Multi-strategy local search memetic method based on two-stage evolutionary framework

Abstract

The invention discloses a multi-strategy local search memetic method based on a two-stage evolutionary framework, and the method comprises the steps: obtaining a path of a vehicle, and enabling the path to serve as a population of an evolutionary algorithm; applying crossover and mutation operators to carry out global search on the population; mixing the offspring and the parent as a new parent population, performing neighborhood search on the new parent population by adopting a local search operator, and selecting an evolution stage based on the current consumed function evaluation times: adopting an exploration strategy in the initial stage of evolution, and exploring a wide decision space by using a niche radius; in the later stage of evolution, the population is developed more finely by using local search; the number of current function evaluation times is increased by the number of population sizes, population restarting is carried out according to the stage of the population, and a processed population is obtained; and obtaining an optimized vehicle path planning scheme according to the processed population. According to the method, the algorithm is effectively prevented from falling into local optimum, and the global search capability and environmental adaptability of the algorithm are enhanced.

Description

Technical Field

[0001] This invention belongs to the field of traffic planning technology, and in particular relates to a multi-strategy local search meme method based on a two-stage evolutionary framework. Background Technology

[0002] Typically, vehicles start from one location, pass through each location once, and finally return to the starting point. The goal of the vehicle routing problem is to find the shortest route for the vehicle. Most variations of the vehicle routing problem focus on finding a single optimal solution, regardless of the existence of multiple high-quality solutions. However, in practice, providing decision-makers with different optimal alternatives is equally important in order to: 1) increase the flexibility of the solution, as multiple solutions help decision-makers act quickly in emergency situations (e.g., traffic congestion due to urban road construction or flight cancellations due to severe weather); 2) enhance the carrying capacity of urban roads, as multiple solutions guide decision-makers to choose different routes, dispersing traffic flow, improving the overall capacity of urban roads, and achieving traffic load balance; 3) satisfy diverse decision preferences, as decision-makers often have unexpressed constraints or subjective preferences in addition to the explicit objective function, and the solution should be able to accommodate such implicit needs. These requirements have led to research on multimodal vehicle routing problems.

[0003] Multimodal problems are prevalent in real-world applications. For example, in vehicle routing problems, multiple shortest paths may exist, allowing decision-makers to select one from several equivalent optimal solutions based on their specific needs. However, research on multimodal problems in the field of discrete optimization is very limited.

[0004] Multimodal vehicle routing problem is an inevitable response to the complex transportation demands of the real world. It breaks through the theoretical boundaries of single-modal optimization, providing an indispensable theoretical framework and solution tools for solving practical routing problems involving multiple route coordination, complex environmental constraints, and the pursuit of comprehensive benefits. Ignoring the crucial dimension of route selection and exchange will cause the optimization results to lose practical application value and fail to meet the increasingly sophisticated decision-making needs in modern logistics, transportation planning, and smart cities. Assume there are multiple feasible paths of equal length: paths A, B, C, and D, which decision-makers can flexibly choose from. When obstacles appear, rendering some paths, such as paths B, C, and D, impassable, decision-makers need to be able to adjust the paths in a timely manner to avoid the obstacles. For single-modal vehicle routing problem optimization algorithms, this situation requires resolving the entire problem. However, multimodal vehicle routing problem optimization algorithms provide multiple alternative solutions, effectively supporting decision-makers to quickly make path selections. For example, when the original path is blocked, the decision-maker can immediately switch to other feasible alternative paths, such as path A. This situation, where paths need to be dynamically adjusted due to obstacles, is very common in the real world, making research on multimodal vehicle path planning problems particularly important.

[0005] Solving the multimodal vehicle routing problem relies on advancements in multimodal intelligent optimization algorithms. These methods aim to efficiently locate multiple global or local optima in the optimization problem, attracting widespread research interest in recent years. To address this issue, many researchers have proposed various mechanisms, including niche mechanisms, congestion distance mechanisms, archiving mechanisms, clustering mechanisms, index mechanisms, and machine learning mechanisms. These mechanisms aim to balance the exploration and exploitation capabilities of the algorithms to identify and maintain multiple optimal solutions within the decision space.

[0006] However, current multimodal optimization algorithms still face several key challenges. First, their convergence performance is often poor, limiting their application in practical problems. Unlike conventional intelligent optimization algorithms, multimodal optimization algorithms typically introduce active exploration mechanisms to cover more decision spaces, which may lead to a decrease in development capabilities, making it difficult to stably converge to the optimal solution within a limited number of function evaluations. Second, existing multimodal optimization problem test suites are generally limited to low-dimensional decision spaces. This is mainly due to the need for intuitive visualization of multimodal characteristics in the decision space. However, such low-dimensional problems are not complex enough for general intelligent optimization algorithms, and their true optimal solutions can often be efficiently obtained in a very small number of iterations, making it difficult to fully evaluate the multimodal processing capabilities of the algorithms. Third, the goal of requiring the algorithm to simultaneously obtain all global and local optimal solutions is inherently contradictory to the core goal of general intelligent optimization algorithms, which aims to efficiently obtain a single high-quality global optimal solution. Fourth, most current research in the multimodal field focuses on continuous domains, with very limited research on discrete multimodal problems. Summary of the Invention

