Path planning method and system based on grouping path search and multi-target fusion

Abstract

The invention provides a path planning method and system based on grouping path search and multi-target fusion. According to the method, optimization is carried out aiming at the characteristics of large package quantity, high timeliness, strict limitation of vehicle capacity and the like of express delivery. In the first stage, through a complementary partition strategy and ACO / LKH3 combination, a large number of high-quality vehicle delivery single paths covering a complex delivery area are rapidly generated. In the second stage, motorcade task allocation is innovatively modeled as a multi-objective 0-1 optimization problem, and the operation cost (mileage) is collaboratively minimized, the package allocation coverage rate is maximized, and the package repeated allocation redundancy is minimized. Through NSGA-II algorithm solution and ILS optimization, the system can generate an optimal or near-optimal delivery path set with high efficiency, high stability and low cost for large-scale express delivery, and the operation efficiency and customer satisfaction of express enterprises are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of operations research, combinatorial optimization and computer application technology, and specifically relates to a high-efficiency solving method for the capacitated vehicle routing problem (CVRP) in the express delivery scenario. The method combines multi-strategy grouping path search and multi-objective optimization algorithm to provide high-quality and low-cost optimal path planning scheme for the delivery task of large-scale customer groups. TECHNICAL BACKGROUND The capacitated vehicle routing problem (CVRP) is a classic problem in the field of logistics and supply chain management, and has far-reaching practical application value in urban delivery services such as express delivery. The core of the CVRP is to plan service paths for a group of customers with specific goods demand, and to seek an optimal path set with the minimum total travel distance or total cost under the constraint of the maximum load capacity of each vehicle. Since the CVRP is an NP-hard problem, the size of its solution space increases exponentially with the number of customers (i.e. the number of express orders).

[0002] One of the mainstream methods to solve large-scale CVRP is the grouping-based heuristic algorithm, which adopts the "divide and conquer" strategy to decompose the large-scale problem into several sub-problems. However, the traditional grouping method has key bottlenecks in the "divide" and "combine" (path splicing) stages: Firstly, the quality of grouping cannot guarantee the global optimum. The grouping process usually relies on local geometric information, and it is difficult to ensure that the grouping scheme can produce a globally optimal solution. Secondly, the efficiency of path splicing is low. The path planning after grouping and the construction of the final path set are usually independent and non-cooperative steps, making it difficult to effectively splice local optimal solutions into high-quality global solutions.

[0003] The traditional method focuses more on how to obtain better grouping, and ignores the challenge of how to more efficiently and accurately perform path "fusion" or "splicing". Therefore, developing an algorithm that can deeply cooperate grouping and path fusion and balance multiple optimization objectives is the key to improving the efficiency of express delivery and reducing operating costs. SUMMARY

[0004] The purpose of the present application is to provide a path planning method based on grouping path search and multi-objective fusion, which solves the cooperative optimization problem of path generation and path splicing in traditional grouping algorithms by constructing a novel two-stage solving framework, and introduces a multi-objective evaluation mechanism in the path fusion stage to obtain a higher-quality, more economical and more complete delivery path scheme.

[0005] To achieve the above purpose, the technical scheme of the present application is as follows: A path planning method based on packet path search and multi-objective fusion, comprising the following steps: S1, using a multi-strategy customer grouping method to initialize customer groups, using at least two complementary grouping strategies to partition customer nodes, the grouping strategies including fan-shaped grouping based on the angle relationship between customer points and distribution centers and K-Means spatial clustering based on the geographical location proximity of customer points.

[0006] S2, for each customer group, an ant colony optimization (ACO) process is independently performed, wherein ACO builds a path by probabilistically selecting the next customer node, the selection is based on path information pheromone τ and inter-node heuristic information η, and parameters α and β are used to control the influence degree of pheromone and heuristic information respectively. Then, for a single optimal path, a high-performance local search algorithm (LKH3) is applied to optimize the best path of each group obtained by ACO to generate a set of high-quality candidate single path sets P={p1,p2,…, pNp}.

[0007] S3, the following multi-objective optimization modeling is performed for the generated single path, the path splicing problem is modeled as a multi-objective 0-1 optimization problem based on a binary decision variable vector x=(x1,x2,…,xNp), wherein xi∈{0,1} represents whether the path pi is selected, and then multi-objective function optimization is performed, the multi-objective optimization problem optimizes at least the following three competing key objective functions, respectively, minimizing the total path length f1, maximizing the number of unique customer coverage f2, and minimizing redundant customer coverage f3.

[0008] S4, for the Pareto front solution, NSGA-II algorithm is used to solve the multi-objective optimization problem, and non-dominated sorting and crowded distance calculation are used to obtain a set of Pareto optimal solutions; S5, the following is the repair and selection of solutions, the solutions in the Pareto front solution set are repaired to handle illegal situations such as uncovered or repeated coverage of customers that may be caused by multi-objective selection, and final optimization is performed, the shortest solution in the complete solution set after repair is selected as the initial solution, and it is input to the iterative local search (ILS) module for further optimization to obtain the final express delivery path planning scheme.

[0009] Further, the step S1 specifically comprises the following steps: using a multi-strategy customer grouping method to initialize customer groups, specifically by using at least two complementary grouping strategies to generate a diversified customer grouping set G groupsThe first strategy is a fan grouping based on the angle between the customer node and the distribution center. This method systematically divides all customer nodes into sectors by iterating through a pre-defined set of angles (θ) and rotating each angle value by 360 degrees. For each customer node c, the algorithm calculates its angle relative to the distribution center and obtains the normalized angle α norm by subtracting the rotation angle. The formula is as follows:

[0010] This formula is used to determine the grouping index idx to which the customer c belongs. This strategy effectively ensures the geographical dispersion of the generated paths. The second strategy is a K-Means spatial clustering based on the geographical proximity of customer nodes. This is a classic clustering method that divides all customer nodes V into N cluster compact clusters. This strategy generates groups based on the geographical proximity between customers, effectively complementing the first strategy. Finally, all grouping results generated by the two strategies are combined to form the input G groups for the subsequent path generation phase.

