Self-adaptive large neighborhood search method based on feasibility time window and forward and backward adjustment algorithm

Abstract

The invention relates to the technical field of logistics distribution, and discloses an adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm, and the method comprises the steps: constructing a vehicle path planning model containing the maximum residence time constraint; randomly generating a coding sequence of a client node as a current solution of the model; calculating feasibility time windows of all client nodes of the current path through a forward and backward adjustment algorithm, and adding the next node of the coding sequence into the current path or taking the vehicle path of the node to be distributed as a new current path; repeating the above steps until the coding sequence is decoded into a plurality of vehicle paths; calculating the total driving cost of the plurality of decoded vehicle paths; obtaining a new solution according to the destruction operator and the repair operator; calculating the total driving cost of the new solution, and updating the operator weight according to whether the new solution is superior to the current solution in the aspect of the total driving cost; and taking the new solution as the current solution, and repeating the above steps until a set termination condition is met. According to the method, the maximum residence time constraint and a feasibility time window dynamic adjustment mechanism are introduced, so that the algorithm can better deal with complex problems in reality, and has higher practical applicability.

Description

Technical Field

[0001] The present invention relates to the field of logistics distribution technology, and in particular to an adaptive large neighborhood search method based on a feasibility time window and a forward and backward adjustment algorithm. Background Art

[0002] The vehicle routing problem with time windows and maximum dwell time is a variant of the classic vehicle routing problem (VRP).

[0003] Patent application number CN115759917A discloses a logistics path planning method based on an improved hybrid ant colony algorithm, aiming to solve the vehicle path planning problem in logistics distribution. Its main technical solutions include:

[0004] (1) Establish a logistics distribution task scheduling network model: Generate a logistics distribution task scheduling network model based on the route relationship between distribution points, the route relationship between distribution points and distribution centers, and the constraint information of each distribution point and distribution route distribution vehicle.

[0005] (2) Comprehensive consideration of multiple objectives: The objective function of the logistics distribution task scheduling network model is established by comprehensively considering the three objectives of minimizing costs, minimizing customer disappointment, and minimizing driver load imbalance.

[0006] (3) Improved hybrid ant colony algorithm: The hybrid ant colony algorithm is improved based on the path planning design of logistics distribution, including the introduction of the saving matrix update probability formula to guide ants to search for paths, the use of piecewise function to improve the pheromone volatility factor, the elite ant colony using the ant week model to update pheromones, the ordinary ants using the ant quantity model to update pheromones, and the use of the 3-opt algorithm to improve the local search ability of the hybrid ant colony algorithm.

[0007] (4) Solving the objective function: The improved hybrid ant colony algorithm is used to solve the objective function, and the NSGA-III fast non-dominated sorting algorithm is used to obtain a better non-dominated solution, and a non-dominated solution set is obtained. The optimal solution for logistics distribution path planning is obtained from the non-dominated solution set.

[0008] Patent application publication number CN110705741A discloses a multi-distribution center vehicle routing optimization method, which aims to solve the multi-distribution center vehicle routing optimization problem. Its main technical solutions include:

[0009] (1) Define the objective function: Establish the objective function of vehicle path optimization, taking into account the penalty function of the vehicle's total driving distance, total carbon emissions, and time window.

[0010] (2) Initialization parameters: set parameters such as ant population size, pheromone heuristic factor, visibility heuristic factor, and conservation matrix heuristic factor.

[0011] (3) Path construction: The next customer node is selected through the roulette method, and the passed customer nodes are stored in the taboo table to construct the vehicle path.

[0012] (4) Local optimization: Use the 3-opt algorithm to perform local optimization on the path to improve the feasibility of the path.

[0013] (5) Update pheromone: Update pheromone according to the segmented pheromone volatility factor, pheromone update method and number of iterations of the improved hybrid ant colony algorithm.

[0014] (6) Non-dominated sorting: Use the NSGA-III algorithm to perform non-dominated sorting on the population, obtain a non-dominated solution set, and select the optimal solution from it.

[0015] Patent application number CN114118621A discloses a logistics distribution path optimization method based on an improved ant colony algorithm, aiming to solve the vehicle path optimization problem in logistics distribution. Its main technical solutions include:

[0016] (1) Establish a low-carbon logistics model: Establish a low-carbon logistics model system, taking into account the carbon emissions of vehicles and transportation costs.

[0017] (2) Design objective function: Design objective function, including minimizing total driving distance, minimizing total carbon emissions, and minimizing penalty functions of time window.

[0018] (3) Improved ant colony algorithm: The probability formula of saving matrix update is introduced to guide ants to search for paths, and the piecewise function is used to improve the pheromone volatility factor. The elite ant colony uses the ant-period model to update pheromones, and the ordinary ants use the ant-quantity model to update pheromones.

[0019] (4) Local optimization: The 3-opt algorithm is used to improve the local search capability of the ant colony algorithm and optimize the path.

[0020] (5) Solving the optimal solution: Solve the objective function by improving the ant colony algorithm to obtain the optimal logistics distribution path.

[0021] Existing vehicle routing methods have the following drawbacks when addressing maximum dwell time constraints: First, traditional methods such as genetic algorithms and ant colony algorithms primarily focus on time windows and capacity constraints, failing to effectively integrate the maximum dwell time constraint at customer nodes. This results in excessively long waiting times for vehicles at customer nodes, reducing resource utilization and increasing logistics costs. For example, while patent application publication number CN115759917A comprehensively considers the three objectives of minimizing costs, minimizing customer frustration, and minimizing driver load imbalance, in practice these objectives can conflict, making simultaneous optimization difficult, especially under the maximum dwell time constraint.

[0022] Secondly, existing algorithms struggle to dynamically adjust the feasibility interval of time windows during route optimization, making them inefficient in handling multi-constraint coupling problems. For example, when a vehicle's stay at a customer node exceeds the maximum allowed time, existing algorithms often fail to adjust the route in a timely manner, resulting in a decrease in overall efficiency. For example, patent application publication number CN110705741A proposes a method for optimizing vehicle routes across multiple distribution centers. However, the method still has certain limitations when dealing with coordination and route optimization between multiple distribution centers. The algorithm's stability can be affected by data fluctuations, leading to unstable route optimization results.

