Vehicle path planning problem optimization method and system for landscape smoothing

Abstract

The invention discloses a vehicle path planning problem optimization method and system for landscape smoothing, and belongs to the technical field of combinatorial optimization algorithms, and the method comprises the steps: randomly generating an initial population for a vehicle path planning problem, constructing a toy problem, and carrying out the optimization of the vehicle path planning problem; the toy problem and the vehicle path planning problem are equal in scale, and the fitness landscape of the solution space has a single-peak characteristic; constructing a fitness function, and evaluating each individual in the population through the fitness function to obtain a fitness value of each individual; executing operation of a selection operator, a crossover operator and a mutation operator to generate a next generation population; and the fitness function design and evaluation and genetic operator operation are repeatedly executed until a preset termination condition is met, and an individual with the minimum original problem objective function value in the evolution process is output to serve as an optimal solution of the vehicle path planning problem. According to the method, local optimum can be jumped out, global exploration and local development are balanced, the solving quality and stability can be improved, and the method has applicability in vehicle path planning.

Description

Technical Field

[0001] This invention belongs to the field of combinatorial optimization technology, specifically relating to an optimization method and system for vehicle path planning problems in landscape smoothing. Background Technology

[0002] The Vehicle Routing Problem (VRP) is a classic NP-hard problem in operations research and combinatorial optimization. Its goal is to plan the optimal routes for a group of vehicles, minimizing total distance, cost, or efficiency while satisfying constraints such as vehicle capacity, customer demand, and time windows. Genetic Algorithms (GA), as a mature metaheuristic algorithm, are widely used to solve the Capacitated Vehicle Routing Problem (CVRP). However, standard GAs face several technical challenges when dealing with complex CVRP instances: the fitness landscape of the CVRP solution space is typically very rugged, with numerous local optima; standard GAs suffer from decreased population diversity in the later stages of the search, easily converging prematurely to a non-globally optimal local solution, resulting in low solution quality; and while the algorithm may converge quickly in the early stages, the slow improvement in solution quality in later stages leads to low overall search efficiency, making it difficult to find high-quality solutions within a limited time. The settings of key parameters such as crossover probability and mutation probability have a significant impact on algorithm performance. However, static parameter settings cannot adapt to the dynamic needs of the algorithm in different search stages, such as global exploration and local development. Therefore, in summary, existing genetic algorithms are prone to getting trapped in local optima, have relatively slow convergence speeds, and require further optimization to improve the stability of solution quality when solving vehicle path problems. Summary of the Invention

[0003] This invention provides an optimization method and system for the vehicle path planning problem in landscape smoothing, aiming to solve the problems of existing genetic algorithms in solving vehicle path problems, such as easy getting trapped in local optima, relatively slow convergence speed, and the need for further optimization of the stability of solution quality.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides an optimization method for vehicle path planning in landscape smoothing, comprising the following steps: S1. Randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem. A feasible solution is a complete set of vehicle routes. S2. Construct a toy problem based on the initial population. The toy problem and the vehicle path planning problem have the same size and the fitness landscape of the solution space has a unimodal characteristic. Construct a fitness function to evaluate each individual in the population and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty. S3. Based on the fitness value of each individual, perform the selection operator, crossover operator, and mutation operator operations in sequence to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. S4. Repeat S2 and S3 until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

[0005] In some implementations, in S1, the fitness value of each individual in the population is calculated using the following formula: ; in, This represents the fitness value of an individual. The cost of the original problem is the total distance traveled by the vehicle corresponding to the individual. These are the weighting coefficients for the toy model. The cost of the toy problem, For diversity weighting coefficients, For diverse rewards, For the penalty weighting coefficient, To constrain penalty items.

[0006] In some implementations, the toy problem is constructed in S2 in the following ways: Based on the solution with the smaller objective function value of the original problem in the current population of the vehicle routing problem, the distribution of fitness values ​​corresponding to each feasible solution in the solution space is adjusted so that there is only one optimal fitness value in the solution space of the toy problem, and the solution corresponding to the optimal fitness value is the solution with the smaller objective function value of the original problem.