[0011] Further, the step S2 specifically includes the following steps: First, for each customer grouping Gi in the customer grouping set G groups obtained in step S1, an ant colony optimization (ACO) process is independently executed. This ACO algorithm is known for its robustness in handling discrete optimization problems and aims to plan paths for customers within the group. During the iterative process of ACO, an ant k probabilistically selects the next customer node j from the current customer node i when constructing the path. The selection is based on a formula that considers the path pheromone (τ i,j ) and the heuristic information (η i,j ) between nodes (i.e., the inverse of the distance). The selection probability P k i,j is as follows:

[0012] where allowed k is the set of next customers that ant k is allowed to access, and parameters α and β control the influence of pheromone and heuristic information on the selection process, respectively. Whenever a batch of ants completes path construction, the algorithm updates the pheromone based on the best path of the current grouping to reinforce the path edges leading to better solutions, thereby guiding subsequent searches.

[0013] Second, for each group of optimal paths found by ACO, a state-of-the-art high-performance local search algorithm (e.g. LKH3) is applied to optimize each individual path. The powerful local search capability of LKH3 ensures that the initial solution obtained by ACO is effectively "polished" to make it closer to the optimal solution. Finally, all the paths optimized by LKH3 are collected as the input for the subsequent path stitching and optimization phase, forming a set of high-quality candidate individual paths P = {p1, p2,..., pNp}.

[0014] Further, the step S3 specifically comprises the following steps: The multi-objective optimization modeling for the generated individual paths, and the subsequent multi-objective function optimization, is specifically constructed as the following multi-objective 0-1 optimization problem: First, the path stitching problem is modeled as a multi-objective 0-1 optimization problem based on a binary decision variable vector x = (x1, x2,..., xNp), where xi e {0, 1} represents whether the ith path pi is selected. Second, the optimization problem simultaneously optimizes at least the following three competing key objective functions, aiming to find a balanced and efficient path subset x* from the candidate path set P, and seek the optimal solution under the constraints of vehicle capacity Q and vehicle number K: Objective f1 (minimize total path length): Its goal is to minimize the total travel distance of the selected paths, directly contributing to reducing operating costs and vehicle fuel consumption.

[0015]

[0016] where Distance(pi) is the total distance of path pi.

[0017] Objective f2 (maximize the number of unique customer coverage): Its goal is to maximize the number of unique customers served, ensuring that the selected routes can fully cover customer demand.

[0018]

[0019] where the function calculates the cardinality (size) of the set of all customers visited by at least one selected path, excluding the distribution center.

[0020] Objective f3 (minimize redundant customer coverage): Its goal is to penalize multiple visits to the same customer and minimize the number of redundant customer coverage in the path set.

[0021]

[0022] where NC is the total number of customers, I(.) is the indicator function, the inner summation counts the number of times each customer j is visited in all selected paths, and (.)+ denotes taking the positive part of the result, which only counts redundant visits.

[0023] Further, the step S4 specifically includes the following steps: The NSGA-II algorithm is used to solve the multi-objective optimization problem, and the specific process includes: first, the algorithm initializes a parent population Pt, the individual of which is a path combination randomly selected from the candidate path set R initial and strictly obeys the constraints such as the number of vehicles K. Then, the algorithm enters an iterative loop to evolve the population through a series of genetic operations, including selecting parent individuals using the tournament selection method, and generating offspring population Qt through crossover (Crossover) and mutation (Mutate) operations, which also strictly obey the constraints such as capacity and number of vehicles. After generating offspring, the algorithm combines the parent and offspring into a temporary population Rt, and performs non-dominated sorting. This non-dominated sorting is the core of NSGA-II, which divides all solutions into different Pareto frontiers based on the performance of the three objective functions (f1, f2 and f3). Subsequently, after selecting the optimal Pareto frontier, the algorithm uses the crowding distance (Crowding Distance) to calculate the sorting of individuals on the frontier to ensure the diversity and uniform distribution of the population, and accordingly selects the next generation population P t+1 . Finally, after all iterations are completed, the algorithm selects a best solution from the final Pareto optimal solution set as the input for the next repair.

[0024] Further, the step S5 specifically includes the following steps: Firstly, the solutions in the Pareto frontier solution set are repaired to deal with the illegal situations such as uncovered or repeatedly covered customers caused by multi-objective selection, and to ensure the integrity and legality of each solution. The repair process specifically includes: for the unserved customers, it is checked whether they can be inserted into the existing path in priority, that is, to find the position with the minimum insertion cost and without violating the vehicle capacity constraint; if all existing paths cannot accommodate the customer, a new vehicle is started for the customer and a new path is created, and the nearest neighbor insertion strategy can be used as a supplement to find a better insertion point. For the repeatedly served customers, the correction is made according to the principle of the lowest cost or the most capacity stressed to ensure that each customer is served only once; wherein, the lowest cost strategy aims to keep the customer in the path with the minimum total distance contribution, and the most capacity stressed strategy aims to keep the customer in the path with the least remaining capacity to release the capacity of other paths. After the repair is completed, the solution with the shortest total path length is selected from the set of complete solutions as the initial solution, and is input to the Iterated Local Search (ILS) module for further optimization to obtain the final high-quality express delivery path planning scheme.

[0025] To achieve the above purpose, the application further provides a path planning system based on grouped path search and multi-objective fusion, comprising: Multi-strategy grouped path search unit: the core function is to build an initial solution space and generate paths. It innovatively uses a complementary multi-strategy customer grouping method to initialize customer partitioning, including fan-shaped grouping based on the angle relationship between customer points and distribution centers, and K-Means spatial clustering based on the geographical location proximity of customer points. By applying multiple grouping strategies, this unit can generate a highly diverse grouping set, effectively avoiding local optimization. Subsequently, for each independent grouping, the system performs a robust Ant Colony Optimization (ACO) process, using pheromone and heuristic information to guide ants to build group path structures, thereby efficiently obtaining initial path structures in a local range.

