A two-stage vehicle routing planning method based on adaptive repartition heuristic algorithm

Abstract

The application discloses a two-stage vehicle routing planning method based on a self-adaptive re-partition heuristic algorithm, which solves a routing planning problem involving two types of fleets, responsible for meeting the mainline transportation and backhaul transportation demands of customers in a two-stage logistics system. The mainline transportation fleet is responsible for transporting goods between warehouses and intermediate facilities (satellite stations), while the feeder fleet operates between satellite stations and customers. The application provides an iterative optimization algorithm with adaptive re-partitioning and edge exchange for the two-stage and backhaul vehicle routing planning problem. The method can effectively decompose the two-stage optimization problem and adaptively refine the partition of the second stage according to the results of the last iteration, thereby helping to find the optimal solution.

Description

Technical Field

[0001] This invention pertains to logistics planning tasks, specifically involving a two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm. Background Technology

[0002] The two-stage vehicle routing problem has wide applications across various industries, including reverse logistics, municipal solid waste management, emergency logistics, and food logistics. By addressing these complex variables, the two-stage vehicle routing model provides a comprehensive framework for developing effective routing strategies to improve operational efficiency and reduce transportation costs, ultimately leading to enhanced overall competitiveness and customer satisfaction. The efficient solution to this problem has significant practical implications for businesses and organizations in the transportation and logistics industry, as it helps simplify operations, reduce costs, and improve overall competitiveness.

[0003] For most two-stage vehicle routing problems, the goal is to determine the optimal routes for two-tiered vehicles in a scenario where some customers have both up-trip (requiring goods to be transported from a warehouse) and return-trip (requiring goods to be transported back to a warehouse). The system comprises two fleets: a mainline transport fleet (Tier 1) and a feeder fleet (Tier 2). The mainline transport fleet is responsible for transporting goods from a central warehouse to intermediate facilities called satellites, while the feeder fleet manages the flow between satellites and customers. Vehicle routes must be designed to minimize travel costs while meeting each customer's up-trip and return needs and adhering to capacity constraints.

[0004] Compared to the traditional vehicle routing problem, the complexity of the two-stage vehicle routing problem stems from the need to simultaneously consider uphill and backhill operations, as well as two levels of path decisions. The key challenge in solving such a complex problem lies in designing efficient and scalable algorithms capable of solving large datasets within a reasonable timeframe. Currently, numerous algorithms exist in industry and academia for solving similar problems, such as exact algorithms, heuristics, and metaheuristic methods. However, each method has its limitations. On the one hand, while exact algorithms can reach the optimal solution, their computational complexity is extremely high, especially with very large problem sizes. On the other hand, heuristic algorithms require the development of problem-specific operators and extensive tuning of algorithm parameters to ensure high-quality solutions and computational efficiency. However, most heuristic methods are very limited in solving large and complex vehicle routing problems. Common operators (e.g., crossover, mutation, and neighborhood structure) primarily adjust the routes between vertices directly. As the problem size increases, the search space grows exponentially, making it difficult for these heuristic methods to find high-quality solutions within a reasonable timeframe. Summary of the Invention

[0005] Purpose of the invention: To address the challenges of trunk and return transportation needs for customers within a two-tier logistics system during actual logistics processes, this invention provides a two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm. This method aims to solve the problems of difficulty and long solution time in solving vehicle routing problems during actual logistics processes for enterprises.

[0006] Technical Solution: A two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm, used to address the trunk transportation and return transportation needs within a two-tier logistics system, comprising the following steps:

[0007] (1) Modeling the two-stage vehicle routing problem using a freight flow model, including:

[0008] Forward cargo flow linehaul, with l ij This represents the forward flow of goods from station i to station j;

[0009] Reverse cargo flow backhaul, with b ij This represents the reverse freight flow from station i to station j;

[0010] The remaining capacity flow remains capacity, in d ij This represents the remaining transport capacity of vehicles between station i and station j;

[0011] The following conditions must be met between the three types of cargo flows:

[0012]

[0013] in This represents the total positive logistics demand at station i. This represents the total reverse logistics demand at station j;

[0014] (2) Model initialization, and the initial partitions are constructed using two rules: the nearest satellite site construction and the maximum positive logistics weight construction.

[0015] The nearest satellite site construction method is based on a greedy strategy, which assigns each customer site to the nearest satellite site as a partition.

[0016] The maximum positive logistics weighting method prioritizes and assigns stations with the highest positive transport capacity.