[0023] Furthermore, existing algorithms are prone to becoming trapped in local optimal solutions and lack global search capabilities, making them unable to provide logistics companies with path planning tools that are more tailored to real-world scenarios. For example, while the improved hybrid ant colony algorithm has improved the efficiency of path optimization to a certain extent, the algorithm's adaptability may be insufficient when dealing with different types of logistics and distribution problems. For example, while patent application publication number CN114118621A considers a low-carbon logistics model, in actual applications, the calculation and optimization of carbon emissions may be affected by multiple factors, making it difficult to accurately control. This is especially true under the constraint of maximum residence time, where the algorithm's adaptability may be insufficient. Summary of the Invention

[0024] In order to solve the above technical problems, the present invention provides an adaptive large neighborhood search method based on a feasibility time window and a forward and backward adjustment algorithm.

[0025] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0026] An adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm comprises the following steps:

[0027] S1, build a vehicle routing model with a maximum dwell time constraint. The objective function is to minimize the total travel cost. The constraints include customer node service uniqueness, vehicle departure and return from the warehouse, flow conservation, capacity constraint, and time window constraint.

[0028] S2, randomly generates a coding sequence of customer nodes as the current solution of the vehicle path planning model;

[0029] S3, taking the vehicle path from the warehouse to the first customer node in the encoding sequence of the current solution as the current path;

[0030] S4, calculating the feasibility time windows of all customer nodes on the current path using a forward-backward adjustment algorithm, and taking the next node in the coding sequence as the node to be assigned; calculating the feasibility time window of the node to be assigned based on the feasibility time windows of all customer nodes on the current path, and determining whether the vehicle can arrive and complete the service within the feasibility time window of the node to be assigned. If so, the node to be assigned is added to the current path; if not, the vehicle path from the warehouse to the node to be assigned is used as the new current path;

[0031] S5, repeating step S4 until the encoded sequence is decoded into multiple vehicle paths; calculating the total driving cost of the decoded multiple vehicle paths using the objective function;

[0032] S6: Select a destruction operator to delete the client node in the current solution and a repair operator to insert the client node in the current solution based on the operator weights, thereby obtaining a new solution; calculate the total travel cost of the new solution through steps S4 and S5, and update the weights of the destruction operator and the repair operator based on whether the new solution is better than the current solution in terms of total travel cost;

[0033] S7: Take the new solution as the current solution and repeat step S6 until the set termination condition is met.

[0034] In one embodiment, constructing a vehicle path planning model with a maximum dwell time constraint specifically includes:

[0035] The vehicle routing model with time windows and maximum dwell time is as follows: there is a central warehouse and several customer nodes. Each customer node has a certain demand and must be served within a specified time window. Each vehicle has a limited capacity and must depart from the warehouse, serve a set of customer nodes, and then return to the warehouse. The goal is to design a set of vehicle routes that meet the following conditions:

[0036] Each client node is served by one and only one vehicle;

[0037] The total cargo volume of each vehicle does not exceed the capacity limit of that vehicle;

[0038] The time when the vehicle arrives at each customer node must be within the time window of the customer node;

[0039] The vehicle's stay time at each customer node does not exceed the maximum stay time;

[0040] The total travel cost is minimized.

[0041] In one embodiment, the parameters of the vehicle path planning model include:

[0042] Node set V = {0, 1, 2, ..., n}, where 0 represents the warehouse node and 1, 2, ..., n represents the 1st to nth customer nodes;

[0043] Vehicle set K;

[0044] The travel cost c from customer node i to customer node j ij ;

[0045] The demand d of customer node i i ;

[0046] The capacity Q of each vehicle;

[0047] The time window of client node i[e i ,l i ], where e i is the earliest service time of client node i, l i is the latest service time of customer node i;

[0048] Service time u at customer node i i ;

[0049] Travel time t from customer node i to customer node j ij ;

[0050] Maximum dwell time MDT of vehicle k k ;

[0051] The decision variables of the vehicle path planning model include:

[0052] A binary variable x indicating whether vehicle k travels from customer node i to customer node j ijk ;

[0053] The time a that vehicle k arrives at customer node i ik ;

[0054] The service start time s of vehicle k at customer node i ik .

[0055] In one embodiment, the objective function is to minimize the total driving cost, specifically including:

[0056] The objective function is: min∑ k∈k ∑ i∈V ∑ j∈V c ij x ijk .

[0057] In one embodiment, the constraints include customer node service uniqueness, vehicle departure from and return to the warehouse, flow conservation, capacity constraints, and time window constraints, specifically including:

[0058] Client node service uniqueness, that is, each client node is served once: ∑ k∈K ∑j∈V x ijk =1, V\{0} represents the node set V without the warehouse node;

[0059] Vehicles depart from the warehouse and return to the warehouse: ∑ j∈V\{0} x 0jk =1,∑ i∈V\{0} x i0k =1,

[0060] Traffic conservation, that is, the vehicle must leave the customer node after reaching it: ∑ i∈V x ihk -∑ j∈V x hjk =0,

[0061] Capacity constraint, that is, the total cargo volume of the vehicle does not exceed the capacity limit of the vehicle: ∑ i∈V d i ∑ j∈V x ijk ≤Q,

[0062] Time window constraints, including:

[0063] Time iteration constraints on vehicle paths: a ik +u i +t ij ≤a j +M(1-x ijk ), M(·) represents the penalty factor, which is an infinite value;

[0064] The vehicle's stay time does not exceed the maximum stay time of the vehicle: a ik ≤s ik ≤a ik +MDT k ,

[0065] The vehicle's service start time needs to be within the customer's time window i ≤s ik ≤l i ,

[0066] Variable scope: x ijk ∈{0,1},a ik ≥0,s ik ≥0.

[0067] In one embodiment, calculating the feasibility time window of all client nodes on the current path by using the forward and backward adjustment algorithm specifically includes:

[0068] The feasibility time window includes the feasible arrival time window and the feasible service start time window. The forward-backward adjustment algorithm gradually reduces and eliminates the infeasible intervals in the time window through iteration, and calculates the feasible arrival time window and feasible service start time window of each customer node on the vehicle path.