[0007] To effectively solve the multimodal vehicle path planning problem, this application proposes a multi-strategy local search meme method. The algorithm employs a two-stage evolutionary framework, dividing the population evolution process into exploration and development phases. A population initialization mechanism based on a greedy algorithm is constructed, and an environment selection method based on niche selection and population maintenance mechanisms is designed to effectively improve the population distribution in the decision space, while maintaining good understandability and operability. To enhance the algorithm's convergence performance, this application introduces an adaptive local search operator based on incremental computation, significantly improving search efficiency. Simultaneously, the algorithm designs a convergence detection strategy: when the optimal solution of the current population shows no improvement after multiple consecutive iterations, the population is considered converged. At this point, the algorithm retains elite individuals and triggers a population restart strategy to maintain population diversity.

[0008] To achieve the above objectives, this application discloses a multi-strategy local meme search method based on a two-stage evolutionary framework, comprising the following steps: Obtain the vehicle's path, including the origin, all points along the way, and the destination; use the vehicle's path as the population for the evolutionary algorithm; A global search is performed on the population using crossover and mutation operators: Pop is generated based on the population size N, and the fitness of the population is calculated; if the count does not reach the maximum function evaluation number, the parent population is crossovered to generate a transition population, and the transition population is mutated to generate the offspring population. The offspring population is mixed with the parent population to form a new parent population. A local search operator is used to perform a neighborhood search on the new parent population, and the evolutionary stage is adaptively selected based on the number of function evaluations consumed so far: an exploration strategy is adopted in the early stage of evolution, that is, to explore a wider decision space by using the radius of the niche; in the later stage of evolution, a convergence strategy is adopted, that is, to develop the population more finely by using local search. Increment the current number of function evaluations (count) by the population size, restart the population based on its current stage, and obtain the processed population. Based on the processed population, an optimized vehicle routing scheme is obtained.

[0009] Furthermore, the environmental selection process dynamically adjusts the parameters and methods of niche selection according to the evolutionary progress: Perform niche calculations and local search operations on the new parent population; Based on the current evolutionary stage of the population, an individual selection strategy is applied: In the exploration phase, solutions based on diversity indicators are prioritized, tending to exhibit higher diversity, whereby the diversity indicator measures the degree of difference between individuals; in the convergence phase, a truncation selection method based on the objective value is adopted to maintain a fixed population size, that is, only a subset of individuals with the best objective value in the population are retained as parents of the next generation. Specifically, the individuals in the population are sorted in ascending order according to the objective function, and the top N individuals are selected, where N represents the population size.

[0010] Furthermore, path similarity metrics are used to quantify the differences between individuals within the population.

[0011] Furthermore, the 2-opt and 3-opt operators are combined and applied as local search operators, with the following specific steps: First, copy the current path to the improved path and initialize the iteration counter; Then, under the condition that there is room for improvement in the path and the maximum number of iterations has not been reached, a new path is generated by traversing all possible path index combinations through a double loop and performing a reversal operation on the path segment [i+1,j]. When the strength value exceeds 0.5 and the iteration limit has not been exceeded, the inner loop is entered to continuously call the 3-Opt optimization operator, improve the path and update the path state and count through the edge swapping strategy, until the termination condition is met, where i is the number of the first loop and j is the number of the second loop. The edge swapping strategy randomly selects three breakpoints in the path, divides the path into four segments A, B, C, and D, and constructs a new path by reversing some segments and adjusting the connection order between segments.

[0012] Furthermore, a dynamic convergence detection mechanism is used to enhance the algorithm's ability to escape local optima: when the population's optimal solution has not improved for K consecutive generations, the population is determined to be trapped in a local convergence state; specifically: During the exploration phase of population evolution, an elite retention strategy is adopted, in which elite individuals in the current population are stored in an elite pool. At the same time, a population initialization algorithm based on diversity enhancement is used to generate new individuals to replace individuals with lower fitness in order to maintain population diversity. During the development phase of population evolution, a local search strategy is adopted to conduct local searches for elite individuals in the current population.

[0013] Furthermore, a stagnation counter mechanism is used to monitor the improvement of the objective function to detect population evolution stagnation; when the stagnation count reaches a preset threshold, a differentiated population restart strategy is implemented based on the current evolutionary stage of the population: If the population is in the exploration phase, a completely new population is generated to achieve a full restart, thereby enhancing the global search capability; If the population is in the development stage, a local search is performed near the optimal solution to restart the process, thereby improving the efficiency of the local search and attempting to escape the local optimum. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a two-stage evolutionary framework, which uses crossover, mutation, and local search operators to explore the decision space and determines the stage selection by evaluating the overhead of a function. Figure 2 This is a diagram illustrating path similarity, where the marked paths represent identical paths, and the length of the marked path corresponds to the similarity score. Figure 3 The 2-opt operator generates a new solution by reversing the subpath between any two nodes. In contrast, the 3-opt operator selects three breakpoints, divides the path into four segments, and constructs a new path by reversing the selected segments and recombining the remaining parts. Figure 4 This diagram illustrates the population restart process. During the exploration phase, the restart operation retains a large number of elite individuals while introducing new individuals to maintain population diversity. In the development phase, only a small number of elite individuals are retained, and local searches are intensified to improve the algorithm's convergence accuracy. Detailed Implementation

[0015] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0016] Before introducing the embodiments of this application, some terms involved in this application will be explained.