[0026] Single path optimization and candidate set generation unit: this unit aims to improve the quality and optimize the initial paths obtained by grouped search, and to build a final candidate solution set. It takes over from the ACO module and applies a high-performance local search algorithm (LKH3) to optimize the best or near-optimal path found for each grouping. LKH3, with its powerful k-opt neighborhood search capability, ensures thorough "polishing" of the initial solution, significantly improving the quality of each single path and making it closer to the optimal solution. Finally, all optimized single paths are collected to form a high-quality, structurally diverse candidate single path set P, providing a solid foundation for the path fusion in the next stage.

[0027] Multi-objective path fusion and solving unit: This unit is the core innovation of the method, and its function is to execute the decision of path splicing and perform Pareto optimization. It creatively models the complex path splicing problem as a multi-objective 0-1 optimization problem, where the decision variable represents whether to select a certain candidate path. The model optimizes three key objectives that compete with each other: minimizing the total path length (economy), maximizing the number of uniquely covered customers (completeness), and minimizing redundant customer coverage (efficiency). To solve this multi-objective problem, this unit uses the efficient NSGA-II algorithm, which divides the solution set into different Pareto frontiers through non-dominated sorting, and uses crowded distance calculation to maintain the diversity and distribution of the solution set, thereby obtaining a set of optimal solutions that balance the three objective functions.

[0028] Solution repair and final optimization unit: The function of this unit is to ensure the legality of the solution and to maximize the accuracy of the final solution. First, the Pareto solution set obtained by multi-objective solving is repaired to handle illegal situations such as uncovered customers (solved by greedy insertion or starting a new vehicle) and repeatedly covered customers (modified by the lowest cost or most capacity stressed principle) caused by optimization trade-offs, ensuring that each solution meets the basic constraints of CVRP. After repair, the algorithm selects the solution with the shortest total path length from the legal solution set as the initial solution and inputs it into the Iterative Local Search (ILS) module. The ILS module further optimizes the initial solution through the alternating method of disturbance and local search, effectively avoids local optimum, and finally stably outputs a high-quality express delivery path planning scheme.

[0029] The beneficial effects of the present application are: Traditional grouping methods often use simple greedy strategies or single-objective evaluation in the path splicing stage, making it difficult to guarantee global optimality. The present application innovatively models path fusion as a multi-objective optimization problem, providing more comprehensive and detailed solution evaluation and selection capabilities. This mechanism enables the algorithm to accurately select the optimal combination from a diverse set of candidate paths, greatly improving global search capability. For express companies, this means that in millions of daily delivery tasks, the total travel distance of each delivery can be minimized, significantly reducing fuel and vehicle wear and tear.

[0030] Another major drawback of existing grouping algorithms is that the path generation and path fusion stages are relatively independent, resulting in insufficient depth of collaborative optimization. The present method combines multi-strategy grouping with the mechanisms of ACO and LKH3 deep local search, ensuring that each candidate path generated in the first stage has extremely high quality. This high-quality candidate set ensures that, when path fusion is performed in the second stage, regardless of which combination is chosen, the constituent units are efficient. This phased high-quality processing achieves deep collaborative optimization of the grouping (path generation) and path splicing (path fusion) stages, effectively overcoming the bottleneck between the "split" and "combine" stages of traditional methods. Therefore, the algorithm can exhibit excellent performance stability and convergence speed when handling large-scale, high-complexity express delivery tasks.

[0031] In actual express delivery operations, route planning not only considers cost (total distance), but also service quality and efficiency. The multi-objective optimization mechanism of the present invention precisely addresses this complex demand, balancing the three key objectives that compete with each other: economy (minimizing total path length f1), completeness (maximizing unique coverage of customers f2), and efficiency (minimizing redundant coverage f3). Avoiding redundant coverage (minimizing f3) is significant because it prevents multiple delivery routes from repeatedly visiting the same customer. In the express delivery scenario, this means avoiding the assignment of the same customer's package to different delivery personnel or the unnecessary multiple passes of a delivery personnel through the same customer point, thereby improving the delivery efficiency of the delivery personnel and reducing the time waste and potential customer complaints caused by path intersections or repeated services during the delivery process. This comprehensive optimization results in a final delivery plan that is the "win-win" solution with the lowest cost, complete service, and highest operational efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0032] The accompanying drawings, which form a part of the present application, are intended to provide further understanding of the present application and are incorporated herein for a purpose of explanations. In the accompanying drawings: Figure 1 The overall flowchart of the embodiment method of the present application; Figure 2 The structure schematic diagram of the embodiment system of the present application. DETAILED DESCRIPTION

[0033] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0034] Embodiment 1 Referring to Figure 1 : A path planning method based on grouping path search and multi-objective fusion, comprising the following steps: S1, using a multi-strategy customer grouping method to initialize customer groups, partitioning customer nodes using at least two complementary grouping strategies, including sector grouping based on the angular relationship between customer points and distribution centers and K-Means spatial clustering based on the geographical proximity of customer points.

[0035] S2, for each customer group, independently performing an ant colony optimization (ACO) process, wherein ACO builds a path by probabilistically selecting the next customer node, the selection being based on path information pheromone τ and inter-node heuristic information η, and using parameters α and β to control the influence of pheromone and heuristic information, respectively. Then, for a single optimal path, a high-performance local search algorithm (LKH3) is applied to optimize the best path obtained by ACO for each group, generating a set of high-quality candidate single-path sets P={p1, p2, …, pNp}.