[0069] The forward adjustment algorithm is used to calculate the path of a given vehicle The feasibility time window of each customer node in ; where 0 and 0' represent the warehouse that the vehicle leaves and the same warehouse that the vehicle arrives at when it returns, Indicates that the vehicle arrives at the hth customer node i on the vehicle path h Time and client node i h Service start time r is the total number of customer nodes in the vehicle path;

[0070] Client node i h The lower bound of the feasible arrival time for:

[0071]

[0072] is client node i h The earliest service time, For client node i h The maximum residence time, Represents customer node i h-1 The lower limit of the feasible service start time, Represents customer node i h-1 Service time, is the travel time of the vehicle from customer node i to customer node j;

[0073] Client node i h The upper limit of the feasible arrival time for:

[0074]

[0075] is client node i h The latest service time, For client node i h-1 The upper limit of the feasible service start time; among them,

[0076]

[0077] The feasible arrival time window is The feasible service start time window is

[0078] The backward adjustment algorithm further optimizes the feasibility time window by propagating constraints forward from subsequent client nodes:

[0079] For the last customer node i in the vehicle path r :

[0080]

[0081] For client node i h , h=1,…,r-1:

[0082]

[0083] In one embodiment, the feasibility time window of the node to be assigned is calculated based on the feasibility time windows of all customer nodes on the current path, and it is determined whether the vehicle can arrive at and complete the service of the node to be assigned within the feasibility time window of the node to be assigned. If so, the node to be assigned is added to the current path; if not, the vehicle path from the warehouse to the node to be assigned is used as the new current path, specifically including:

[0084] For each current client node i r , evaluate the subsequent customer node i h Whether it is possible to insert it to the end of the current vehicle path to form a longer feasible loop:

[0085] Through the current client node i r Feasible service start time window Calculate customer node i h Feasibility reaches the time window are client nodes i h The feasibility reaches the lower and upper limits of the time window; are client nodes i r The lower and upper limits of the feasible service start time window;

[0086] Determine whether: or is client node i h The earliest service time, For client node i h The maximum residence time, is client node i h The latest service time of client node i; if so, the subsequent client node i h It cannot form a loop with the current vehicle path; if not, the subsequent customer node ih Ability to insert at the end of the current vehicle path.

[0087] In one embodiment, the selective destruction operator deletes the client node in the current solution, specifically comprising:

[0088] The destruction operator is used to remove client nodes from the current solution to expand the search space. When the destruction operator is applied, a certain number of client nodes are removed from the vehicle path corresponding to the current solution and added to the deleted node set R. The destruction operator includes:

[0089] Random customer deletion: Randomly select and delete a specified number of customer nodes, and add the deleted customer nodes to R. Each customer node has an equal probability of being selected until the required number of customer nodes are deleted.

[0090] Continuous customer deletion: delete multiple consecutive customer nodes and add the deleted customer nodes to R;

[0091] Minimum customer path deletion: Identify the minimum customer node paths in the current solution and delete all customer nodes in these paths, adding the deleted customer nodes to the deleted node set R;

[0092] Most customer paths deleted: Identify the paths with the most customer nodes in the current solution, delete all customer nodes in these paths, and add the deleted customer nodes to the deleted node set R;

[0093] Path deletion: randomly select and completely delete several paths in the current solution, and add the deleted client nodes to the deleted node set R;

[0094] Partial path deletion: Randomly select a path in the current solution, then randomly select a customer node on the path, and add the deleted customer node to the deleted node set R.

[0095] In one embodiment, the selective repair operator inserts a client node into the current solution, specifically comprising:

[0096] After deleting a client node, the repair operator reinserts each client node in the deleted node set R into the current solution in a specific order. The repair operator includes:

[0097] Random insertion: insert the customer nodes in the deleted node set R into the path corresponding to the current solution in random order;

[0098] Greedy insertion: For each customer node in the deleted node set R, traverse the path to find a suitable insertion position, satisfy the problem constraints and form a new path. Customer nodes that cannot be inserted into the existing path will be added to the beginning or end of the path corresponding to the current solution;

[0099] End insertion: Randomly disrupt the order of the client nodes in the deleted node set R, and insert all client nodes consecutively to the end of the path corresponding to the current solution;

[0100] Insert at the beginning: Randomly disrupt the order of the client nodes in the deleted node set R, and insert all client nodes consecutively to the beginning of the path corresponding to the current solution.

[0101] In one embodiment, the updating of the weights of the destruction operator and the repair operator according to whether the new solution is better than the current solution in terms of total travel cost specifically includes:

[0102] Each destruction operator and repair operator has a fraction π k and a probability measure ω k ;

[0103] In each iteration, we first calculate the probability metric ω of each destruction operator based on k The destruction operator is selected according to the roulette wheel, and the probability of each destruction operator being selected is Delete the client node from the current solution; then again based on the probability ω of each repair operator k The repair operator is selected according to the roulette wheel, and the probability of each repair operator being selected is The deleted client nodes are reinserted into the current solution to form a new solution; h is the total number of destruction operators or repair operators;

[0104] Then the total driving cost of the new solution is evaluated, and π is updated according to the performance of the new solution. k and ω k The value of

[0105] If the new solution performs better than the optimal solution, the fraction of destruction and repair operators that are selected is π k The first score σ1 is increased and the new solution is taken as the new optimal solution;

[0106] If the new solution performs better than the current solution but worse than the optimal solution, the fraction of the destruction and repair operators selected is π k Both increase the second fraction σ2;

[0107] If the new solution performs worse than the current solution, the simulated annealing algorithm is used to decide whether to accept the new solution; if the new solution is accepted, the fraction of the selected destruction operator and repair operator is π k Both increase the third fraction σ3;

[0108] According to the fraction π k Update the probability measure of the destruction operator and the repair operator:

[0109]

[0110] u k Indicates whether the destruction operator or repair operator is used in the current iteration, u k =0 means that the destruction operator or repair operator is not used; u k =1 means that the destruction operator or repair operator is used; ρ represents the smoothing parameter, which is used to control the learning speed of the operator weight;

[0111] In the current iteration, if the new solution performs better than the optimal solution, the temperature of the simulated annealing algorithm will increase; otherwise, the current temperature will decrease at a cooling rate of 0.9.