[0017] 1. Multimodal Optimization: Multimodal intelligent optimization methods aim to identify multiple global or local optima in optimization problems. Based on the type of decision variables, multimodal optimization problems can be divided into continuous multimodal optimization problems and discrete multimodal optimization problems. In continuous multimodal optimization problems, there are multiple distinct solutions in the decision space (e.g., solution...). , and These parameters, when mapped to the target space, correspond to the same objective function value. For solving continuous optimization problems, the first or second derivative of the objective function is typically used to identify critical points and analyze their properties, thereby guiding the determination of the search direction and step size.

[0018] 2. Solution Space of Discrete Optimization Problems: These problems consist of a finite or countably infinite number of discrete decision variables. They typically fall into the NP-hard category, meaning that finding the exact global optimum in polynomial time is generally infeasible under computational complexity theory. Therefore, practical solutions primarily rely on heuristic methods or exact algorithms to obtain high-quality feasible solutions. However, the computational complexity of exact algorithms often increases exponentially with the problem's dimensionality, making them difficult to apply to large-scale problem instances. In contrast, population-based evolutionary algorithms exhibit significant advantages in handling discrete optimization problems. Their population members can directly manipulate the natural discrete representation of the problem's solutions, efficiently exploring the global and local solutions space through selection, crossover, and mutation operators, thus effectively handling the inherently complex structure of the discrete solution space.

[0019] 3. Intelligent Algorithms: In solving multimodal optimization problems, intelligent algorithms can be viewed as a process of exploring and developing the decision space. Generally, focusing too much on exploration will find more feasible solutions, but will also slow down the algorithm's convergence speed; while focusing too much on development can accelerate the population convergence speed, but is prone to getting trapped in local optima. Intelligent algorithms include niche algorithms, neighborhood-based genetic algorithms, etc.

[0020] While these methods demonstrate significant effectiveness in handling multimodal optimization problems, they still have some limitations. On the one hand, as the number of global optima in a multimodal optimization problem increases, the probability of these methods finding all global optima gradually decreases; on the other hand, for high-dimensional and highly complex problems, these fixed methods are almost ineffective.

[0021] To address the aforementioned limitations, this application proposes a multi-strategy local search meme method for solving the multimodal vehicle routing problem. This application aims to obtain all globally optimal solutions while balancing the exploration and exploitation capabilities of multimodal algorithms. In summary, the main contributions are as follows: This application combines a diversity-driven population initialization mechanism, adaptive niche technology, and a population restart strategy. These components collectively enhance the algorithm's global exploration capability. Simultaneously, the integration of specialized local search operators significantly enhances its local exploitation capability. Therefore, this application can effectively locate multiple global optima.

[0022] This application proposes a two-stage evolutionary framework, dividing the population evolution process into two phases: exploration and development. This division effectively improves the robustness of the algorithm in both global search and local optimization. Therefore, the algorithm in this application can simultaneously solve the vehicle routing problem and stably obtain high-quality approximate global optimal solutions in practical applications.

[0023] refer to Figure 1 The diagram shown illustrates the two-stage evolutionary framework of this application. This framework utilizes crossover, mutation, and local search operators to explore the decision space and determines the stage selection by evaluating the overhead of a function.

[0024] Obtaining multiple well-distributed optimal solutions is one of the core objectives of multimodal evolutionary algorithms. To achieve this, existing multimodal evolutionary algorithms typically embed crowding distance in the decision space into the environment selection strategy. For low-dimensional problems, such methods are effective in obtaining multiple equivalent optimal solutions. However, there is a certain conflict between the convergence of the objective space and the diversity of the decision space. Overemphasizing the diversity of the decision space can impair the convergence of high-dimensional problems. To better balance the convergence and diversity of the decision space, this application proposes a novel two-stage evolutionary mechanism. First, crossover and mutation operators are applied to perform a global search on the population; then, a local search operator is used for a neighborhood search. The framework adaptively selects the evolutionary stage based on the number of function evaluations consumed so far: in the early stage of evolution, an exploratory strategy is adopted, that is, exploring a wider decision space using a larger niche radius; in the later stage of evolution, a convergence strategy is adopted, that is, stopping the exploration of the decision space by the niche and instead using local search to develop the population more finely. This mechanism can effectively enhance the convergence of the evolutionary process, thereby obtaining as many optimal solutions as possible, and has the potential to be applied to other multimodal evolutionary algorithms. The entire pseudocode of this application is described in Algorithm 1.