[0036] S3, the following multi-objective optimization modeling is performed for the generated single paths, the path concatenation problem is modeled as a multi-objective 0-1 optimization problem based on a binary decision variable vector x=(x1, x2, …, xNp), where xi∈{0,1} represents whether the path pi is selected, and the following multi-objective function optimization is performed, the multi-objective optimization problem optimizes at least the following three competing key objective functions, respectively, minimizing the total path length f1, maximizing the number of uniquely covered customers f2, and minimizing redundant customer coverage f3.

[0037] S4, for the Pareto front solution, the NSGA-II algorithm is used to solve the multi-objective optimization problem, and the non-dominated sorting and crowding distance calculation are used to obtain the Pareto optimal solution set; S5, the following is the repair and selection of solutions, the solutions in the Pareto front solution set are repaired to handle illegal situations such as uncovered or repeatedly covered customers that may be caused by multi-objective selection, and the final optimization is performed, the shortest total path length is selected from the complete solution set after repair as the initial solution, and it is input to the iterative local search (ILS) module for further optimization to obtain the final express delivery path planning scheme.

[0038] In a specific example, the step S1 specifically includes the following steps: Using a multi-strategy customer grouping method to initialize customer groups is the starting point of the method, which aims to provide diversified and high-quality sub-problem inputs for subsequent path search, thereby avoiding falling into local optimum. In the actual operation scene of express delivery, the distribution center often needs to handle a large number of orders located in different directions and different density areas. Therefore, at least two complementary grouping strategies are used to generate a diversified customer group set Ggroups In urban delivery, customer points are distributed radially around the distribution center. If only relying on geographical proximity, a long route can span multiple directions. Therefore, this method introduces angle-based sector grouping to solve the directional clustering problem. This method systematically divides all customer nodes into sectors by iterating a pre-set angle set (θ) and rotating 360 degrees for each angle value. For example, if θ = 60 degrees is set, the entire delivery area can be divided into 6 sectors, each corresponding to an initial grouping. For each customer node c (i.e. a to-be-received address), the algorithm calculates its angle relative to the distribution center and obtains the normalized angle α norm by subtracting the rotation angle. Using the formula:

[0039] where idx is the grouping index to which the customer c belongs. The advantage of this strategy is that it forcibly ensures the geographical dispersion of the generated path. For example, if two customers A and B are geographically close but located in two different 60-degree sectors relative to the distribution center D, they will be assigned to different initial groupings. This can effectively encourage the subsequent ACO algorithm to search for high-quality paths in different directions, especially suitable for solving long-distance distribution trunk path optimization problems across regions.

[0040] As a supplement to angle grouping, this method also uses K-Means spatial clustering based on the geographical proximity of customer points. In actual delivery areas, customer demand often exists in local high-density areas (such as large residential areas or commercial complexes). K-Means is a classic clustering method that divides all customer nodes V into pre-set N cluster clusters. This strategy generates groupings based on the Euclidean distance between customers, ensuring that customers in the same grouping have high geographical concentration, thereby optimizing the "floor sweeping" or "slice distribution" path of the courier in the local area. This grouping result effectively complements the angle grouping, avoiding the limitations of a single grouping strategy.

[0041] Finally, all grouping results generated by the above two complementary strategies (e.g. multiple sector grouping results and multiple K-Means clustering results) are collected as input G groups to the subsequent path generation phase. Through this multi-strategy grouping initialization, this method greatly enriches the structure and diversity of the initial path, providing a high-quality starting point for the second phase of path fusion.

[0042] In a specific example, the step S2 specifically comprises the following steps: For each customer group, an Ant Colony Optimization (ACO) process is independently executed and single optimal path optimization is performed, aiming to transform the sub-problems generated in the previous step of grouping into high-quality single delivery paths, and to build a candidate set of optimal paths. This process embodies the double guarantee of the method in terms of path quality, and for each customer group Gi in the customer group set G obtained in step S1 groups , an Ant Colony Optimization (ACO) process is independently executed. In the practice of express delivery, each group Gi can be regarded as a potential service area of a delivery vehicle. The ACO algorithm, with its powerful distributed search capability, simulates the process of ants searching for the shortest path to plan the optimal visiting order of customers in the group. In the iterative process of ACO, when constructing a path, ant k probabilistically selects the next customer node j from the current customer node i, and the selection is based on a formula that takes into account the path pheromone τ ij and the heuristic information η ij between nodes (i.e., the reciprocal of the distance). The core formula of the selection probability P k ij is as follows:

[0043] where parameters α and β control the degree of influence of pheromone and heuristic information on the selection process, respectively. For example, for high-priority express delivery areas, the influence of pheromone on path selection can be increased by adjusting the α and β parameters, so that it tends to explore the excellent paths found. Whenever a batch of ants completes path construction, the algorithm updates the pheromone according to the best path of the current group, thereby strengthening the path edges leading to better solutions. This mechanism effectively utilizes swarm intelligence to find a low-cost initial path structure for each group.

[0044] After the end of the Ant Colony Optimization cycle, for each best path of the group found by ACO, a high-performance local search algorithm (LKH3) recognized in the industry is applied for single path optimization. In the express industry, small optimizations of paths can bring huge cumulative economic benefits. LKH3, with its powerful k-opt neighborhood search capability, thoroughly "polishes" and "optimizes" the initial paths obtained by ACO. For example, if an initial path contains an inefficient crossing or detour link (such as A→B→C→D), LKH3 will try to reconstruct it into a shorter and more efficient path (such as A→C→B→D) using k-opt operations (such as 2-opt or 3-opt exchange). This optimization ensures that each candidate path itself is highly optimized, significantly improving its quality. Finally, all paths optimized by LKH3 constitute a high-quality candidate single path set P = {p1, p2, …, pNp} used by the method for path splicing in the next stage.