[0007] In some implementations, in S2, the constraint penalty term includes an Euclidean distance penalty term, which is used to impose a penalty on individuals that violate distance constraints or vehicle load constraints; violating distance constraints means that the travel distance of the vehicle path corresponding to the individual exceeds a preset distance threshold, and violating vehicle load constraints means that the total load of the vehicle path corresponding to the individual exceeds the vehicle's rated capacity.

[0008] In some implementations, the operation of selecting the operator in S3 specifically includes: Let the first The generation population is: ; in, To determine the population size, a tournament selection method is used to select parent individuals from the population, with each selection made from the population... Randomly selected Individuals constitute the candidate set And select the individual with the best fitness value as the parent individual: ; in For the size of the candidate set, For the parent generation.

[0009] Furthermore, in S3, the crossover operator operates as follows: The parent individuals obtained through the selection operator are crossovered according to a preset probability. Pairing is performed, and a crossover operation is executed on the successfully paired parent individuals. The child individuals are generated by reorganizing the customer access order or sub-path structure in the path encoding of the parent individuals using the following formula: ; in, , For paired parent individuals, , This is the generated child individual; if the crossover operation is not triggered, the child individual directly inherits the structure of the corresponding parent individual.

[0010] In some implementations, in S3, the convergence state of the population is determined by a population diversity index, which is calculated using the following formula: ; in, For the first Population diversity indicators of the generation, For population size, and The first The first generation of the population The and the first Individual, It indicates the degree of difference between individuals.

[0011] Furthermore, in S3, the mutation probability is dynamically adjusted as follows: Preset diversity threshold Stasis detection window length and minimum improvement threshold , No. The optimal fitness value of the generation is , No. The optimal fitness value of the generation is When the following conditions are met: ; Adjust the mutation probability to the increased mutation probability. Otherwise, adjust the mutation probability to the reduced mutation probability. ,and .

[0012] Furthermore, in S3, the degree of difference between individuals is calculated based on the distance of the path encoding or the difference of the edge set; the preset difference characteristic is that the average degree of difference between an individual and all other individuals in the population is greater than a preset difference threshold. The average degree of difference is calculated based on the edit distance or structural difference of the solution encoding, and the diversity reward is proportional to the average degree of difference.

[0013] This invention also provides an optimization system for the landscape-smoothed vehicle path planning problem, used to implement the aforementioned optimization method for the landscape-smoothed vehicle path planning problem. The system includes an initialization module, a fitness function design and evaluation module, a genetic operator operation module, and an iteration and termination module, wherein: The initialization module is used to: randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem, and a feasible solution is a complete set of vehicle paths. The fitness function design and evaluation module is used to: construct a toy problem based on the initial population, where the toy problem and the vehicle path planning problem are of equal size and the fitness landscape of the solution space exhibits a unimodal characteristic; construct a fitness function, evaluate each individual in the population through the fitness function, and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty terms. The genetic operator operation module is used to: based on the fitness value of each individual, sequentially execute the selection operator, crossover operator, and mutation operator to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. The iteration and termination module is used to repeatedly execute the fitness function design and evaluation module and the genetic operator operation module until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

[0014] Compared with existing technologies, the present invention provides an optimization method and system for vehicle path planning in landscape smoothing, which has the following advantages: This invention presents an optimization method for vehicle path planning in a landscape smoothing environment. By employing solution space smoothing techniques, it reduces the ruggedness of the optimized landscape, decreases the number of local optimum traps, and significantly improves the probability of the algorithm finding a globally optimal solution or a high-quality solution. This invention utilizes the synergistic effect of adaptive parameter adjustment and diversity maintenance strategies, making the algorithm more intelligent and robust during the search process. Experimental results demonstrate that the LSADGA (Landscape Smoothing Adaptive Genetic Algorithm) used in this method exhibits advantages over the original GA genetic algorithm in terms of final cost, convergence speed, and result stability.