[0112] Compared with the prior art, the beneficial technical effects of the present invention are:

[0113] Significantly reduce operating costs: The present invention significantly reduces the operating costs of logistics companies by optimizing the vehicle's residence time at customer nodes, reducing waiting time and improving resource utilization.

[0114] Improve path planning efficiency: The present invention makes path planning more efficient and accurate through the collaborative optimization of forward and backward adjustment algorithms, and can quickly generate the optimal path that meets all constraints.

[0115] Enhanced algorithm robustness: This invention integrates the adaptive large neighborhood search algorithm with the simulated annealing mechanism, so that the algorithm can effectively avoid falling into the local optimal solution when facing complex problems, and has stronger robustness and stability.

[0116] Improve supply chain efficiency: This invention optimizes the logistics and distribution process and improves the overall efficiency of the supply chain by providing a route planning tool that is more in line with actual scenarios.

[0117] Enhanced reality applicability: The present invention introduces a maximum residence time constraint and a dynamic adjustment mechanism for the feasibility time window, so that the algorithm of the present invention can better cope with complex problems in reality and has stronger real-world applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 Flowchart of a method in an embodiment of the present invention. DETAILED DESCRIPTION

[0119] A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0120] Purpose of the present invention:

[0121] (1) Integrating Maximum Dwell Time Constraints: Existing vehicle routing problems with time windows (VRPTW) primarily focus on time windows and capacity constraints, ignoring the maximum dwell time constraints of vehicles at client nodes. This often results in reduced resource utilization and increased logistics costs due to excessive waiting times. This invention introduces a maximum dwell time constraint to optimize the dwell time of vehicles at client nodes, improve resource utilization efficiency, and reduce operating costs.

[0122] (2) Improved dynamic adjustment capabilities: Traditional algorithms have difficulty dynamically adjusting the feasibility interval of the time window during path optimization and are unable to efficiently handle multi-constraint coupling problems. This invention uses a forward and backward adjustment algorithm to dynamically optimize the time window, ensuring the feasibility of the path while satisfying multiple constraints.

[0123] (3) Enhanced algorithm robustness: Existing algorithms are prone to falling into local optimal solutions and lack global search capabilities. This invention integrates the adaptive large neighborhood search (ALNS) algorithm with the simulated annealing mechanism to balance global search and local optimization, avoid falling into local optimal solutions, and improve the robustness and stability of the algorithm.

[0124] (4) Improved practical applicability: Traditional methods lack real-world applicability and cannot effectively solve complex problems in the real world. By introducing a maximum dwell time constraint and a dynamic adjustment mechanism for the feasibility time window, this invention provides logistics companies with a path planning tool that is more in line with real-world scenarios, thereby reducing operating costs and improving supply chain efficiency.

[0125] 1. Problem description and mathematical model construction:

[0126] 1.1, Problem Description:

[0127] The vehicle routing problem with time windows and maximum dwell time (abbreviated as VRPTW-MDT) involved in the present invention is a variant of the classic vehicle routing problem (VRP). This problem has broad application prospects and important practical significance in many fields such as logistics distribution, transportation scheduling and supply chain management. Specifically, the VRPTW-MDT problem not only requires optimizing the vehicle's driving path to minimize the total cost (for example, the total driving distance, the number of vehicles used, etc.), but also needs to simultaneously meet the customer's time window constraints and the maximum dwell time constraints of the vehicle at the customer node. By rationally planning the vehicle's driving route and service time, the logistics distribution efficiency can be effectively improved, the operating cost can be reduced, and the customer satisfaction can be improved. The vehicle routing problem with time windows considering the maximum dwell time can be described as: there is a central warehouse and several customer nodes. Each customer node has a certain demand and must be within a specified time window [e i ,l i ] is served, where e i is the earliest service time, l i is the latest service time. Each vehicle has limited capacity and must depart from the warehouse, serve a group of customers, and then return to the warehouse. The goal is to design a set of vehicle routes that satisfy the following conditions:

[0128] (1) Each client node is served by only one vehicle;

[0129] (2) The total cargo volume of each vehicle does not exceed its capacity limit;

[0130] (3) The time when the vehicle arrives at each customer node must be within its time window;

[0131] (4) The vehicle's stay time at each customer node does not exceed the maximum stay time;

[0132] (5) Minimize total cost (such as total distance traveled, number of vehicles used, etc.).

[0133] 1.2, Mathematical model:

[0134] The VRPTW problem can usually be expressed by the following mathematical model:

[0135] Parameters include:

[0136] V = {0, 1, 2, ..., n}: node set, where 0 represents the warehouse and 1, 2, ..., n represents the customer node;

[0137] K: vehicle set;

[0138] cij : the travel cost (such as distance or time) from node i to node j;

[0139] d i : the demand of customer node i;

[0140] Q: The capacity of each vehicle;

[0141] [e i ,l i ]: time window of client node i;

[0142] u i : service time at customer node i;

[0143] t ij : Travel time from node i to node j;

[0144] MDT k : The maximum dwell time of vehicle k.

[0145] The decision variables include:

[0146] x ijk : Binary variable, indicating whether vehicle k travels from node i to node j;

[0147] a ik : The time when vehicle k arrives at customer node i;

[0148] s ik : The starting service time of vehicle k at customer node i.

[0149] Related data can be stored in Table 1, c ij It can be calculated from the x and y coordinates of the client node.