[0025] Algorithm 1: Input: Population size N, maximum number of function evaluations (MaxFEs), maximum number of stagnations (MaxStagnation) Output: Optimized path and solution (pspf) 1: Pop ← Initialization(N) 2: Fitness ←CalFitness (Pop) 3: while count < MaxFEs do 4: Parent ← Crossover (Pop) 5: Off ← Mutation (Parent) 6: Pop ← [Off; Pop] 7: [Pop, count] ← Localsearch(Pop, Off, count) 8: Fitness ← CalFitness(Pop) 9: Stage ← StageJudgment(count, MaxFEs) 10: Pop ← EnvSelection(Pop, Stage) 11: count ← count + size(Pop) 12: Pop← PopulationRestart(Pop, Stage) 13: end while 14: pspf← Post-processing(Pop) First, a parent population Pop is generated based on the population size N. The fitness of the population is calculated; fitness is the path length of the vehicles, with shorter path lengths indicating better individual performance. If the count (count) has not reached the maximum function evaluation number (MEF), the populations are crossbred to create an interim population. This interim population is then mutated to generate offspring. The offspring population is mixed with the parent population to form a new parent population. The new parent population, offspring population, and count are used together for a local search to obtain an updated population. The count and the MEF are compared to determine the current stage. Based on the current stage, an environment selection is performed, and the count is incremented by the population size. The population is then restarted based on its current stage to obtain the processed population. Based on the processed population, an optimized vehicle path planning scheme is obtained. The maximum MEF is set according to the application scenario; in one embodiment, the maximum MEF is set to 50000 × C, where C represents the number of cities.

[0026] For multimodal vehicle path planning problems, the same objective function value may lead to different solutions. Therefore, if a convergence-first strategy is simply adopted to select a solution from the joint population, the algorithm will struggle to fully explore the decision space and is likely to get stuck in local optima. Clearly, it is desirable to retain better-performing solutions while maintaining population diversity in the decision space, but this is often conflicting. To address this issue, in one embodiment, this application first employs a niche selection mechanism to explore the decision space by constructing multiple niches to retain individuals with good diversity and remove similar individuals. By doing so, it ensures that the next generation retains the currently found optimal solution while maintaining population diversity. After removing similar solutions, individuals are selected based on path length and diversity. To better construct and improve niches, this application uses an adaptive method in the algorithm, dynamically adjusting the parameters and methods of niche selection according to the evolutionary process. The environment selection process is shown in Algorithm 2.

[0027] Algorithm 2: Environment Selection Input: Joint population Pop, population size N, diversity threshold DiversityThreshold, niche radius NichingRadius Output: Updated population Pop 1: Pop NichingSelection(Pop,,NichingRadius,DiversityThreshold,N) 2: Pop SortRows(Pop, N+2) 3: if Num(Pop) > N and count ε × MaxFEs then 4: elite ← Pop(1 : min(elitenum, size(Pop, 1))) 5: RemainingSolution←Pop(elitenum +l :end,:) 6: Remain←DiversityScores(RemainingSolution) 7: Selected ←RemainSortldx(1:min(N-elitenum, length(sortIdx)) 8: Pop ← [elite; Selected] 9: end if 10: if Num(Pop)>N and count >ε × MaxFEs then 11: Pop←sortrows(partial, N+2) 12: Pop ← partial(l:Popsize,:) 13: end if Specifically, the parent and offspring populations are first merged to form a joint population. Then, niche calculations and local search operations are performed on the joint population (lines 1-2). Based on the population's current evolutionary stage (exploration or development), an appropriate individual selection strategy is applied. During the exploration phase, solutions based on diversity indicators (i.e., the degree of difference between individuals) are preferentially retained, tending to exhibit higher diversity (lines 4-9). Conversely, during the convergence phase, a truncation selection method based on the objective value is used to maintain a fixed population size (lines 10-13).

[0028] In the local search mechanism, the algorithm's evolutionary stage is first determined based on the count. During the exploration phase, a lower search intensity is set, performing a 2-opt local search on individuals in the population. During the development phase, a higher search intensity is set, further executing a 3-opt local search based on the 2-opt operation. The algorithm first calculates the number of evaluations. This application integrates both 2-opt and 3-opt local search operators and uses incremental computation to evaluate the solution's performance. To keep the total number of operations consistent with the number of operations required for a complete evaluation, the number of operations is adjusted before each incremental computation. That is, in use When there are two paths in the matrix, for Perform the assignment so that (If a single evaluation uses two of the above assignments for comparative analysis), where This refers to the dimensions of the problem. Similarly, in use... When there are three paths in the matrix, for Perform the assignment so that ,in The dimensions of the problem.

[0029] refer to Figure 2 The diagram illustrates path similarity, where marked paths represent identical paths, and the length of the marked path corresponds to the similarity score.

[0030] The path similarity score metric primarily measures the maximum similarity between the algorithm's output solution sets. It evaluates the similarity between paths by calculating the Hamming distance (i.e., the number of different elements at the same position). A higher value indicates a greater number of different paths, meaning a lower maximum similarity. The formula can be expressed as: in and There are two paths of length N. and Let k and k represent the two elements arranged at position k. It is an indicator function: .

[0031] To effectively quantify the differences among individuals within a population, this application constructs a path similarity index. This index assesses the similarity between solutions by counting the number of differing segments in the path sequences between individuals. Path a represents the optimal solution for the current population, while paths b, c, and d represent examples of other individuals in the population. In the figure, paths 1 and 2 share the same starting point, while paths 1 and 3 share the same ending point.