[0015] On the other hand, the vehicle path planning optimization system of the present invention for landscape smoothing decomposes the complex optimization process into modular improvement points. The idea is clear, easy to implement, and can be conveniently applied to different types of CVRP and other combinatorial optimization problems, thus having certain applicability. Attached Figure Description

[0016] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0017] Figure 1 This is a flowchart illustrating an optimization method for vehicle path planning in landscape smoothing according to the present invention. Figure 2 This is a flowchart illustrating the Landscape Smoothing Adaptive Genetic Algorithm (LSADGA) in the landscape smoothing vehicle path planning problem optimization method of the present invention. Figure 3 This is the optimal solution to the original CVRP problem in the landscape smoothing vehicle path planning optimization method of the present invention; Figure 4 In an embodiment of the vehicle path planning optimization method for landscape smoothing of the present invention, a standardized circular layout diagram is formed through heuristic spatial transformation; Figure 5 This diagram illustrates a comparison of the convergence performance of the landscape smoothing vehicle path planning optimization method of the present invention with that of the traditional genetic algorithm in the CVRP test. Figure 6This is a schematic diagram illustrating the experimental results of the impact of different diversity weight values ​​on the final cost of the algorithm in an embodiment of the vehicle path planning problem optimization method for landscape smoothing according to the present invention. Figure 7 This is a schematic diagram illustrating the experimental results of the impact of different constraint penalty weight values ​​on the algorithm performance in an embodiment of the vehicle path planning problem optimization method for landscape smoothing according to the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0021] It should be noted that the apparatus and methods disclosed in the embodiments herein can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments herein. In this regard, each block in a flowchart or block diagram may represent a module, program, or part of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system to perform the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0022] In addition, the functional modules in the various embodiments of this article can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0023] How can we provide an efficient optimization algorithm that can escape local optima, balance global exploration with local exploitation, and improve the quality and stability of the solution?

[0024] like Figure 1 As shown, the present invention provides an optimization method for vehicle path planning in landscape smoothing, comprising the following steps: S1. Randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem. A feasible solution is a complete set of vehicle routes. S2. Construct a toy problem based on the initial population. The toy problem and the vehicle path planning problem have the same size and the fitness landscape of the solution space has a unimodal characteristic. Construct a fitness function to evaluate each individual in the population and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty. S3. Based on the fitness value of each individual, perform the selection operator, crossover operator, and mutation operator operations in sequence to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. S4. Repeat S2 and S3 until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

[0025] This invention provides an optimization method for a vehicle path planning problem with smoothed landscape. It first generates an initial population containing complete feasible solutions for vehicle paths, providing a solution space foundation for the algorithm's search. Then, it constructs a toy problem with the same size as the original problem but exhibiting a unimodal fitness landscape. This unimodal characteristic significantly reduces the number of local optima and smooths the landscape. Combined with a fitness function weighted by the cost of the original problem, the cost of the toy problem, diversity rewards, and constraint penalties, this effectively guides the algorithm to focus on high-quality topologies in the early stages of the search, avoiding premature entrapment in local optima based on path length. The constraint penalties ensure solution feasibility, while the diversity rewards provide a technical basis for maintaining population vitality. In the genetic operator operations, dynamically adjusting the mutation probability to adapt to the population's convergence state and the solution's improvement stagnation state achieves a dynamic balance between global exploration and local development. The invention's design of providing diversity rewards to individuals with preset differential characteristics prevents genetic homogenization in the later stages of the population and enhances the algorithm's ability to escape local optima. Through iterative optimization until the termination condition is met, the individual with the smallest objective function value in the original problem is output, ensuring the high quality of the optimization results. This invention significantly improves the search efficiency, solution quality, and stability of the algorithm through the synergistic effect of solution space smoothing, adaptive parameter adjustment, and population diversity maintenance, making it suitable for practical vehicle path planning scenarios.

[0026] Furthermore, this invention transforms fitness evaluation from a general description into a precise and quantifiable operation through the calculation of fitness values, improving the consistency of algorithm execution. In the toy problem, the fitness value distribution is adjusted based on solutions with smaller objective function values ​​in the current population, ensuring that the unimodal characteristic of the toy problem accurately points to the region of high-quality solutions, and strengthening the guiding role of solution space smoothing on the algorithm. The constraint penalty term and constraint violation judgment criteria of this invention make constraint control more targeted, effectively reducing the generation of invalid solutions and ensuring that the optimization results meet the distance and vehicle load requirements in practical applications.