[0045] In a specific example, the step S3 specifically comprises the following steps: The multi-objective optimization modeling for the generated single path and the subsequent multi-objective function optimization are the core innovative points of the method. By constructing a multi-objective 0-1 optimization problem, the method solves the complex decision-making problem of selecting the optimal combination from a large number of high-quality candidate paths. The path splicing problem is modeled as a multi-objective 0-1 optimization problem, and the model takes the high-quality candidate single path set P = {p1, p2, …, pNp} output by S2 as input. Assuming that a certain express distribution center needs to serve 100 customers (orders), through S2 step, we generate Np= 500 high-quality candidate paths (for example, p1 covers customers {1, 3, 5, 8, 10} with a distance of 15 km; p2 covers {3, 7, 9, 11} with a distance of 10 km). The goal of the model is to select a set of paths that are the shortest in total mileage, serve all 100 customers, and have the least number of repetitions from the 500 paths.

[0046] The model is based on a binary decision variable vector x = (x1, x2, …, xNp), where xi e {0, 1} represents whether the ith path pi is selected. The optimization problem optimizes the following three competing key objective functions simultaneously to find the Pareto optimal solution set from the economic, completeness, and efficiency dimensions. Objective f1 (minimize total path length - economy), which aims to minimize the total distance of the selected paths. In express operation, this is the most direct cost indicator.

[0047]

[0048] If paths p1 and p2 are finally selected, the value of f1 is Distance(p1) + Distance(p2) = 15 km + 10 km = 25 km. This objective encourages the algorithm to select high-quality paths that are short in distance themselves.

[0049] Objective f2 (maximize the number of uniquely covered customers - completeness), which aims to ensure that all express orders to be delivered can be arranged on an effective route. Its goal is to maximize the number of uniquely served customers.

[0050]

[0051] Path p1 covers {1, 3, 5, 8, 10} (5), and path p2 covers {3, 7, 9, 11} (4). If both are selected, the uniquely covered customer set is {1, 3, 5, 7, 8, 9, 10, 11}. At this time, the value of f2 is 8. This objective ensures that the algorithm does not miss any express order.

[0052] Objective f3 (minimize redundant customer coverage - efficiency), this objective penalizes multiple visits to the same customer, minimizes the number of redundant customer coverage in the path set, directly improves the delivery efficiency of the courier.

[0053]

[0054] In the above example, customer 3 exists in both pi and p2, i.e. is visited twice. Therefore, the number of redundant coverage is (2-1)=1, and the rest of the customers are visited once, with a redundant coverage of 0. At this time, the value of f3 is 1. This objective penalizes such inefficient repeated service. By minimizing f3, the algorithm encourages the final path set to be such that each customer (package order) is served by only one courier (one path), greatly improving operational efficiency and avoiding waste of path resources. By simultaneously optimizing these three objectives and solving them with the NSGA-II algorithm, the output of this unit is a set of Pareto optimal solutions that balance cost, completeness, and efficiency. These solutions represent the optimal path combination trade-off scheme under the current constraint conditions, for the final decision maker to choose or enter the next stage of optimization.

[0055] In a specific example, the step S4 specifically comprises the following steps: Using the NSGA-II algorithm to solve the multi-objective optimization problem is the key implementation mechanism of the method in the path fusion stage. Since the three objective functions (f1 distance, f2 coverage, f3 redundancy) defined in S3 compete with each other, single-objective optimization cannot obtain a comprehensive optimal solution. The introduction of the NSGA-II algorithm enables the method to efficiently find a set of Pareto optimal solutions that balance all objectives.

[0056] The specific process includes: first, the algorithm initializes a parent population Pt, whose individuals (Chromosomes) represent path combinations x randomly selected from 500 candidate paths, and strictly obeys the constraints such as the number of vehicles K and the vehicle capacity Q. Next, the algorithm enters an iterative loop to continuously evolve the population through a series of genetic operations: Selection (Selection): Use tournament selection to preferentially select individuals that perform better on the three objectives. Crossover (Crossover): Perform path combination exchange operations on the selected parent individuals to generate new path combinations (child population Qt). Mutation (Mutate): Randomly change the path selection state of the child individuals (for example, change xi from 0 to 1, i.e. add or remove a path) to increase the diversity of the population.

[0057] After generating offspring Qt, the algorithm merges the parent Pt and offspring Qt into a temporary population Rt and performs two core operations of NSGA-II. The first is Non-Dominated Sort, which is the foundation of multi-objective optimization. It divides all path combination solutions into different Pareto fronts F1, F2, … based on the performance of the three objective functions (f1, f2, f3). Suppose there are solution A and solution B in Rt. Solution A has attributes (f1 = 100km, f2 = 98km, f3 = 2km), and solution B has attributes (f1 = 105km, f2 = 100km, f3 = 0km). Since solution A is not as good as solution B in f2 and f3, and the difference in f1 is not large, both of them can be non-dominated to each other and are located in the optimal front F1. Non-dominated sorting can ensure that any solution in the optimal solution set cannot be completely dominated by other solutions in all objectives, thus providing the express company with a set of optimal path combination options. After selecting the optimal Pareto front (e.g. F1), the algorithm sorts the individuals on the front using Crowding Distance calculation. Crowding distance is used to measure the density between a solution and its adjacent solutions. The larger the distance, the sparser the solution, the more valuable it is. On F1, if there is a solution that focuses on extremely low f1 (lowest cost), and another solution that focuses on extremely low f3 (zero redundancy), the crowding distance calculation will tend to retain the solution between the two, thus ensuring that the final solution set can provide complete trade-off options from "lowest cost but slightly redundant" to "zero redundancy but slightly higher cost". This has guiding significance for the express company's operation decision-making with different priorities.

[0058] Finally, after all iterations are complete, the algorithm selects a best solution from the final Pareto optimal solution set as the input for the next repair. This output is one or more path combination schemes, each representing the best balance point between cost, service integrity, and efficiency.