[0150] Table 1

[0151] serial number Demand X coordinate Y coordinate Time window start time Time window end time Service Hours Maximum residence time 1 59 6.2 0.64 840 1142 5 73 2 50 28.03 14.24 174 535 5 81 3 65 11 -15 238.5 494 5 93 4 15 5 -15 444 665 5 83 5 15 -16.06 13.69 988 1216 5 99 6 86 28.03 14.24 132 480 5 55 7 59 6.2 0.64 840 2000 5 55 8 50 28.03 14.24 174 2000 5 86 9 65 11 -15 238.5 2000 5 65

[0152] 1.3, objective function:

[0153] Minimize the total driving cost: min∑ k∈K ∑ i∈V ∑ j∈V c ij x ijk ;

[0154] 1.4, Constraints:

[0155] (1) Each client node is served once: ∑ k∈K ∑ j∈V x ijk =1,

[0156] (2) The vehicle departs from the warehouse and returns to the warehouse: ∑ j∈V\{0} x 0jk =1,∑ i∈V\{0} x i0k =1,

[0157] (3) Traffic conservation (a vehicle must leave a customer after arriving at the customer): ∑ i∈V x ihk -∑ j∈V x hjk =0,

[0158] (4) Capacity constraint (the total delivery volume of the vehicle does not exceed the vehicle's load capacity): ∑ i∈V d i ∑ j∈V x ijk ≤Q, (5) Time window constraints, including:

[0159] Time iteration constraints on vehicle paths: a ik +u i +t ij ≤a j +M(1-x ijk ), The vehicle's stay time does not exceed the maximum stay time of the vehicle: a ik ≤s ik ≤a ik +MDT k , The vehicle's service start time needs to be within the customer's time window: i ≤s ik ≤l i ,

[0160] (6) Variable range: x ijk ∈{0,1},a ik ≥0,s ik ≥0.

[0161] 2. Forward and backward adjustment algorithm design:

[0162] 2.1, Maximum residence time

[0163] The maximum dwell time refers to the maximum allowed dwell time of a vehicle after arriving at a customer's location. Even if a vehicle arrives at a customer's location within the customer's time window, it can still remain for a period of time, as long as service begins within the customer's time window. This benefit not only helps balance the time distribution of nodes along the route, avoiding long wait times due to arriving at a customer node too early, thereby improving vehicle utilization, but also effectively responds to unforeseen circumstances such as traffic congestion and temporary loading and unloading delays, enhancing the flexibility and robustness of route planning. Furthermore, by properly setting the maximum dwell time, the intensity of vehicle scheduling can be alleviated to a certain extent, providing dispatchers with more room for maneuver and further optimizing the overall efficiency and cost of logistics distribution.

[0164] 2.2, Feasibility Time Window

[0165] In order to solve the problem of how long a vehicle should stay at a customer node, the present invention introduces the concept of a feasibility time window. The feasibility time window is divided into a feasibility arrival time window and a feasibility service start time window. Each demand point is associated with a feasibility arrival time window and a feasibility service start time window. The feasibility arrival time window represents the set of all times when the vehicle can reach the customer location while satisfying the current path constraints. The feasible service start time window represents the set of all times when the vehicle can start providing services to the customer while satisfying the current path constraints. in Indicates arrival at customer i h time, Indicates that in i h The feasibility arrival time window at . Similarly, let in Indicates that in i h The time when the service starts, Indicates that in i h For example, factory 1 has demand A with a time window of [10, 20] and a maximum vehicle dwell time of 5. Then the feasible arrival time window of demand A is [5, 20] and the feasible service start time window is [10, 20].

[0166] 2.3, forward and backward adjustment algorithm:

[0167] If a vehicle needs to serve multiple demands sequentially along a route, each demand will affect its feasibility window due to the aforementioned time iteration constraints. This paper has developed a forward-backward adjustment algorithm that can effectively calculate the feasible arrival time window and feasible service start time window for each customer on the route. The core concept of this algorithm is to gradually narrow and eliminate the infeasible intervals in the time window through iteration.

[0168] (1) Forward adjustment algorithm:

[0169] The forward adjustment algorithm is used to calculate the given path The feasibility time window of each node in . Among them, 0 and 0' represent warehouses, Represents the hth customer node i on the path h Arrival time and service start time

[0170] For the earliest and latest arrival times and

[0171]

[0172] This formula indicates that the earliest arrival time of the first node is the earliest service time of the node minus the maximum stay time. For subsequent nodes, the earliest arrival time is determined by the service end time of the previous node, the vehicle travel time, and the earliest service time of the node.

[0173]

[0174] For the latest arrival time, the latest arrival time of the first node is directly the latest service time specified by it, while the latest arrival time of subsequent nodes is determined by the latest arrival time, service time and travel time of the previous node, and cannot exceed the latest service time of the node.

[0175] For the earliest and latest service times and

[0176]

[0177] Through this process, the forward adjustment algorithm gradually determines the feasible arrival time and service start time of each node based on the previous nodes.

[0178] (2) Backward adjustment algorithm:

[0179] The backward adjustment algorithm further optimizes the time window by propagating constraints forward from subsequent nodes to ensure that the time window of the entire path is feasible.

[0180] For the last node i in the path r :

[0181]

[0182] The above formula indicates that the above four values ​​of the last customer node remain unchanged.

[0183] For nodes h=1,…,r-1:

[0184]

[0185] This adjustment algorithm systematically optimizes the feasible arrival time window and feasible service start time window for each node on the path through forward and backward adjustments. By iteratively applying forward and backward adjustments, the feasibility of the entire path is ensured while satisfying all time constraints. The above formulas are necessary for path feasibility. Through this dynamic adjustment method, the feasible path is continuously and dynamically adjusted to gradually find feasible arrival time windows and service start time windows that meet the feasibility of the entire path.

[0186] 3. Adaptive large neighborhood search algorithm process based on feasibility time window and forward and backward adjustment algorithm:

[0187] 3.1, such as Figure 1 As shown in FIG, the adaptive large neighborhood search algorithm based on the feasibility time window and the forward and backward adjustment algorithm specifically includes the following steps:

[0188] Step 1, generation of initial solution:

[0189] Describe the method for generating the initial solution, such as randomly generating a node list of length n.

[0190] Step 2, decoding process:

[0191] Path segmentation and decoding: Describes how to decode the current path into a set of feasible routes through the path segmentation procedure.

[0192] S1: Calculate the feasibility time windows of all nodes on the current path through the forward and backward adjustment algorithm.

[0193] S2: Calculate the feasibility arrival time window of the next node based on the feasibility service start time window of the current path.