[0027] This invention employs a tournament-style selection process and a crossover operator. The selection operator statistically preserves superior path structures and maintains population diversity, while the crossover operator expands the search space by reorganizing the customer access order or sub-path structure in the parent path encoding, thereby improving the quality and diversity of the offspring population. Furthermore, the quantitative criteria for determining the population convergence state make the adjustment of mutation probabilities more operable, and the diversity reward ensures precise and controllable maintenance of population diversity, balancing the algorithm's exploration capability and development efficiency, and improving the algorithm's robustness and stability.

[0028] This invention presents a landscape smoothing optimization method for the vehicle path planning problem (CVRP). It proposes a novel Landscape Smoothing Adaptive Genetic Algorithm (LSADGA) for CVRP, smoothing the solution space of the original problem and guiding the algorithm towards efficient convergence to the global optimum by combining adaptive parameter adjustment and diversity maintenance strategies. This invention introduces a toy problem cost term into the fitness function of the genetic algorithm. Constructed based on high-quality solutions to the original problem, it can be considered a simplified or abstract version of the original CVRP, with a smoother solution space and fewer local optima. By weighting and combining the toy problem cost with the original problem cost, a new and smoother fitness evaluation landscape is constructed. This effectively guides the algorithm to focus on the optimal topological structure of the solution in the early stages of the search, avoiding premature entrapment in local optima based on path length.

[0029] Furthermore, the vehicle path planning optimization method for landscape smoothing in this invention features an adaptive parameter control mechanism. Addressing the static setting problem of key parameters such as mutation probability in genetic algorithms, a dynamic adjustment mechanism is introduced. Based on the population convergence and solution improvement stagnation during the algorithm's iteration process, parameters such as mutation probability are dynamically adjusted to achieve a better balance. To prevent premature convergence, this invention designs a reward mechanism based on diversity assessment. By calculating the differences among individuals in the population in real time, solutions with high diversity and those significantly different from other solutions are rewarded or weighted in the fitness assessment, incentivizing the population to maintain high genetic diversity and enhancing the algorithm's ability to escape local optima. For potential constraint violations in path planning, this invention introduces a Euclidean distance penalty term in the fitness function to ensure that the generated solutions are optimized while satisfying basic constraints.

[0030] This invention also provides an optimization system for the landscape-smoothed vehicle path planning problem, used to implement the aforementioned optimization method for the landscape-smoothed vehicle path planning problem. The system includes an initialization module, a fitness function design and evaluation module, a genetic operator operation module, and an iteration and termination module, wherein: The initialization module is used to: randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem, and a feasible solution is a complete set of vehicle paths. The fitness function design and evaluation module is used to: construct a toy problem based on the initial population, where the toy problem and the vehicle path planning problem are of equal size and the fitness landscape of the solution space exhibits a unimodal characteristic; construct a fitness function, evaluate each individual in the population through the fitness function, and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty terms. The genetic operator operation module is used to: based on the fitness value of each individual, sequentially execute the selection operator, crossover operator, and mutation operator to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. The iteration and termination module is used to repeatedly execute the fitness function design and evaluation module and the genetic operator operation module until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

[0031] The present invention will be further described in detail below through specific embodiments.

[0032] like Figure 1 As shown, the optimization method for vehicle path planning in landscape smoothing according to the present invention mainly follows these steps: Step 1: Initialization; An initial population is randomly generated, where each individual represents a feasible solution to the CVRP problem (a complete set of vehicle paths).

[0033] Step 2: Fitness Function Design and Evaluation This invention uses a fitness function to determine the fitness value of each individual in the population. It consists of the following weighted components: ; in, This represents the fitness value of an individual. The cost of the original problem is the total distance traveled by the vehicle corresponding to the individual. These are the weighting coefficients for the toy model. The cost of the toy problem, For diversity weighting coefficients, For diverse rewards, For the penalty weighting coefficient, To constrain penalty items.