[0032] Local search is an optimization method based on neighborhood structure, which improves the quality of solutions by iteratively searching for better solutions within the neighborhood of the current solution. (Reference) Figure 3 In the study of the Vehicle Routing Problem (TSP), 2-opt and 3-opt are the most widely used local search operators. The 2-opt operation splits the current path into two independent segments by removing two non-adjacent edges, and then reconnects the segments in different ways to construct a new feasible path. Similarly, the 3-opt operation involves removing and replacing three edges to generate a new path.

[0033] The core mechanism of the local search algorithm lies in defining the neighborhood generation rules and neighborhood selection strategy for the solution. The 2-opt operator generates a new path by reversing the order of sub-paths between any two nodes in the path; the 3-opt operator selects three breakpoints to divide the path into four segments A, B, C, and D, and constructs a new path by reversing some segments and adjusting the connection order between segments. To improve the algorithm performance, in one embodiment, this application integrates the 2-opt and 3-opt operators, the specific implementation of which is detailed in Algorithm 3.

[0034] Input: Population size N, elite population Pop, search intensity intensity, number of evaluations count, path length matrix cost Output: Updated elite population Pop, updated count of ratings 1: iteration ← 0 2: improved ← true 3: maxIteration ← N*intensity 4: while improved and iterations < maxIterations do 5: improved ← false 6: for route Pop do 7: [route, count, improved] ←2opt(route, N, cost, count, MaxFEs) 8: iteration ← iteration +1 9: end for 10: end while 11: if intensity >0.5 and iteration < maxIteration then 12: improved ← true 13: while improved and iteration < maxIteration do 14: improved ← false 15: for route Pop do 16: [route, count, improved] ← 3opt(route, N, cost, count,MaxFEs) 17: iterations ← iterations +l 18: end for 19: end while 20: end if First, copy the current path to the improved path and initialize the iteration counter. Then, under the condition that the path still has room for improvement and the maximum number of iterations has not been reached, traverse all possible path index combinations through a nested loop, perform a reversal operation on the path segment [i+1,j] to generate a new path. When the strength value exceeds 0.5 and the iteration limit has not been exceeded, enter the inner loop to continuously call the 3-Opt optimization operator, improve the path and update the path state and count through the edge swap strategy, until the termination condition is met.

[0035] The local search operator design proposed in this application represents an innovative integration of traditional 2-opt and 3-opt strategies, rather than a simple superposition. Existing local search methods are typically limited to the application of a single search operator. While these methods are simple to implement, they often require an excessive number of objective function evaluations when exploring large-scale decision spaces. Although the 3-opt operator has higher computational complexity, in specific problem instances, it can discover high-quality solutions that the 2-opt operator cannot achieve with relatively fewer evaluations.

[0036] Based on the above observations, this application proposes a dynamically adaptive hybrid local search mechanism: when the algorithm detects a high-intensity search phase, the system selectively performs a 3-opt local search on most individuals in the population; while in the normal search intensity phase, it mainly relies on the computationally more efficient 2-opt operator for local optimization. This adaptive operator selection strategy based on search intensity significantly improves the balance between solution space exploration and development, enhancing population diversity while ensuring search efficiency, thus effectively avoiding premature convergence. Experimental results show that this hybrid local search strategy exhibits significant advantages in solving multimodal vehicle path optimization problems.

[0037] When applying MMEAs to solve the MMTSP, the population is prone to premature convergence. In one embodiment, to enhance the algorithm's ability to escape local optima, a dynamic convergence detection mechanism is designed. When the optimal solution of the population does not improve for K consecutive generations, the population is determined to be trapped in a local convergence state. During the exploration phase of population evolution, an elite retention strategy is adopted, storing elite individuals in the current population into an elite pool. Simultaneously, a population initialization algorithm based on diversity enhancement is used to generate new individuals, replacing those with lower fitness to maintain population diversity. This strategy ensures the inheritance of the current optimal solution while effectively expanding the search space by introducing exploratory new solutions, balancing the algorithm's development and exploration capabilities. During the development phase of population evolution, a local search strategy is adopted, performing local searches on the elite individuals in the current population. This strategy helps the population escape local optima by conducting detailed local searches on elite individuals, thereby improving the overall optimization effect.

[0038] To address the potential population stagnation issue during evolution, this application proposes a stagnation counter mechanism. This mechanism detects population stagnation by monitoring the improvement of the objective function. When the stagnation count reaches a preset threshold, the system implements differentiated population restart strategies based on the current evolutionary stage of the population. If the population is in the exploration stage, a complete restart is achieved by generating a completely new population to enhance global search capabilities. If the population is in the development stage, a restart is achieved by performing a local search near the optimal solution to improve local search efficiency and attempt to escape local optima.

[0039] refer to Figure 4 The diagram illustrates the population restart process. During the exploration phase, the restart operation retains a large number of elite individuals while introducing new individuals to maintain population diversity. In the development phase, only a small number of elite individuals are retained, and local searches are intensified to improve the algorithm's convergence accuracy.