[0194] S3: Determine whether the node can be inserted into the current path. If not, it means that the path needs to be split.

[0195] S4: If insertion is possible, update the feasibility time windows of all nodes on the path.

[0196] S5: Repeat the above process to decode the current path into several vehicle paths.

[0197] Step 3, solution evaluation:

[0198] According to the designed objective function, the decoded path set is evaluated, the total cost and other objective function values ​​are calculated, and the quality of the solution is judged.

[0199] Step 4, adaptive large neighborhood search:

[0200] Select a destruction operator to destroy the current solution;

[0201] Select the repair operator to repair the current solution;

[0202] Execute step 2 and step 3 to evaluate the current solution;

[0203] Adaptively update operator scores and other parameters based on evaluation results;

[0204] Repeat step 4 until the algorithm terminates. The specific details of the algorithm are as follows.

[0205] 3.2, Adaptive Large Neighborhood Search:

[0206] The adaptive large neighborhood search (ALNS) algorithm consists of two main parts, namely, deletion and repair and weight adaptation. The ALNS algorithm framework is shown in Table 2. The ALNS algorithm contains deletion operators and insertion operators, and the operator k has a fraction π k and a probability measure ω k Starting from a feasible solution, in each iteration, we first select the deletion operator based on the roulette wheel to delete the customer from the current solution (row 5 of Table 2), and then select the insertion operator based on the roulette wheel again to reinsert the deleted customer into the current solution to form a new solution (row 6 of Table 2). The new solution is then evaluated and π is updated based on its performance. k and ω k Initially, all π k The value is set to 0, all ω k The value is set to 1. In each iteration, the probability of each deletion / insertion operator being selected among h deletion / insertion operators is After obtaining a new solution and evaluating its performance, the operator score is updated. If the selected operator k finds a better solution than the known optimal solution, its score π k Increase σ1 (row 16 of Table 2). If the operator finds a solution that is better than the current solution but worse than the known optimal solution, increase σ2 (row 20 of Table 2). In order to prevent the algorithm from falling into a local optimal solution, the present invention sets a simulated annealing algorithm, which has a certain probability of accepting a suboptimal solution. If the solution is worse than the existing solution, it enters the simulated annealing probability acceptance criterion. If it is still accepted in the end, the operator's score is increased by σ3 (row 11 of Table 2). The probability metric of operator k is updated according to the score metric. The calculation formula is as follows, u k Indicates whether the operator is used in the current iteration, u k When it is equal to 0, it means that the operator is not used and the probability metric does not need to be updated. If it is equal to 1, it is updated according to the following formula (row 21 of Table 2).

[0207]

[0208] If a better solution is found during the search, the temperature will be increased, so that further search is conducted in the neighborhood of the current solution space (line 18). If no better solution is found in the current iteration, the current temperature is reduced at a cooling rate of 0.9. In Table 2, the termination temperature T end is the stopping temperature threshold of the simulated annealing algorithm, and the current temperature T is reduced to T end When , the simulated annealing algorithm terminates. T0 represents the starting temperature of the simulated annealing algorithm, which is usually set to a higher value.

[0209] Table 2

[0210]

[0211]

[0212] 3.3, Destruction Operator:

[0213] The primary goal of the destruction operator is to expand the search space by removing nodes from the current solution. Each operation aims to explore a different region of the solution space. When a removal operator is applied, a specific number of nodes are removed from the solution path and added to the set of removed nodes R. The following is the destruction operator implemented in the ALNS algorithm of our invention:

[0214] Random client deletion: This operation randomly selects and deletes a specified number of nodes and adds the deleted nodes to the set R. Each node has an equal probability of being selected. The random deletion process continues until the required number of nodes are deleted.

[0215] Continuous client deletion: This operation deletes a continuous block of nodes from the solution x and adds these nodes to the set R. Since nodes in the same path are adjacent, deleting a continuous block may interrupt the path, resulting in potential path splitting.

[0216] Minimum Client Path Removal: This operation identifies the minimum node paths in the current solution x and removes all nodes in these paths, adding them to the set R. By removing the shortest paths, this operation promotes the formation of longer cycles, thereby reducing the total number of paths and expanding the solution space.

[0217] Most Customer Path Removal: This operation identifies the paths with the most nodes in the current solution x and removes all nodes from those paths, adding them to the set R. By removing the longest path, this operation allows exploration of a larger solution neighborhood. Most Customer Path Removal can use subsequent Insertion operations to reinsert nodes from the shortest path into other paths, resulting in longer cycles and fewer paths.

[0218] Path Deletion: This operation randomly selects and completely deletes several paths in the current solution.

[0219] Partial Path Deletion: This operation randomly selects a path from the current solution x and then randomly selects a node on that path. It deletes all nodes before or after that node. This partial deletion helps explore the solution space by changing the structure of the selected path, opening up new optimization possibilities.

[0220] 3.4, Repair Operator:

[0221] In this section, the present invention introduces two insertion operations, which are usually used after the destruction operator. After deleting a node, each node in the set R is reinserted into the solution x in order to form a new solution.

[0222] Random Insertion: This operation inserts the nodes removed from the set R into the path of x″ in a random order.

[0223] Greedy insertion: For each deleted node, the path is traversed to find a suitable position that satisfies the problem constraints and forms a new path. Nodes that cannot be inserted into the existing path are added to the beginning or end of the solution.

[0224] End Insertion: This operation randomly shuffles the order of the nodes in R and then inserts the nodes at the end of the solution.

[0225] Insert at the beginning: Similar to insert at the end, this operation randomly shuffles the order of the nodes in R, but inserts all nodes consecutively to the beginning of the solution.

[0226] 3.5, Decoding and Solution Evaluation:

[0227] The initial solution is to randomly generate a list of length n, where each node appears only once and does not contain 0 nodes.