[0034] C oThe cost of the original problem is typically the total distance traveled along all vehicle paths. Used to achieve solution space smoothing. It is proportional to the average dissimilarity of the current individual and other individuals in the population. Dissimilarity can be calculated based on the edit distance or structural dissimilarity of the encoded solution. The penalty value imposed on solutions that violate distance or load constraints. , , These are the coefficients of the toy model weight, diversity weight, and penalty weight, respectively, and are important hyperparameters of the algorithm.

[0035] Step 3: Genetic Operator Operations After evaluating the fitness of the current population, genetic operators are executed to generate the next generation. This process follows the classic genetic algorithm framework, including three stages: selection, crossover, and mutation, and incorporates an adaptive parameter adjustment mechanism to enhance the algorithm's search capability.

[0036] 1) Selection Operator Let the first The generation population is: , in, To determine the population size, this invention employs a tournament selection method to select parent individuals from the population. Each time, from the population... Randomly selected Individuals constitute the candidate set And select the individual with the best fitness value as the parent individual: ; The selection mechanism ensures that individuals with higher fitness have a greater statistical probability of being selected, thus guaranteeing that the superior path structure can be inherited during evolution. At the same time, due to the randomness of the candidate set, a certain proportion of suboptimal individuals are retained to enter the next generation to maintain population diversity.

[0037] 2) Crossover operator The parent individuals obtained through the selection operator are crossovered according to a preset probability. Pair them up and perform a crossover operation to generate offspring individuals. Let the parent individual be... and Then the crossover operation can be represented as: ; The crossover operator reorganizes the customer access order or sub-path structure in the parent path encoding, enabling child individuals to inherit the superior local structure of the parent while forming new path combinations, thereby expanding the search range of the solution space. If the crossover operation is not triggered, the child individuals directly inherit the structure of the parent individuals.

[0038] 3) Mutation Operator To prevent genetic homogenization and local optima in the later stages of evolution, mutation operations are performed on newly generated offspring individuals with a certain mutation probability. Let the offspring individual be (x^{(c)}), and its mutation operation can be expressed as: ; in, For the first The mutation probability of a generation.

[0039] 4) Adaptive mutation probability adjustment mechanism Unlike traditional genetic algorithms that use a fixed mutation probability, this invention adjusts the mutation probability based on the algorithm's running state. Adaptive adjustments are made. First, the population diversity index is defined as: ; in, Represents an individual and The difference between them is calculated based on the distance of the path encoding or the difference of the edge set.

[0040] An algorithm is considered to be at risk of getting trapped in a local optimum if any of the following conditions are met: ; in: The preset diversity threshold; Indicates the first The optimal fitness of the generation; This is the length of the stall detection window; This represents the minimum improvement threshold. In the above situation, appropriately increasing the mutation probability to enhance the randomness of the search can be expressed as follows: ; Through an adaptive mutation probability adjustment mechanism, this invention can enhance global exploration capabilities during the search stagnation phase and strengthen local development capabilities during the solution continuous improvement phase.

[0041] Step 4: Iteration and Termination Repeat steps two and three until the preset maximum number of iterations is reached or the solution is satisfied after multiple consecutive generations without further optimization. Finally, output the best individual found throughout the entire evolutionary process as the optimal solution to the problem.

[0042] like Figure 3 As shown, Figure 3 and Figure 4 This is an embodiment of the convex hull, in Figure 3 and Figure 4As can be seen, if a different vehicle access order is used than that shown in the figure, the total distance obtained will definitely be worse than the original order. In other words, by placing all cities in a convex hull, a particular solution can be rewarded while other solutions are penalized, thus making the landscape of the solution space exhibit a unimodal characteristic. Figure 3 and Figure 4 An embodiment of the toy problem based on convex hull construction is given. In this embodiment, all cities are arranged on the same convex hull and connected sequentially according to a preset vehicle access order to form a closed path without intersecting edges. Figure 3 and Figure 4 The vehicle access order shown corresponds to the optimal solution of this convex hull problem. For this type of convex hull problem, based on the triangle inequality and the relevant theories of k-Opt local search, it can be proven that this access order is the unique k-Opt optimal solution. Any other vehicle access scheme that deviates from this order will introduce path intersections or longer edges, thus increasing the total travel distance. Therefore, by constructing the city as a convex hull structure and using the solution corresponding to this optimal access order as the reward, a better fitness value can be assigned to this solution in the fitness evaluation, while other solutions are subject to relative penalties. This makes the constructed toy problem solution space exhibit a unimodal characteristic, thereby achieving a smoothing guidance of the fitness landscape of the original vehicle routing problem.