[0059] In a specific example, the step S5 specifically comprises the following steps: First, the solution x* in the Pareto front solution set obtained by NSGA-II is repaired to handle illegal situations such as uncovered or repeatedly covered customers that may be caused by multi-objective selection. This is crucial for express delivery that needs to ensure that all packages are delivered without causing chaos of repeated delivery. For customers (orders) not served (not covered by the selected path): The repair process will first check whether the customer (order) can be greedily inserted into the existing selected path, i.e. find the position with the minimum insertion cost and without violating the vehicle capacity constraint. Suppose the order of customer C 101 is not covered in the path combination x* selected by NSGA-II. The algorithm will check whether C 101whether it can be inserted into some position in the existing paths p1, p2, … with the minimum additional travel distance, without overloading. If all existing delivery vehicles (paths) are fully loaded or the insertion cost is too high, the algorithm will start a new vehicle and create a new path, ensuring that the orders of C 101 The repair process corrects the orders according to the cost-minimizing or capacity-tightest principle, ensuring that each customer is served only once. Assuming that the order of customer C3 is covered by both p1 (cost contribution 2km) and p5 (cost contribution 3km). With the cost-minimizing strategy, the algorithm will keep customer C3 in p1 and remove it from p5, thus minimizing the total distance. With the capacity-tightest strategy, if the remaining capacity of p1 is 10 units and the remaining capacity of p5 is 2 units (tighter), the algorithm will keep customer C3 in p5 to release 10 units of capacity in p1, providing space for future possible new order insertion. These two strategies have their own focus, ensuring the uniqueness of single-service in the path set and the efficiency of resource utilization.

[0060] After the repair is completed, from this set of complete and legal solutions, the solution x best with the shortest total path length is selected as the initial solution and input to the Iterated Local Search (ILS) module for further fine optimization. The ILS module explores a wider solution space by alternating between destruction and reconstruction. In the context of delivery distribution, this means making a small number of structural disturbances to the repaired path scheme (e.g. randomly removing a few customers and re-inserting them), and then applying high-performance local search (e.g. 2-opt, 3-opt) for reconstruction. This mechanism effectively avoids the local optimal solution produced by the NSGA-II optimization and repair process, and further optimizes the connection between paths and the order within paths. Finally, the ILS module, with its strong convergence ability, obtains a high-quality delivery distribution path planning scheme.

[0061] Embodiment 2 To achieve the above purpose, see Figure 2 The present application also provides a path planning system based on grouping path search and multi-objective fusion, comprising: Multi-strategy grouping path search unit: The core function is to build the initial solution space and generate paths. It innovatively adopts complementary multi-strategy customer grouping methods to initialize customer partitions, including sector grouping based on the angle relationship between customer points and distribution centers, and K-Means spatial clustering based on the geographical proximity of customer points. By applying multiple grouping strategies, this unit can generate a highly diverse set of groups, effectively avoiding local optimization. Subsequently, for each independent group, the system performs a robust ant colony optimization (ACO) process, using pheromone and heuristic information to guide ants to build intra-group path structures, thereby efficiently obtaining initial path structures in a local range.

[0062] Single path optimization and candidate set generation unit: This unit aims to improve the quality and optimize the initial paths obtained by the grouping search, and to build the final candidate solution set. It takes over from the ACO module and applies a high-performance local search algorithm (LKH3) to optimize the best or near-best path found for each group. LKH3, with its powerful k-opt neighborhood search capability, ensures thorough "polishing" of the initial solution, significantly improving the quality of each single path and making it closer to the optimal solution. Finally, all finely optimized single paths are collected to form a high-quality, structurally diverse candidate single path set P, providing a solid foundation for the next stage of path fusion.

[0063] Multi-objective path fusion and solution unit: This unit is the core innovation of the method, and its function is to perform path splicing decisions and perform Pareto optimization. It creatively models the complex path splicing problem as a multi-objective 0-1 optimization problem, where decision variables represent whether to select a candidate path. This model optimizes three key competing objectives simultaneously: minimizing total path length (economy), maximizing the number of uniquely covered customers (completeness), and minimizing redundant customer coverage (efficiency). To solve this multi-objective problem, this unit uses the efficient NSGA-II algorithm to divide the solution set into different Pareto frontiers through non-dominated sorting, and uses crowding distance calculation to maintain the diversity and distribution of the solution set, thereby obtaining a set of optimal solutions that balance the three objective functions.

[0064] The function of the solution repairing and final optimization unit is to ensure the legality of the solution and to improve the accuracy of the final solution. First, the Pareto solution set obtained by multi-objective solving is repaired to deal with the illegal conditions caused by optimization selection, such as uncovered customers (through greedy insertion or starting a new vehicle solution) and repeatedly covered customers (through the lowest cost or most stressed capacity principle correction), to ensure that each solution meets the basic constraints of CVRP. After repairing, the algorithm selects the solution with the shortest total path length from the legal solution set as the initial solution and inputs it into the iterative local search (ILS) module. The ILS module further optimizes the initial solution through the alternating disturbance and local search, effectively avoids local optimization, and finally stably outputs a high-quality express delivery path planning scheme.

[0065] In another aspect, the application also discloses a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to make the processor execute steps of the method.

[0066] In another aspect, the application also discloses a computer device, which comprises a memory and a processor, and the memory stores a computer program, and the computer program is executed by the processor to make the processor execute steps of the method.

[0067] In another embodiment provided in the application, a computer program product containing instructions is also provided, which makes a computer execute the mobile source emission prediction method based on the timing feature migration in any of the above embodiments when the computer program product is run on the computer.

[0068] It can be understood that the system, device and storage medium provided by the embodiments of the application correspond to the method provided by the embodiments of the application, and the explanation, examples and beneficial effects of the related content can refer to the corresponding part in the above method.

