighbor in the solution set x . The smaller the IGD value, the better the algorithm performance.

[0109] Hypervolume metric: HV measures the Hypervolume of the target space enclosed by the solution set and the predefined reference point Zr, and the formula is: .

[0110] where MN VOL denotes the Lebesgue measure. The larger the value of HV, the better the performance of the algorithm.

[0111] Wilcoxon rank-sum test is a non-parametric statistical method used to evaluate whether there is a significant difference between the medians of paired sample sets. Due to its distribution-free nature, it is particularly suitable for scenarios involving small sample sizes or data that violate the normality assumption, thus providing a robust method for performance comparison across algorithms under different experimental conditions.​

[0112] The number of decision variables of each benchmark problem n and the number of objective functions m are as follows: For CF benchmark problems, the number of decision variables of CF1-CF10 n is set to 10. The number of objective functions of CF9 and CF10 m is 3, and the number of objective functions of the rest of CF benchmark problems m is 2.

[0113] For DASCMOP benchmark problems, the number of decision variables n is set to 30. The number of objective functions of DASCMOP7-DASCMOP9 m is 3, and the number of objective functions of the rest of DASCMOP7 m is 2.

[0114] For LIRCMOP benchmark problems, the number of decision variables of LIRCMOP1-LIRCMOP14 n is set to 10, in which the number of objective functions of LIRCMOP13 and LIRCMOP14 m is 3, and the number of objective functions of the rest of LIRCMOP benchmark problems m is 2.

[0115] The other parameter settings of each comparison algorithm are set according to the data of the respective original paper. For the five advanced comparison algorithms, the main parameter settings are as follows: The population size of all constraint multi-objective evolutionary algorithms N is set to 100.

[0116] The stopping condition of all constraint multi-objective evolutionary algorithms is set to 100,000 function evaluations.

[0117] The parameter settings of each algorithm refer to the settings of the original literature.

[0118] The phase transition parameter for controlling the transition of the evolutionary phase β is set to 0.4.

[0119] Experimental results: For the Inverse Generational Distance (IGD), the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking performed well on 19 out of 33 test problems across the three test sets. The best performance of BiCo algorithm, CCMO algorithm, CTAEA algorithm, CMOEAMS algorithm, and EMCMO algorithm was 4, 4, 1, 4, and 1, respectively. Through the comprehensive performance analysis of 33 test problems in the three test sets, the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking showed balanced ability in handling various types of boundaries. In contrast, the BiCo algorithm performed well in LIRCMOP test problems, fully exploiting its development of infeasible solutions, but performed poorly on DASCMOP test problems. The CCMO algorithm performed relatively well on DASCMOP test problems but poorly on CF test problems. Wilcoxon rank-sum test results showed that the BiCo algorithm, CCMO algorithm, CTAEA algorithm, CMOEAMS algorithm, and EMCMO algorithm were significantly lower than the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking on 21, 21, 26, 23, and 22 test problems, respectively.

[0120] For the Hypervolume indicator, the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking performed well on 19 test problems, while the BiCo algorithm, CCMO algorithm, CTAEA algorithm, CMOEAMS algorithm, and EMCMO algorithm performed well on 5, 5, 1, 3, and 1 test problems, respectively. However, Wilcoxon rank-sum test showed that the BiCo algorithm, CCMO algorithm, CTAEA algorithm, CMOEAMS algorithm, and EMCMO algorithm performed worse than the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking on 21, 22, 26, 22, and 32 problems, respectively. It is clear that the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking is overall superior to existing algorithms in most of the three test problems.

[0121] In one possible embodiment, the convergence results of the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-task were plotted on the CF6, DAS-CMOP9, and LIR-CMOP9 problems, compared with the BiCo, CCMO, CTAEA, CMOEAMS, and EMCMO algorithms. Convergence results on the CF6 problem (where the feasible region is both narrow and long) show that the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-task excels at finding diverse Pareto boundaries, while the BiCo, CCMO, CTAEA, CMOEAMS, and EMCMO algorithms fail to converge to the true Pareto boundary during the search process. Convergence results on the DAS-CMOP9 problem (where the search space is large and the feasible region is relatively dispersed) show that the BiCo, CCMO, CTAEA, CMOEAMS, and EMCMO algorithms have relatively discrete distributions during the search process, indicating that the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-task is more robust and has a more uniform spatial distribution of the search space. Convergence results on the LIR-CMOP9 problem (with a narrow and fragmented feasible region) show that the BiCo, CTAEA, and CMOEAMS algorithms cannot fully converge to the boundary, while the CCMO and CMOEAMS algorithms are more robust. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks has the best performance.