[0043] The effectiveness of the vehicle path planning optimization method and system for landscape smoothing proposed in this invention will be verified through experiments.

[0044] like Figure 5 As shown, a comparative experiment was conducted on a publicly available CVRP standard test instance. Figure 5 The experimental results show that: The LSADGA method proposed in this invention achieves a significantly lower final cost than the original GA method, and the final converged cost is also significantly lower. The curve descent rate is also faster, and the standard deviation is smaller, indicating that this invention not only provides higher solution quality but also boasts faster convergence and better algorithm stability.

[0045] Sensitivity analysis of key parameters determined their optimal value range, providing reliable guidance for the practical application of the algorithm. Based on the sensitivity analysis results in the experimental progress report, optimal or near-optimal value ranges can be set for these weights.

[0046] like Figure 6 As shown in the experiment, the diversity weight shows that when the value is around 0.25, the algorithm can achieve the lowest final cost on multiple test instances, indicating that appropriate diversity rewards help the algorithm escape local optima.

[0047] like Figure 7As shown in the figure, the Euclidean distance penalty weight experiment shows that it performs best when it is around 0.2, indicating that a reasonable penalty helps the algorithm to better handle distance constraints.

[0048] In summary, this invention constructs a toy problem with the same size as the original problem but a smoother fitness landscape. Then, a weighted combination of the toy problem and the original problem is performed to obtain a smoother problem that retains the landscape characteristics of the original problem. This toy problem serves as a guiding problem for the genetic algorithm. Combined with an adaptive parameter adjustment mechanism and a diversity maintenance strategy, this avoids the genetic algorithm getting trapped in low-quality local optima in vehicle path planning, thereby improving the search efficiency and solution quality of the genetic algorithm. This invention demonstrates superior convergence and stability on multiple standard CVRP instances and shows good performance and practicality in large-scale, multi-constraint real-world path planning scenarios.

[0049] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Anyone skilled in the art can readily implement the present invention according to the description and above. Any modifications, alterations, or equivalent variations made using the technical content disclosed above are equivalent embodiments of the present invention. Furthermore, any modifications, alterations, or variations made to the above embodiments based on the essential technology of the present invention are still within the protection scope of the present invention.

Claims

1. An optimization method for vehicle path planning in landscape smoothing, characterized in that, Includes the following steps: S1. Randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem. A feasible solution is a complete set of vehicle routes. S2. Construct a toy problem based on the initial population. The toy problem and the vehicle path planning problem have the same size and the fitness landscape of the solution space has a unimodal characteristic. Construct a fitness function to evaluate each individual in the population and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty. S3. Based on the fitness value of each individual, perform the selection operator, crossover operator, and mutation operator operations in sequence to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. S4. Repeat S2 and S3 until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

2. The optimization method for vehicle path planning in landscape smoothing according to claim 1, characterized in that, In S1, the fitness value of each individual in the population is calculated using the following formula: ； in, This represents the fitness value of an individual. The cost of the original problem is the total distance traveled by the vehicle along the corresponding path for the individual. These are the weighting coefficients for the toy model. The cost of the toy problem, For diversity weighting coefficients, For diverse rewards, For the penalty weighting coefficient, To constrain penalty items.

3. The optimization method for vehicle path planning in landscape smoothing according to claim 1, characterized in that, In S2, the toy problem is constructed in the following ways: Based on the solution with the smaller objective function value of the original problem in the current population of the vehicle routing problem, the distribution of fitness values ​​corresponding to each feasible solution in the solution space is adjusted so that there is only one optimal fitness value in the solution space of the toy problem, and the solution corresponding to the optimal fitness value is the solution with the smaller objective function value of the original problem.