[0040] Figure 4 This demonstrates the varying effectiveness of population restart strategies at different evolutionary stages. In the exploration phase, to fully explore the solution space and acquire diversity information, a strategy of retaining most elite solutions is adopted, and a greedy algorithm is used for population initialization and restart. This mechanism randomly generates feasible solutions, aiming to promote a broad search of the solution space. Conversely, in the development phase, the population objective shifts to accelerating convergence. At this point, a local search restart mechanism is adopted, retaining a small number of elite solutions, using existing information to guide the population to focus on the optimal solution region.

[0041] In the exploration phase of population evolution, to broaden the exploration of the decision space, the algorithm employs a diversified path generation method based on path difference, thus preserving most of the evolutionary information. Based on this, by integrating the population initialization mechanism of the greedy algorithm, a large number of representative new solutions can be efficiently generated, greatly expanding the population's understanding of the decision space and facilitating a more comprehensive search for optimal solutions. During the development phase, this algorithm, based on the fixed optimal path solutions, strives to explore as many different path planning methods as possible. To this end, a local search operator combining 2-opt and 3-opt operators is designed. Unlike previous approaches relying solely on a single operator, this operator can dynamically adjust the local search intensity according to the population evolution stage, increasing the proportion and number of path operations, thereby achieving more effective convergence. Furthermore, the local search only updates individuals when there is anticipated room for improvement, significantly reducing unnecessary computational overhead.

[0042] To evaluate the performance of this application on the multimodal vehicle routing problem, six effective evolutionary algorithms were selected as benchmark comparison algorithms, including: Genetic Algorithm (GA), Crowd Distance-Based Genetic Algorithm (CGA), Fitness Sharing-Based Genetic Algorithm (ShGA), Niche Scale Adaptive Genetic Algorithm (NAGA), Niche Genetic Algorithm (NGA), and Niche Memory Algorithm (NMA). Specifically, GA serves as the basic algorithm. CGA and ShGA are variants of GA, respectively maintaining population diversity by introducing crowd distance and fitness sharing mechanisms. NAGA further integrates a niche scale adaptive mechanism and a dynamic peak identification mechanism on the basis of ShGA. NMA and NGA are algorithms specifically designed for solving the multimodal vehicle routing problem.

[0043] To ensure fairness in the algorithm comparison, the population size N for all algorithms was set to 150. The maximum number of function evaluations was dynamically adjusted according to the type of test problem, set to 60,000 for the first 12 test problems and 1,200,000 for the last 13. Furthermore, all evolutionary algorithms used simulated binary crossover and polynomial mutation algorithms to generate offspring. The specific parameters of each comparison algorithm were set according to the original literature. For this application, the hyperparameter for algorithm stage transitions was set to 0.4; that is, when the number of evaluations was less than or equal to 0.4 * MaxFEs, the algorithm was in the exploration stage; when the number of evaluations was greater than 0.4 * MaxFES, the algorithm was in the development stage.

[0044] To comprehensively evaluate the performance of this application, two benchmark sets were used: the MSTSP benchmark set and the TSPLIB standard benchmark set. The MSTSP benchmark set contains 25 problem instances, further divided into three categories: simple MSTSP, geometrically structured MSTSP, and composite MSTSP. Simultaneously, to examine the algorithm's performance in solving single-modal vehicle path planning problems, five TSP problem instances were selected from the TSPLIB standard benchmark set for evaluation.

[0045] For multimodal optimization problems, two main evaluation metrics are used: And DI, respectively, are as follows: index: It is a combined metric of precision (P) and recall (R), used to evaluate the quality of the obtained solution; ; Where TP is the number of optimal solutions obtained by the algorithm, and FP is the number of non-optimal solutions obtained by the algorithm; ; Where FN is the number of optimal solutions missed by the algorithm. In fact, the sum of TP and FN equals the total number of optimal solutions in the benchmark set. Based on the values ​​of P and R, The calculation is as follows: In the evaluation indicators, The parameter is typically set to 1, which gives equal weight to precision (P) and recall (R). However, in scenarios where there are a large number of optimal solutions in the test cases, identifying representative solutions is more critical than exhaustively enumerating all solutions. Based on this consideration, this application will... The value was set to 0.3 to enhance the weight of precision in the overall evaluation, thereby more accurately reflecting the representative quality of the obtained solutions. Furthermore, the three evaluation metrics employed—precision (P), recall (R), and the overall metric (…)—… — Its values ​​are all real numbers in the interval [0, 1]. In particular, there are two boundary cases: (1) When the algorithm identifies all expected solutions under ideal conditions, The index reaches its maximum value of 1; (2) when the algorithm fails to identify any valid solution, The indicator reached its minimum value of 0.

[0046] Diversity Metric: The diversity metric (DI) is another important indicator for evaluating algorithm performance. It is determined when all algorithms fail to find the desired solution. All values ​​are zero. At this point, DI can be used to further differentiate the performance of different algorithms. Drawing inspiration from evolutionary multi-objective optimization, DI aims to measure the diversity of the solution set ultimately provided by the algorithm, specifically reflecting the degree to which the solution set converges to different optimal solutions in the true optimal solution set (P). This metric is defined based on the average maximum similarity between the obtained solution set and individuals in the reference set (P), and its calculation formula is as follows: in, For the true solution set, The solution set obtained by the algorithm For arrangement with solution set The maximum shared distance among all permutations is calculated using the following formula: in, and They represent and The set of edges; express and The intersection; express The number of edges in the path. The shared distance metric applies to the set of edges in the path, not the absolute node positions. Therefore, solutions with different absolute node orders but the same set of visited edges will be identified as the same solution.