[0122] In one possible embodiment, the IGD convergence curves of the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks were plotted on CF1, CF2, DASCMOP3, DASCMOP9, DASCMOP7, and LIRCMOP10. The results show that the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks exhibits lower curves and faster convergence speeds in most cases, demonstrating good performance in terms of convergence and diversity. Furthermore, compared to other algorithms, the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks generates smoother curves, implying that the method not only performs better but also demonstrates good and competitive performance on most test sets.

[0123] In a constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks, the stage transition parameter β is set to control the transition of evolutionary stages. In one possible embodiment, to study the impact of different stage transition parameters β, MaxFES is set to 100000, and the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks is presented. β IGD results for 24 test functions with parameters of 0, 0.2, 0.4, 0.6, 0.8, and 1. On the CF test set, when the parameters...β = 0.8, 2 best results are obtained. When parameter β = 0.4, 5 best results are obtained by the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking. When β = 0 or 1, it means that the evolutionary stage is in the early or late stage completely. Although most of the best results are obtained on some test suites, the algorithm is not suitable for effective knowledge transfer in two stages. In summary, the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking performs best when β = 0.6. Therefore, on the CF test set, β = 0.6; on the DASCMOP test set, β = 0.8; on the LIRCMOP test set, β = 0.4.

[0124] In other possible embodiments, the constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multitasking of the present application can also be applied to the field of constrained multi-objective evolutionary problems such as test resource allocation problems, vehicle routing problems, Web service location allocation problems, etc.

[0125] In the embodiments of the present application, a multi-task structure is set, each task corresponds to a different constraint strategy, and independent development promotes mutual support to improve search efficiency. Among them, the main task adopts a constrained multi-objective evolutionary algorithm based on dynamic constraint processing as an optimizer, the first auxiliary task adopts a constrained multi-objective evolutionary algorithm based on dynamic change of constraint boundary as an optimizer, and the second auxiliary task adopts a multi-objective evolutionary algorithm based on ignoring constraints as an optimizer. In combination with two-stage evolutionary operation, in the early evolutionary operation, temporary populations of the three tasks are constructed respectively, the corresponding optimizers are used for environmental selection of the three temporary populations, and the populations of the three tasks are updated. In the late evolutionary operation, initial temporary populations of the three tasks are constructed respectively, three transmission populations are determined, three final temporary populations fused with the transmission populations and the original populations are constructed, the corresponding optimizers are used for environmental selection of the three final temporary populations, and the populations of the three tasks are updated. In summary, the effectiveness and accuracy of the constrained multi-objective vehicle scheduling are improved.

[0126] In the early evolutionary operation, before constructing the temporary populations of the three tasks, a preset number of individuals are randomly selected from the main task population as main task pairing parents, a preset number of individuals are selected from the first auxiliary task population and the second auxiliary task population as first auxiliary task pairing parents and second auxiliary task pairing parents respectively by using binary tournament selection method, and the convergence of the population is improved.

[0127] The constraint boundary of the current generation is calculated, the constraint boundary of each generation is gradually reduced, the temporary population of the first auxiliary task is divided into two individual sets according to the constraint boundary, the environment selection is performed according to the state of the two individual sets, and the population of the first auxiliary task is updated, thereby establishing a high degree of correlation with the main task.

[0128] In the late evolution operation, before constructing the initial temporary populations of the three tasks, the binary tournament selection method is used to select a preset number of individuals from the main task population, the first auxiliary task population and the second auxiliary task population as the main task mating parent, the first auxiliary task mating parent and the second auxiliary task mating parent, thereby improving the convergence of the population.

[0129] In the late evolution operation, the success rates of the three mating parents and the corresponding offspring populations are calculated respectively, the three transmission populations are determined based on the success rates, the final temporary population of the main task is constructed by fusing the main task population and the first auxiliary task transmission population and the second auxiliary task transmission population, the final temporary population of the first auxiliary task is constructed by fusing the first auxiliary task population and the second auxiliary task offspring population, and the final temporary population of the second auxiliary task is constructed by fusing the second auxiliary task population and the first auxiliary task offspring population, thereby guiding the migration of high-quality individuals across tasks, achieving effective knowledge transfer, and enhancing the optimization ability of the main task.

[0130] Although the preferred embodiments of the present application have been described, those skilled in the art can make further changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all the changes and modifications falling within the scope of the present application.