4. The optimization method for vehicle path planning in landscape smoothing according to claim 1, characterized in that, In S2, the constraint penalty term includes an Euclidean distance penalty term, which is used to impose a penalty on individuals who violate distance constraints or vehicle load constraints; violating distance constraints means that the travel distance of the vehicle path corresponding to the individual exceeds a preset distance threshold, and violating vehicle load constraints means that the total load of the vehicle path corresponding to the individual exceeds the vehicle's rated capacity.

5. The optimization method for vehicle path planning in landscape smoothing according to claim 1, characterized in that, In S3, the operation of selecting the operator specifically includes: Let the first The generation population is: ； in, To determine the population size, a tournament selection method is used to select parent individuals from the population, with each selection made from the population... Randomly selected Individuals constitute the candidate set And select the individual with the best fitness value as the parent individual: ； in For the size of the candidate set, For the parent generation.

6. The optimization method for vehicle path planning in landscape smoothing according to claim 5, characterized in that, In S3, the operation mode of the crossover operator is as follows: The parent individuals obtained through the selection operator are crossovered according to a preset probability. Pairing is performed, and a crossover operation is executed on the successfully paired parent individuals. The child individuals are generated by reorganizing the customer access order or sub-path structure in the path encoding of the parent individuals using the following formula: ； in, , For paired parent individuals, , This is the generated child individual; if the crossover operation is not triggered, the child individual directly inherits the structure of the corresponding parent individual.

7. The optimization method for vehicle path planning in landscape smoothing according to claim 1, characterized in that, In S3, the convergence state of the population is determined by the population diversity index, which is calculated using the following formula: ； in, For the first Population diversity indicators of the generation, For population size, and The first The first generation of the population The and the first Individual, It indicates the degree of difference between individuals.

8. The optimization method for vehicle path planning in landscape smoothing according to claim 7, characterized in that, In S3, the mutation probability is dynamically adjusted as follows: Preset diversity threshold Stasis detection window length and minimum improvement threshold , No. The optimal fitness value of the generation is , No. The optimal fitness value of the generation is When the following conditions are met: ； Adjust the mutation probability to the increased mutation probability. Otherwise, adjust the mutation probability to the reduced mutation probability. ,and .

9. The optimization method for vehicle path planning in landscape smoothing according to claim 7, characterized in that, In S3, the difference between individuals is calculated based on the distance of the path encoding or the difference of the edge set; the preset difference characteristic is that the average difference between an individual and all other individuals in the population is greater than a preset difference threshold. The average difference is calculated based on the edit distance or structural difference of the solution encoding, and the diversity reward is proportional to the average difference.

10. A landscape-smoothing vehicle path planning problem optimization system, used to implement the landscape-smoothing vehicle path planning problem optimization method according to any one of claims 1-9, characterized in that, It includes an initialization module, a fitness function design and evaluation module, a genetic operator operation module, and an iteration and termination module, among which: The initialization module is used to: randomly generate an initial population for the vehicle routing problem. Each individual in the initial population is a feasible solution to the vehicle routing problem, and a feasible solution is a complete set of vehicle paths. The fitness function design and evaluation module is used to: construct a toy problem based on the initial population, where the toy problem and the vehicle path planning problem are of equal size and the fitness landscape of the solution space exhibits a unimodal characteristic; construct a fitness function, evaluate each individual in the population through the fitness function, and obtain the fitness value of each individual. The fitness function is composed of a weighted combination of the original problem cost, the toy problem cost, the diversity reward, and the constraint penalty terms. The genetic operator operation module is used to: based on the fitness value of each individual, sequentially execute the selection operator, crossover operator, and mutation operator to generate the next generation population; In the mutation operator operation, the stagnation state is improved based on the convergence state of the population and the objective function value of the solution, and the mutation probability is dynamically adjusted; in the fitness evaluation, population diversity is maintained by giving diversity rewards to individuals with preset differential characteristics in the population. The iteration and termination module is used to repeatedly execute the fitness function design and evaluation module and the genetic operator operation module until the preset termination condition is met, and output the individual with the smallest objective function value in the original problem during the evolution process as the optimal solution to the vehicle path planning problem.

Images