[0069] In the embodiments described above, all or some of the steps can be implemented by hardware, software, firmware or any combination thereof. When implemented by software, all or some of the steps can be implemented in the form of one or more computer programs or program elements. The computer programs reside (at least temporarily) in a memory of a computer during execution. The memory can be a RAM memory, a flash memory, a ROM memory, an EPROM memory, or any other suitable memory. The memory can be integral to or separate from the computer. The computer programs can be written in any suitable programming language, such as C, C++, Java, Visual Basic, etc. The computer programs can be written in assembly or machine language, if desired. The computer programs can be distributed over network coupled file servers, or can be distributed by any other suitable means.

[0070] It is to be understood that the terminology "first", "second", etc. used herein merely for the purpose of distinguishing one entity or action from another, and does not necessarily imply these entities or actions are mutually exclusive or are either temporal or spatial priorities of one another. Moreover, the terms "comprising", "including", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. In other words, any of the steps of the processes, methods, articles, or apparatuses described herein can be performed in any order or simultaneously, unless otherwise indicated by context.

[0071] Each of the embodiments described in the specification adopt a related manner, and the same or similar parts between each of the embodiments can be referred to each other. Each of the embodiments focuses on the difference from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiments.

[0072] The above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalent features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A path planning method based on grouped path search and multi-objective fusion, applicable to vehicle path planning with capacity constraints in express delivery scenarios, characterized in that, Includes the following steps: S1. Initialize customer groups using a multi-strategy customer grouping method, and partition customer nodes using at least two complementary grouping strategies, including sector grouping based on the angular relationship between customer points and distribution centers and K-Means spatial clustering based on the geographical proximity of customer points. S2. For each customer group, independently execute the Ant Colony Optimization (ACO) process. Ant Colony Optimization constructs a path by probabilistically selecting the next customer node. The selection criteria include path pheromone τ and inter-node heuristic information η, and the parameters α and β are used to control the influence of pheromone and heuristic information, respectively. Then, optimize the single optimal path. For the best path of each group obtained by ant colony optimization, apply the Local Search Algorithm (LKH3) to optimize the single path, generating a set of high-quality candidate single paths P={p1,p2,…,pNp}. S3. Perform multi-objective optimization modeling on the generated single path, and model the path splicing problem as a multi-objective 0-1 optimization problem. The optimization problem is based on a binary decision variable vector x=(x1,x2,…,xNp), where xi∈{0,1} indicates whether the path pi is selected. Next, perform multi-objective function optimization. The multi-objective optimization problem simultaneously optimizes at least the following three competing key objective functions, namely minimizing the total path length f1, maximizing the number of uniquely covered customers f2, and minimizing redundant customer coverage f3. S4. For solving the Pareto front, the NSGA-II algorithm is used to solve the multi-objective optimization problem. The Pareto optimal solution set is obtained by non-dominated sorting and crowding distance calculation. S5. Finally, the solution is repaired and selected. The solutions in the Pareto front solution set are repaired to handle illegal situations such as uncovered or duplicated customers that may be caused by multi-objective selection. The final optimization is performed. The solution with the shortest total path length is selected from the repaired complete solution set as the initial solution and input into the Iterative Local Search (ILS) module for further optimization to obtain the final express delivery route planning scheme.

2. The path planning method based on grouped path search and multi-objective fusion according to claim 1, characterized in that, Step S1 specifically includes the following steps: A multi-strategy customer grouping approach is used to initialize customer groups, specifically by employing at least two complementary grouping strategies to generate a diverse set of customer groups G. groups ; The first strategy is sector grouping based on the angular relationship between customer points and distribution centers. This method systematically divides all customer nodes into sectors by iterating over a preset set of angles (θ) and rotating each angle value by 360 degrees. For each customer node c, the algorithm calculates its angle relative to the distribution center and obtains the normalized angle α by subtracting the rotation angle. norm The formula is as follows: This formula is used to determine the grouping index idx to which customer c belongs; The second strategy is K-Means spatial clustering based on the geographical proximity of customer points, used to divide all customer nodes V into N. cluster This strategy generates compact clusters based on the geographical proximity of customers, effectively complementing the first strategy. Finally, all grouping results generated through these two strategies are aggregated and used as input G for the subsequent path generation stage. groups .

3. The path planning method based on grouped path search and multi-objective fusion according to claim 1, characterized in that, Step S2 specifically includes the following steps: First, for the customer group set G obtained in step S1 groups Each customer group G in i Each ant independently executes the Ant Colony Optimization (ACO) process. During the iterative process of ACO, when constructing a path, ant k probabilistically selects the next customer node j from the current customer node i, based on a factor that considers path pheromones (τ). i,j ) and heuristic information between nodes (η) ij That is, the formula for the reciprocal of distance; The probability of choice P k i,j The core formula is: Among them, allowed k is the next set of clients that ant k is allowed to access. The parameters α and β control the influence of pheromones and heuristic information on the selection process, respectively. After each batch of ants completes path construction, the algorithm updates the pheromones according to the best path of the current group to strengthen the path edges leading to better solutions, thereby guiding subsequent searches. Secondly, after the ant colony optimization cycle ends, for the best path found by the ant colony optimization for each group, the high-performance local search algorithm (LKH3) is applied to optimize the single path. Finally, all paths optimized by the Local Search Algorithm (LKH3) are collected and used as input for subsequent path splicing and optimization stages, forming a high-quality set of candidate single paths P={p1,p2,…, pNp}.