[0131] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. A constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks, characterized in that, Includes the following steps: Step 1: Obtain the constrained multi-objective vehicle scheduling problem and decompose it into three tasks, including the main task, the first auxiliary task, and the second auxiliary task. The main task employs a constrained multi-objective evolutionary algorithm based on dynamic constraint processing as the optimizer. The first auxiliary task uses a constrained multi-objective evolutionary algorithm based on dynamic changes in constraint boundaries as the optimizer; The second auxiliary task uses a multi-objective evolutionary algorithm based on ignoring constraints as the optimizer; Step two: Initialize the population and parameters for the three tasks respectively; Step 3: Determine whether the current iteration is in the early or late stage based on the number of evaluations and the stage transition parameters; Step 4: If the current iteration stage is in the early stage, perform the early evolution operation; if the current iteration stage is in the late stage, perform the late evolution operation. In the early evolutionary operation, temporary populations for three tasks are constructed respectively, and the corresponding optimizers are used to perform environmental selection on the three temporary populations and update the populations for the three tasks. In the later evolutionary operation, initial temporary populations for three tasks are constructed respectively, three transmission populations are determined, and three final temporary populations that merge the transmission populations and the original populations are constructed. The corresponding optimizers are used to perform environmental selection on the three final temporary populations and update the populations of the three tasks. Step 5: Return to Step 3 and iterate until the maximum number of iterations is reached. Output the main task population at this point as the final feasible non-dominated solution set for vehicle scheduling.

2. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 1, characterized in that, In step three, when the number of evaluations is less than the product of the stage transition parameter and the maximum number of evaluations, the current iteration stage is determined to be in the early stage; when the number of evaluations is greater than or equal to the product of the stage transition parameter and the maximum number of evaluations, the current iteration stage is determined to be in the late stage. In step four, the number of evaluations is updated at the end of each iteration.

3. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 1, characterized in that, In the early evolutionary operation, before constructing temporary populations for the three tasks, a preset number of individuals are randomly selected from the main task population as main task mates, and a preset number of individuals are selected from the first auxiliary task population and the second auxiliary task population as first auxiliary task mates and second auxiliary task mates respectively using a binary competitive selection method. The main task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population are generated based on the main task paired parent, the first auxiliary task paired parent, and the second auxiliary task paired parent, respectively.

4. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 3, characterized in that, The temporary population of the main task is constructed by merging the main task population, the main task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population. The temporary population of the first auxiliary task is constructed by merging the population of the first auxiliary task, the offspring population of the first auxiliary task, and the offspring population of the second auxiliary task; The temporary population of the second auxiliary task is constructed by merging the population of the second auxiliary task with the offspring population of the first auxiliary task and the offspring population of the second auxiliary task.

5. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 1, characterized in that, The constrained multi-objective evolutionary algorithm based on dynamically changing constraint boundaries includes: Calculate the constraint boundary of the current generation, and gradually decrease the constraint boundary of each generation; Based on the constraint boundary, the temporary population of the first auxiliary task is divided into two sets of individuals; Environmental selection is performed based on the state of the two types of individual sets, and the first auxiliary task population is updated.

6. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 5, characterized in that, The process of selecting an environment based on the states of the two types of individual sets and updating the first auxiliary task population includes: In the temporary population of the first auxiliary task, individuals with a total constraint violation level less than or equal to the constraint boundary are merged into the first population set, and individuals with a total constraint violation level greater than the constraint boundary are merged into the second population set. When the first set of individuals is empty, environmental selection is performed on the second set of individuals to update the first auxiliary task population; When the first set of individuals is not empty and is less than or equal to the population size, environmental selection is performed on the entire first set of individuals and part of the second set of individuals, and the first auxiliary task population is updated. When the first set of individuals is larger than the population size, environmental selection is performed on the first set of individuals to update the first auxiliary task population.

7. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 1, characterized in that, In the later evolutionary operation, before constructing the initial temporary populations for the three tasks, a binary competitive selection method is used to select a preset number of individuals from the main task population, the first auxiliary task population, and the second auxiliary task population as the main task pairing parents, the first auxiliary task pairing parents, and the second auxiliary task pairing parents, respectively. The main task offspring population, the first auxiliary task offspring population, and the second auxiliary task offspring population are generated based on the main task paired parent, the first auxiliary task paired parent, and the second auxiliary task paired parent, respectively.

8. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 7, characterized in that, The initial temporary population of the main task is constructed by merging the main task population and the main task offspring population; The initial temporary population of the first auxiliary task is constructed by merging the population of the first auxiliary task and the offspring population of the first auxiliary task; The initial temporary population of the second auxiliary task is constructed by fusing the population of the second auxiliary task and the offspring population of the second auxiliary task.

9. The constrained multi-objective vehicle scheduling method based on dynamic constraints and evolutionary multi-tasks as described in claim 7, characterized in that, In the later evolutionary operation, the success rates of the three paired parents and their corresponding offspring populations are calculated respectively, and the three transmission populations are determined based on the success rates. The final temporary population of the main task is constructed by merging the main task population with the first auxiliary task transmission population and the second auxiliary task transmission population; The final temporary population of the first auxiliary task is constructed by merging the population of the first auxiliary task and the offspring population of the second auxiliary task; The final temporary population of the second auxiliary task is constructed by merging the population of the second auxiliary task with the offspring population of the first auxiliary task.

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