[0228] For example, Table 3 can represent the coding sequence of nine customer requirements:

[0229] Table 3

[0230] 1 5 8 3 4 2 9 6 7

[0231] The path segmentation program is used to decode the coded sequence according to a certain segmentation algorithm to obtain a set of feasible routes and evaluate them. r ), evaluate the nodes traversed later (e.g. i h ) Can it be inserted into the last node i of the current path? r Finally, a longer feasibility loop is formed. Specifically including:

[0232] S1: Calculate the feasibility time window of all nodes on the current path through the forward and backward adjustment algorithm;

[0233] S2: Through i r Feasible service start time window Calculate customer node i h Feasibility reaches the time window

[0234] S3: If found or When the vehicle is in i h After the maximum waiting time of the node is still earlier than the opening time of the current node time window, or the vehicle reaches i at the earliest h The node time is later than the latest time of the node time window, which means that it cannot form a loop with the previous path, which means that the previous vehicle is at the last service customer node i. r After returning to the warehouse, another vehicle leaves the warehouse and first serves customer node i h .

[0235] S4: On the contrary, it means i h If the last position of the current path can be inserted, the feasibility time windows of all nodes on this path will be updated using the forward and backward adjustment algorithm.

[0236] S5: Similarly, the current solution can be decoded into several vehicle paths, so that the solution can be evaluated.

[0237] The key technical points of the present invention are:

[0238] (1) Introduction of Feasibility Time Window: This paper introduces the concepts of feasible arrival time window and feasible service start time window for the first time. The feasible arrival time window represents the set of all times when a vehicle can reach a customer's location while satisfying the current path constraints; the feasible service start time window represents the set of all times when a vehicle can start providing service to a customer while satisfying the current path constraints. The introduction of this concept makes path planning more flexible and accurate, and can effectively cope with complex constraints.

[0239] (2) Collaborative optimization of forward-backward adjustment algorithms: This paper develops a forward-backward adjustment algorithm that iteratively reduces and eliminates infeasible intervals in the time window. The forward adjustment algorithm starts from the path starting point and calculates the earliest / latest arrival time and service time for each node; the backward adjustment algorithm propagates constraints backward from the path end point to further compress the infeasible interval. By continuously eliminating infeasible time intervals as the vehicle traverses the route, the time window is iteratively refined, eliminating infeasible segments in the feasibility time window of each demand, and ensuring the feasibility of the path.

[0240] (3) Diverse destruction and repair operators: This paper designs a variety of destruction and repair operators in the adaptive large neighborhood search algorithm. Destruction operators include random customer deletion, continuous customer deletion, minimum customer path deletion, maximum customer path deletion, path deletion, and partial path deletion, which expand the search space by deleting nodes; repair operators include random insertion, greedy insertion, end insertion, and beginning insertion, which form new paths by reinserting nodes. The diverse design of these operators enables the algorithm to fully explore the solution space and improve the quality of the solution.

[0241] (4) Dynamic Weight Update Mechanism: This invention adjusts the selection probability in real time based on the performance of the operators, enabling the algorithm to adaptively select the optimal operator combination. The introduction of this mechanism improves the adaptability and efficiency of the algorithm, enabling it to better cope with different problem scenarios.

[0242] (5) Simulated Annealing Integration: This invention uses a simulated annealing mechanism to accept suboptimal solutions with a certain probability, preventing the algorithm from prematurely converging to a local optimal solution. The temperature update formula is T = T × 0.9, which allows the algorithm to maintain a certain degree of randomness during the search process and enhances global search capabilities.

[0243] (6) Decoding Strategy Optimization: This invention dynamically splits routes based on feasible time windows to ensure that maximum dwell time constraints are met. For example, if a node's feasible arrival time window conflicts with that of a subsequent node, a new vehicle route is initiated. This strategy optimization makes route planning more rational and efficient, effectively reducing operating costs.

[0244] Example 1:

[0245] A logistics company in a certain city needs to provide delivery services to 20 customer nodes every day. Each customer node has a specific time window and demand, and the maximum dwell time of the vehicle is 2 hours. Traditional methods often cause vehicles to wait too long at customer nodes, which not only makes it easy for drivers to face fines, but also increases operating costs. This patent can solve the company's problems.

[0246] Implementation steps:

[0247] Data collection: Collect information such as the location, demand, time window, etc. of customer nodes, as well as the capacity and maximum dwell time of vehicles.

[0248] Initial solution generation: Randomly generate an initial path planning solution to ensure that each customer node is served once, and the vehicle departs from the warehouse and returns to the warehouse.

[0249] Enables an adaptive large neighborhood search algorithm: This algorithm optimizes the initial solution through a variety of destruction and repair operators to generate a new path planning solution. These operations include destruction operators such as random customer deletion, continuous customer deletion, minimum customer path deletion, maximum customer path deletion, path deletion, and partial path deletion, as well as repair operators such as random insertion, greedy insertion, end insertion, and beginning insertion.

[0250] Simulated annealing mechanism: According to the simulated annealing mechanism, suboptimal solutions are accepted with a certain probability to prevent the algorithm from falling into the local optimal solution.

[0251] Decoding and Evaluation: Applying a forward-backward adjustment algorithm, the feasible arrival time window and feasible service start time window for each customer node are calculated to ensure the feasibility of the route. The generated route plan is decoded and evaluated, and metrics such as total driving cost and vehicle utilization are calculated.

[0252] Example 2:

[0253] An industrial manufacturing enterprise needs to provide raw material distribution services for multiple production links. Each production link has strict time windows and maximum residence time constraints, and the maximum residence time of a vehicle is 3 hours.

[0254] Implementation steps:

[0255] Data collection: Collect information such as the location, demand, time window, etc. of the production process, as well as the capacity and maximum dwell time of the vehicle.

[0256] Initial solution generation: Randomly generate an initial path planning solution to ensure that each production link is served once, and the vehicle departs from the warehouse and returns to the warehouse.

[0257] Forward and backward adjustment algorithm: Apply the forward and backward adjustment algorithm to calculate the feasible arrival time window and feasible service start time window of each production link to ensure the feasibility of the path.

[0258] Adaptive large neighborhood search algorithm: Through a variety of destruction operators and repair operators, the initial solution is optimized to generate a new path planning scheme.

[0259] Simulated annealing mechanism: According to the simulated annealing mechanism, suboptimal solutions are accepted with a certain probability to prevent the algorithm from falling into the local optimal solution.