4. The path planning method based on grouped path search and multi-objective fusion according to claim 1, characterized in that, Step S3 specifically includes the following steps: Multi-objective optimization modeling is performed on the generated single path, followed by multi-objective function optimization, specifically constructed as the following multi-objective 0-1 optimization problem: First, the path splicing problem is modeled as a multi-objective 0-1 optimization problem. The optimization problem is based on a binary decision variable vector x=(x1,x2,…,xNp), where xi ∈{0,1} indicates whether the i-th path pi is selected. Secondly, the optimization problem simultaneously optimizes at least three competing key objective functions, aiming to find a balanced and efficient subset of paths x* from the candidate path set P, and to seek the optimal solution under constraints such as vehicle capacity Q and number of vehicles K: Objective f1, which is to minimize the total path length, aims to minimize the total distance traveled along the selected path, directly targeting reduced operating costs and vehicle fuel consumption. The formula is as follows: Where Distance(pi) is the total distance of path pi; Objective f2, or maximizing the number of uniquely covered customers, aims to maximize the number of unique customers served, ensuring that the selected route fully covers customer needs. The formula is as follows: The function calculates the cardinality of the set of all customers visited by at least one selected path, excluding distribution centers; Objective f3, or minimizing redundant customer coverage, aims to penalize multiple visits to the same customer and minimize the number of redundant customer coverages in the path set, as shown in the following formula: Where NC is the total number of customers, I(.) is an indicator function, the inner summation calculates the number of times each customer j is visited in all selected paths; (.)+ indicates taking the positive part of the result, this function only calculates redundant visits.

5. The path planning method based on grouped path search and multi-objective fusion according to claim 1, characterized in that, Step S4 specifically includes the following steps: The NSGA-II algorithm is used to solve multi-objective optimization problems. The specific process includes: First, the algorithm initializes a parent population Pt, whose individuals are selected from the candidate path set R. initial The system randomly selects a combination of paths, while strictly adhering to constraints such as the number of vehicles K. Next, an iterative loop is entered, through a series of genetic operations to continuously evolve the population, including using tournament selection to select parent individuals, and using operations such as crossover and mutation to generate the offspring population Qt. These operations also strictly adhere to constraints such as capacity and number of vehicles. After generating offspring, the parent and offspring are merged into a temporary population Rt, and a non-dominated sort is performed. This non-dominated sort is the core of NSGA-II, which divides all solutions into different Pareto fronts based on the performance of three objective functions f1, f2 and f3. Subsequently, after selecting the optimal Pareto front, the individuals on the front are ranked using crowding distance calculations to ensure population diversity and uniform distribution, and the next generation population P is selected accordingly. t+1 ; Finally, after all iterations are completed, an optimal solution is selected from the final Pareto optimal solution set as the input for the next step of repair.

6. The path planning method based on grouped path search and multi-objective fusion according to claim 1, characterized in that, Step S5 specifically includes the following steps: First, the solutions in the Pareto front solution set are repaired to handle illegal situations such as uncovered or duplicated customers that may be caused by multi-objective selection, so as to ensure the integrity and legality of each solution. This repair process specifically includes: for unserved customers, first check whether they can be greedily inserted into the existing path, that is, find the position with the lowest insertion cost and without violating vehicle capacity constraints; if all existing paths cannot accommodate the customer, then start a new vehicle and create a new path for them, and the nearest neighbor insertion strategy can be used as a supplement to find a better insertion point. For customers who require repeated services, adjustments are made based on the principles of lowest cost or most strained capacity to ensure that each customer is served only once. The lowest cost strategy aims to keep the customer on the path that contributes the least to their total distance, while the most strained capacity strategy aims to keep the customer on the path with the least remaining capacity to free up capacity on other paths. After the repair is completed, the solution with the shortest total path length is selected from this complete set of solutions as the initial solution, and it is input into the Iterative Local Search (ILS) module for further optimization to obtain the final high-quality express delivery route planning scheme.

7. A path planning system based on grouped path search and multi-objective fusion, characterized in that, include: Multi-strategy grouped path search unit: used to construct the initial solution space and generate paths; Single path optimization and candidate set generation unit: used to improve and optimize the quality of the initial paths obtained by group search, and to construct the final candidate solution set; Multi-objective path fusion and solution unit: used to make decisions on path splicing and perform Pareto optimization; Solution Repair and Final Optimization Unit: Used to repair the Pareto solution set obtained from multi-objective solution to handle illegal situations that may be caused by optimization trade-offs, such as uncovered customers (solved by greedy insertion or starting new vehicles) and duplicate covered customers (corrected by the principle of lowest cost or most limited capacity), to ensure that each solution satisfies the basic constraints of CVRP. After the repair, the algorithm selects the solution with the shortest total path length from the legal solution set as the initial solution and inputs it into the Iterative Local Search (ILS) module. The Iterative Local Search (ILS) module further optimizes the initial solution by alternating between perturbation and local search, effectively avoiding local optima, and finally outputting a stable and high-quality express delivery route planning solution.

8. A path planning system based on grouped path search and multi-objective fusion according to claim 7, characterized in that, The multi-strategy grouping path search unit uses complementary multi-strategy customer grouping methods to initialize customer partitions, including sector grouping based on the angular relationship between customer points and distribution centers, and K-Means spatial clustering based on the geographical proximity of customer points. Subsequently, for each independent group, the system performs a robust ant colony optimization (ACO) process, using pheromones and heuristics to guide ants in constructing intra-group path structures, thereby efficiently acquiring initial path structures within a local scope.

9. A path planning system based on grouped path search and multi-objective fusion according to claim 7, characterized in that, The single path optimization and candidate set generation unit, which is inherited from the ant colony optimization module, optimizes the best or near-best path found by each group using a high-performance local search algorithm (LKH3). Finally, all optimized single paths are aggregated to form a high-quality, structurally diverse candidate single path set P, providing a solid foundation for the path fusion in the next stage.

10. A path planning system based on grouped path search and multi-objective fusion according to claim 7, characterized in that, The multi-objective path fusion and solution unit models the complex path splicing problem as a multi-objective 0-1 optimization problem, where the decision variable represents whether to select a candidate path. The model simultaneously optimizes three competing key objectives: minimizing the total path length (economy), maximizing the number of uniquely covered customers (completeness), and minimizing redundant customer coverage (efficiency). To solve this multi-objective problem, this unit employs the efficient NSGA-II algorithm, which divides the solution set into different Pareto fronts through non-dominated sorting and uses crowding distance calculation to maintain the diversity and distribution of the solution set, thereby obtaining an optimal solution set that balances the three objective functions.

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