[0017] This allocation process can be viewed as a 0-1 knapsack problem, and the allocation result can be obtained using a dynamic programming algorithm.

[0018] (3) For each partition, solve the problem based on the improved tabu algorithm;

[0019] In the tabu search algorithm, the neighborhood selection strategy is a best-solution-first strategy, and a tabu list is established. Solutions in the tabu list will not be adopted by the neighborhood selection strategy. However, when its step size reaches half of the total maximum number of iterations, the neighborhood selection strategy will ignore the tabu list.

[0020] (4) Determine the weights of various operators and reorganize the partitions;

[0021] (5) The improved tabu algorithm is used to solve it twice, and the quality of the solution is evaluated according to the objective function. The simulated annealing criterion determines whether to accept the solution.

[0022] (6) Repeatedly execute the above steps (3)-(5) until the solution obtained meets the preset requirements, and then output the optimal solution.

[0023] Furthermore, step (2) specifically includes the following process:

[0024] Suppose there are n customer sites, and their forward logistics demands are w1, w2, ... w n Let j represent the total load in the current state, and define ψ. ij The optimal solution for the first i customers with a capacity limit of j is ψ, which represents the maximum load under that condition. When considering more customers, ψ... ij Each update is performed according to the following formula:

[0025]

[0026] In the above method, the operators in step (4) include six types: farthest distance removal, weighted worst-case removal, random removal, nearest insertion, regression insertion, and random insertion; among which:

[0027] The furthest distance removal option removes the customer site that is furthest from the satellite within that partition.

[0028] The most recently inserted site is the customer site closest to the satellite.

[0029] The weighted worst-case removal is a weighted sum that takes into account customer demand and site distance. The weights are calculated as follows:

[0030]

[0031] Random removal and random insertion mean randomly selecting sites for deletion or insertion.

[0032] Furthermore, step (4) uses the roulette wheel selection criterion to select operators, with each operator having equal weight in the initial state; Ω + and Ω - For the set of destruction operators and the set of repair operators, for each destruction operator ω + and ω- Each will have a weight θ i In the j-th iteration, the weights will be updated according to the following formula:

[0033]

[0034] In the above formula, λ1λ2 are the reaction coefficients, μ is a Boolean variable that takes the value 1 when the solution is better than the previous solution and 0 otherwise, and Δf is the sum of the two solutions s. j With s j-1 The difference, f(s) j ) represents the objective function value of this solution.

[0035] In the above method, the probability P of accepting a new solution in the simulated annealing criterion described in step (5) is:

[0036]

[0037] Where Δf is the difference between the objective functions of the old and new solutions, and T c Current temperature:

[0038]

[0039] Where T0 is the initial temperature, and loop is the current loop number. max Let P be the maximum loop limit and P be the minimum acceptance probability.

[0040] Beneficial effects: Compared with existing precise algorithms and heuristic algorithms, this invention can quickly search for high-quality solutions in the two-stage vehicle routing problem, and can provide theoretical guidance for logistics companies. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a cargo flow model;

[0042] Figure 2 This is a schematic diagram of the adaptive repartitioning algorithm;

[0043] Figure 3 This is a graph showing the results analysis under different operator structures. Detailed Implementation

[0044] To illustrate the technical solution disclosed in this invention in detail, a specific description is provided below.

[0045] This invention proposes a two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm. This method is a hybrid algorithm combining the advantages of divide-and-conquer and large-scale neighborhood search algorithms. The divide-and-conquer approach decomposes the massive two-stage vehicle routing problem into several easier-to-solve basic vehicle routing problems, which are then solved using an improved tabu algorithm. Simultaneously, an adaptive repartitioning heuristic adjusts the partitions of the divide-and-conquer approach. During this adjustment, multiple operators are employed, and their weights are adjusted based on historical improvement magnitudes. This process is repeated N times, and after multiple iterations, the optimal solution tends to stabilize.

[0046] In this implementation, based on Figure 1 The illustrated model uses three types of cargo flows to model a two-stage logistics process, including forward cargo flow (linehaul), and... ij This represents the forward freight flow from station i to station j; the reverse freight flow, represented by b. ij This represents the reverse cargo flow from station i to station j; the remaining capacity flow is represented by d. ij This represents the remaining transport capacity of vehicles between station i and station j. The following conditions must be met for the three types of freight flows to be compatible:

[0047]

[0048] in This represents the total positive logistics demand at station i. This represents the total reverse logistics demand at station j. Figure 1 The example shown is a simple three-way logistics model based on a single satellite station and three customers. In this logistics model, the total forward logistics demand, total reverse logistics demand, and remaining capacity between each station are presented.