[0047] To evaluate the algorithm's performance in solving the multimodal vehicle routing problem, experiments were conducted on the standard MSTSP benchmark set. This benchmark set contains 25 test cases, and the experimental results are summarized below.

[0048] : The metric is used to measure the quality of the solution, with higher scores corresponding to better solutions. The proposed algorithm was compared with six comparative algorithms on 25 MSTSP instances. Experimental comparison of the metrics. As shown in Table 1, the experimental results confirm that this application achieves significantly better performance on all 25 test questions. Results. In contrast, the six comparative algorithms performed poorly on complex MSTSP instances, particularly struggling with large-scale urban MSTSPs. This may be attributed to the excessive number of evaluations consumed during the exploration of the decision space, making it difficult for the algorithms to converge to the optimal solution. Conversely, the two-stage framework adopted in this application effectively ensures a balance between exploration and development.

[0049] DI: The DI metric is used to evaluate the diversity of solutions; a higher DI value indicates better solution diversity. As shown in Table 1, this application and CGA exhibit relatively good diversity performance on the overall MSTSP instance set. For simple and geometric MSTSP instances, GA, NMA, CGA, NGA, and NAGA show good diversity performance; however, these algorithms show a significant decrease in diversity performance on complex MSTSP instances. In contrast, ShGA and NAGA have unsatisfactory diversity results on all problem instances. Overall, the compared algorithms achieve better diversity results on simple MSTSP instances with smaller decision variable sizes. Notably, this application demonstrates superior overall performance across all evaluation metrics.

[0050] Table 1. Average rank for each algorithm category on the MSTSP test suite: Execution Time: Execution time (ET) is another key metric for evaluating algorithm performance. For NP-hard problems, computational costs increase dramatically with city size. Specifically, this application demonstrates robust performance across all problem types, without exhibiting the significant runtime increase seen in CGA on simpleMSTSP and CompositeMMTSP instances. For MSTSP1 (9 cities), the average execution time (in seconds), ranked in ascending order, is: CGA (0.61), this application (0.67), ShGA (0.81), GA (1.07), NMGA (1.19). For the larger MSTSP25 (66 cities), the execution time ranking changes: this application (28.33), GA (44.32), ShGA (82.11), CGA (134.20), NMGA (218.43). This observation indicates that the execution time of NMGA, CGA, and ShGA increases rapidly with city size. In contrast, the execution time of this application is less affected by the increase in city size.

[0051] Solving the Vehicle Routing Problem (TSP) using multimodal optimization algorithms faces a key challenge: it is often impossible to determine in advance whether the target TSP instance possesses significant multimodal properties. If the target problem is inherently unimodal, using multimodal evolutionary algorithms may lead to decreased solution efficiency or slower convergence. However, this challenge can be effectively addressed through the following strategies: 1) Optimality Guarantee: Well-designed multimodal algorithms, with their powerful global exploration and local exploitation capabilities, have the potential to asymptotically converge to the global optimum regardless of whether the problem's modality is determined. 2) Feasibility Guarantee: Even if precise convergence to the global optimum is not achieved, the multimodal mechanism can facilitate the discovery of multiple high-quality local optima. This provides valuable suboptimal alternatives for practical applications, thereby enhancing the algorithm's robustness and applicability.

[0052] To evaluate the performance of the algorithm in solving the single-modal vehicle routing problem (TSP), this application uses the TSPLIB standard test set for experimental verification. TSPLIB, a well-known TSP benchmark library, contains 112 TSP instances. In the experiments, we applied three algorithms—Genetic Algorithm (GA), Compact Genetic Algorithm (CGA), and Adaptive Neighborhood Local Search (as described in this application)—to solve eight of the TSP instances. The maximum number of function evaluations (MaxFEs) for each algorithm was uniformly set to 50000 × N (where N is the number of cities).

[0053] First, we evaluate the ability of each algorithm to locate the global optimum. Table 2 summarizes the shortest path lengths obtained by each algorithm on each instance, with the optimal results marked in bold. As shown in the table, this application obtained the optimal path length on all test instances, significantly outperforming GA and CGA.

[0054] Table 2 shows the shortest path among all the comparison algorithms on different test sets: As shown in Tables 1 and 2, this application exhibits excellent performance in the multimodal domain. Outstanding performance in terms of metrics, ranking among the top in all grouped test questions. The proposed algorithm achieves the highest values ​​across all tests, ranking first in all 31 test problems. Furthermore, it comprehensively outperforms other algorithms in the Derivative Inference (DI) metric, achieving the best ranking across all test problems. In single-modal tests, the proposed algorithm also demonstrates higher stability, converging more reliably to an acceptable solution, and its overall performance surpasses other comparative algorithms. The comprehensive experimental results demonstrate that this proposed algorithm is a competitive multimodal evolutionary algorithm suitable for solving both multimodal and single-modal vehicle path planning problems.