[0049] Figure 2 This is a schematic diagram of the overall framework of the adaptive repartitioning heuristic structure provided by the present invention. The algorithm obtains an initial solution from the initialization rules. The initial solution assigns each customer site to a satellite site, which is responsible for the logistics and delivery tasks of the assigned sites. The site assignments are then adjusted according to the repartitioning rules, and the process is iterated repeatedly until the exit criterion is met.

[0050] A two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm is proposed. In step (2), two rules are used: nearest satellite station construction and maximum forward logistics weight construction. The nearest satellite station construction method is based on a greedy strategy, assigning each customer station to the nearest satellite station as a partition. The maximum forward logistics weight construction method prioritizes assigning stations to the stations with the highest forward logistics capacity. This allocation process can be regarded as a 0-1 knapsack problem, and the allocation result is obtained using a dynamic programming algorithm. Specifically, assuming there are n customer stations and forward logistics demands w1, w2...w n Let j represent the total load in the current state. Define ψ. ij The optimal solution is given for the first i customers with a capacity limit of j, which represents the maximum load under that condition. When considering more customers, ψ... ij Each update is performed according to the following formula:

[0051]

[0052] The two-stage vehicle path planning method based on the adaptive repartition heuristic algorithm, in step (3), uses an improved tabu search algorithm to solve for sub-results.

[0053] Furthermore, in the tabu search algorithm, the neighborhood selection strategy is a best-solution-first strategy, and a tabu list is established. The length of the tabu list is set to the number of customer sites, n. Solutions in the tabu list will not be adopted by the neighborhood selection strategy. However, after a certain step size, the neighborhood selection strategy will ignore the tabu list. Here, the step size is set to half of the total maximum number of iterations.

[0054] The two-stage vehicle routing method based on the adaptive repartitioning heuristic algorithm includes six preset operators: farthest distance removal, weighted worst-case removal, random removal, nearest insertion, regression insertion, and random insertion. Farthest distance removal removes the customer station furthest from the satellite in the partition; nearest insertion inserts the customer station closest to the satellite. Weighted worst-case removal is a weighted sum considering customer demand and station distance, with the weights calculated as follows:

[0055]

[0056] Random removal and random insertion mean randomly selecting sites for deletion or insertion.

[0057] In this method, the probability P of accepting a new solution in the simulated annealing criterion is:

[0058]

[0059] Where Δf is the difference between the objective functions of the old and new solutions, and Tc Current temperature:

[0060]

[0061] Where T0 is the initial temperature, and loop is the current loop number. max Let P be the maximum loop limit and P be the minimum acceptance probability. In this example, the minimum acceptance probability P = 0.06, and the initial temperature is set to 1.

[0062] In this algorithm, the roulette wheel selection criterion is used to select operators, and each operator has an equal weight in the initial state. Ω + and Ω - For the set of destruction operators and the set of repair operators, for each destruction operator ω + and ω _ Each will have a weight θ i In the j-th iteration, the weights will be updated according to the following formula:

[0063]

[0064] In the above formula, λ1λ2 are the reaction coefficients, μ is a Boolean variable that takes the value 1 when the solution is better than the previous solution, and 0 otherwise. Δf represents the sum of the two solutions s. j With s j-1 The difference, f(s) j ) represents the objective function value of this solution.

[0065] In this example, reaction coefficients λ1 = 0.07, λ2 = 10, and initial weights θ are selected. i All values ​​are set to 1. For small-scale cases (those with fewer than 32 customer sites), the total number of iterations is set to 32. For large-scale cases, the total number of iterations is set to 128. The maximum solution time is also limited to 900 seconds.

[0066] The present invention will be compared and verified below.

[0067] The adaptive repartitioning heuristic algorithm and the adaptive large-scale neighborhood algorithm described in this invention were compared using a widely validated two-stage vehicle routing problem dataset. This dataset has a known best solution, facilitating the assessment of solution quality. The solution algorithm was written in Python and interpreted and executed by a Python interpreter under Linux. The solution results are shown in Table 1. The results show that the method described in this invention can achieve the same results as the known optimal solution in Set2a, Set2b, Set2c, Set3a, and Set3c. Compared to the adaptive large-scale neighborhood algorithm, it can provide solution results closer to the known optimal solution under the same constraints. The average difference from the known optimal solution is only 0.43%.

[0068] Table 1 compares the adaptive repartitioning heuristic algorithm and the adaptive large-scale neighborhood algorithm.

[0069]

[0070] See Figure 3 The figure illustrates the impact of each operator described in this invention on the algorithm. In this experiment, Set2a, Set2b, Set4b, and Set5 from Table 1 were selected as validation datasets for customer numbers of 21, 32, 50, and 100, respectively. In the Greedy-Repart strategy, only greedy operators were used, including four strategies: farthest removal, worst-weight removal, nearest insertion, and regression insertion. In the Random-Repart strategy, only random operators were used, including two strategies: random removal and random insertion. Compared to random strategies, the greedy strategy achieved relatively better results. However, in any problem size, the lack of operators will affect the quality of the solution, resulting in a 0.2%-3% performance loss compared to having all operators. In summary, the algorithm provided by this invention can improve the quality of solutions in two-stage vehicle pathing scenarios within a limited solution time, making it very suitable for solving two-stage vehicle pathing problems.

Claims

1. A two-stage vehicle routing method based on an adaptive repartitioning heuristic algorithm, used to address the trunk transportation and return transportation needs within a two-tier logistics system, characterized in that... Includes the following steps: (1) Modeling the two-stage vehicle routing problem using a freight flow model, including: positive cargo flow linehaul, to Indicates site Arrive at the station Positive cargo flow; Reverse cargo flow backhaul, to Indicates site Arrive at the station Reverse cargo flow; The remaining capacity flow remains capacity. Indicates site Arrive at the station Remaining vehicle capacity; The following conditions must be met between the three types of cargo flows: in Indicates at the site Positive total logistics demand at that time Indicates on the site Total reverse logistics demand at that time; (2) Model initialization, and the initial partitions are constructed using two rules: the nearest satellite site construction and the maximum positive logistics weight construction. The nearest satellite site construction method is based on a greedy strategy, which assigns each customer site to the nearest satellite site as a partition. The maximum positive logistics weighting method prioritizes assigning stations to those with the highest positive transport capacity. The allocation process can be viewed as a 0-1 knapsack problem. The allocation result is obtained using a dynamic programming algorithm, as follows: Assume there are... Each customer site has the following forward logistics needs: , This indicates the total load in the current state, and defines... For in front Number of customers, capacity limit is The optimal solution at that time is the maximum load under that condition; when considering more customers, It will be updated according to the following formula: ； (3) For each partition, solve the problem based on the improved tabu search algorithm; In the improved tabu search algorithm, the neighborhood selection strategy is a best solution priority strategy, and a tabu list is set up. Solutions in the tabu list will not be adopted by the neighborhood selection strategy; however, when its step size reaches half of the total maximum number of iterations, the neighborhood selection strategy will ignore the tabu list. (4) Determine the weights of various operators and reorganize the partitions; The operators include six types: farthest distance removal, weighted worst-case removal, random removal, nearest insertion, regression insertion, and random insertion; among which: The furthest distance removal option removes the customer site that is furthest from the satellite within that partition. The most recently inserted site is the customer site closest to the satellite. The weighted worst-case removal is a weighted sum that takes into account customer demand and site distance. The weights are calculated as follows: Random removal and random insertion mean randomly selecting sites for deletion or insertion. Operators are selected using the roulette wheel selection criterion, with each operator having an equal weight set in the initial state. and For the set of destruction operators and the set of repair operators, for each destruction operator... and There will be a weight. , in the In this iteration, the weights will be updated according to the following formula: In the above formula, The reaction coefficient, It is a Boolean variable that takes the value 1 when the solution is better than the previous solution, and 0 otherwise. For two solutions and The difference, This is the objective function value of the solution. (5) The improved tabu search algorithm is used to solve it twice, and the quality of the solution is evaluated according to the objective function. The simulated annealing criterion determines whether to accept the solution. In the simulated annealing criterion, the probability of accepting a new solution is... for: in This represents the difference in objective functions between the old and new solutions. Current temperature: in The initial temperature, This represents the current loop count. The maximum loop limit, The lowest probability of acceptance; (6) Repeatedly execute the above steps (3)-(5) until the solution obtained meets the preset requirements, and then output the optimal solution.

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