[0055] To more effectively monitor the population optimization process, this application integrates a dual evaluation mechanism for the quality of the optimal solution and the path difference. The specific implementation process is as follows: The algorithm first saves the best individual in the current population and its solution as an evaluation benchmark. Subsequently, after each iteration, the system checks whether the overall optimal solution of the population has improved. If the optimal solution fails to achieve a breakthrough, the degree of difference between the individuals in the optimal solution set and the previously saved individuals is further evaluated. When there is no significant difference between the two, the system determines that the population evolution has stagnated and updates the stopping counter. This refined evolutionary state detection mechanism can achieve a dynamic balance between convergence and diversity during the optimization process, effectively preventing the algorithm from getting trapped in local optima while maintaining the exploratory vitality of the population. This significantly enhances the algorithm's global search capability and environmental adaptability, providing more reliable technical support for solving complex combinatorial optimization problems.

[0056] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0057] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component, even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although a particular feature of this disclosure has been disclosed with respect to only one of several implementations, such feature may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0058] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0059] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A multi-strategy local search memetic method based on a two-phase evolutionary framework, characterized in that, The method comprises the following steps: acquiring a path of a vehicle, including a starting point, all passing points and a terminal point; and taking the path of the vehicle as a population of an evolutionary algorithm; applying a crossover and mutation operator to implement a global search on the population: generating a parent population Pop according to the population size N, calculating the fitness of the population, if the count count has not reached the maximum number of function evaluations, crossing the parent population to generate a transition population, and mutating the transition population to generate an offspring population; mixing the offspring population and the parent population as a new parent population, performing a neighborhood search on the new parent population by using a local search operator, and adaptively selecting an evolutionary stage based on the current consumed number of function evaluations count: in the early stage of evolution, an exploration strategy is used, that is, a niche radius is used to explore a wider decision space; in the later stage of evolution, a convergence strategy is used, that is, a local search is used to develop the population more finely; increasing the current consumed number of function evaluations count by the population size, and performing population restart according to the stage of the population to obtain a processed population; obtaining an optimized vehicle path planning scheme according to the processed population.

2. The multi-strategy local search memetic method based on a two-stage evolutionary framework according to claim 1, characterized in that, The environment selection process dynamically adjusts the parameters and methods of niche selection according to the evolution process, specifically including: performing niche calculation and local search operations on the new parent population; applying an individual selection strategy according to the current evolutionary stage of the population: in the exploration stage, solutions based on a diversity index are preferentially retained, and solutions showing diversity are preferred, the diversity index measuring the difference between individuals; in the convergence stage, a truncation selection method based on the target value is used to maintain a fixed population size, that is, only a part of individuals with the optimal target value in the population are retained as the parents of the next generation, and the specific implementation method is to sort the individuals in the population in ascending order according to the target function, and select the first N individuals, N representing the population size.

3. The multi-strategy local search memetic method based on a two-stage evolutionary framework according to claim 1, wherein, A path similarity index is used to quantify the difference between individuals in the population.

4. The multi-strategy local search memetic method based on a two-stage evolutionary framework according to claim 1, wherein, The 2-opt and 3-opt operators are fused as a local search operator, and the specific steps are as follows: first, copy the current path to the improved path, and initialize the iteration counter; then, under the condition that the path has improvement space and the maximum number of iterations has not been reached, traverse all possible path index combinations through double loops, perform a reverse operation on the path segment [i+1, j] to generate a new path, when the strength value exceeds 0.5 and the iteration does not exceed the limit, enter the inner loop to continuously call the 3-Opt optimization operator, improve the path by using an edge exchange strategy, and update the path state and count until the termination condition is met, where i is the number of the first layer loop, and j is the number of the second layer loop; the edge exchange strategy randomly selects three breakpoints in the path, divides the path into four segments A, B, C and D, and constructs a new path by reversing part of the segments and adjusting the connection order between the segments.

5. The multi-strategy local search memetic method based on a two-stage evolutionary framework according to claim 1, wherein, A dynamic convergence detection mechanism is used to enhance the ability of the algorithm to escape from a local optimal solution: when the optimal solution of the population has not been improved for K generations in succession, it is determined that the population is in a local convergence state; specifically: In the exploration stage of population evolution, the elite individuals in the current population are stored in the elite library by using the elite preservation strategy, and new individuals are generated by using the population initialization algorithm based on diversity enhancement to replace the individuals with lower fitness to maintain the diversity of the population; In the development stage of population evolution, the local search strategy is used to perform local search on the elite individuals in the current population.

6. The multi-strategy local search memetic method based on a two-stage evolutionary framework according to claim 1, wherein, The stagnation counter mechanism is used to monitor the improvement of the objective function to detect the stagnation of population evolution; when the stagnation count reaches the preset threshold, the differentiated population restart strategy is implemented according to the evolution stage of the current population: If the population is in the exploration stage, a completely new population is generated to achieve complete restart to enhance the global search ability; If the population is in the development stage, local search is performed around the optimal solution to achieve restart to improve the local search efficiency and try to jump out of the local optimum.

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