[0260] Decoding and evaluation: Decode and evaluate the generated path planning solution, and calculate indicators such as total driving cost and vehicle utilization.

[0261] Example 3:

[0262] A fresh food delivery company needs to provide fresh food delivery services to multiple supermarkets and restaurants. Each customer node has strict time windows and maximum dwell time constraints, and the maximum dwell time of a vehicle is 1 hour.

[0263] Implementation steps:

[0264] Data collection: Collect information such as the location, demand, time window, etc. of customer nodes, as well as the capacity and maximum dwell time of vehicles.

[0265] Initial solution generation: Randomly generate an initial path planning solution to ensure that each customer node is served once, and the vehicle departs from the warehouse and returns to the warehouse.

[0266] Forward-backward adjustment algorithm: Apply the forward-backward adjustment algorithm to calculate the feasible arrival time window and feasible service start time window of each customer node to ensure the feasibility of the path.

[0267] Adaptive large neighborhood search algorithm: Through a variety of destruction operators and repair operators, the initial solution is optimized to generate a new path planning scheme.

[0268] Simulated annealing mechanism: According to the simulated annealing mechanism, suboptimal solutions are accepted with a certain probability to prevent the algorithm from falling into the local optimal solution.

[0269] Decoding and evaluation: Decode and evaluate the generated path planning solution, and calculate indicators such as total driving cost and vehicle utilization.

[0270] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown in sequence as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times. The order of execution of these steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a portion of the steps or stages in other steps.

[0271] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0272] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. It is intended that all variations within the meaning and range of equivalents of the claims be embraced herein, and any reference signs in the claims should not be construed as limiting the claims to which they relate.

[0273] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. An adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm, characterized in that: The following steps are involved: S1, build a vehicle routing model with a maximum dwell time constraint. The objective function is to minimize the total travel cost. The constraints include customer node service uniqueness, vehicle departure and return from the warehouse, flow conservation, capacity constraint, and time window constraint. S2, randomly generates a coding sequence of customer nodes as the current solution of the vehicle path planning model; S3, taking the vehicle path from the warehouse to the first customer node in the encoding sequence of the current solution as the current path; S4, calculating the feasibility time windows of all customer nodes on the current path using a forward-backward adjustment algorithm, and taking the next node in the coding sequence as the node to be assigned; calculating the feasibility time window of the node to be assigned based on the feasibility time windows of all customer nodes on the current path, and determining whether the vehicle can arrive and complete the service within the feasibility time window of the node to be assigned. If so, the node to be assigned is added to the current path; if not, the vehicle path from the warehouse to the node to be assigned is used as the new current path; S5, repeating step S4 until the encoded sequence is decoded into multiple vehicle paths; calculating the total driving cost of the decoded multiple vehicle paths using the objective function; S6, according to the operator weight, select the destruction operator to delete the client node in the current solution, and select the repair operator to insert the client node in the current solution to obtain a new solution; Calculate the total travel cost of the new solution through steps S4 and S5, and update the weights of the destruction operator and the repair operator based on whether the new solution is better than the current solution in terms of total travel cost; S7: Take the new solution as the current solution and repeat step S6 until the set termination condition is met.

2. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The construction of a vehicle path planning model with a maximum dwell time constraint specifically includes: The vehicle routing model with time windows and maximum dwell time is as follows: there is a central warehouse and several customer nodes. Each customer node has a certain demand and must be served within a specified time window. Each vehicle has a limited capacity and must depart from the warehouse, serve a set of customer nodes, and then return to the warehouse. The goal is to design a set of vehicle routes that meet the following conditions: Each client node is served by one and only one vehicle; The total cargo volume of each vehicle does not exceed the capacity limit of that vehicle; The time when the vehicle arrives at each customer node must be within the time window of the customer node; The vehicle's stay time at each customer node does not exceed the maximum stay time; The total travel cost is minimized.

3. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 2, characterized in that: The parameters of the vehicle path planning model include: Node set V = {0, 1, 2, ..., n}, where 0 represents the warehouse node and 1, 2, ..., n represents the 1st to nth customer nodes; Vehicle set K; The travel cost c from customer node i to customer node j ij ; The demand d of customer node i i ; The capacity Q of each vehicle; The time window of client node i[e i ,l i ], where e i is the earliest service time of client node i, l i is the latest service time of customer node i; Service time u at customer node i i ; Travel time t from customer node i to customer node j ij ; Maximum dwell time MDT of vehicle k k ; The decision variables of the vehicle path planning model include: A binary variable x indicating whether vehicle k travels from customer node i to customer node j ijk ; The time a that vehicle k arrives at customer node i ik ; The service start time s of vehicle k at customer node i ik .

4. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 3, characterized in that: The objective function is to minimize the total driving cost, which specifically includes: The objective function is: min∑ k∈K ∑ i∈V ∑ j∈V c ij x ijk .

5. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 3, characterized in that: The constraints include customer node service uniqueness, vehicle departure and return from the warehouse, flow conservation, capacity constraints, and time window constraints. Specifically, they include: Client node service uniqueness, that is, each client node is served once: The node set V represents the node with warehouse nodes removed; The vehicle departs from the warehouse and returns to the warehouse: Traffic conservation, that is, after a vehicle reaches a customer node, it must leave the customer: Capacity constraint, that is, the total cargo volume of the vehicle does not exceed the capacity limit of the vehicle: Time window constraints, including: Time iteration constraints on vehicle paths: Represents the penalty factor, which is an infinite value; The vehicle's dwelling time does not exceed the vehicle's maximum dwelling time: The vehicle's service start time needs to be within the customer's time window Variable scope: x ijk ∈{0,1},a ik ≥0,s ik ≥0.

6. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The feasibility time window of all client nodes on the current path is calculated by the forward and backward adjustment algorithm, specifically including: The feasibility time window includes the feasible arrival time window and the feasible service start time window. The forward-backward adjustment algorithm gradually reduces and eliminates the infeasible intervals in the time window through iteration, and calculates the feasible arrival time window and feasible service start time window of each customer node on the vehicle path. The forward adjustment algorithm is used to calculate the path of a given vehicle The feasibility time window of each customer node in ; where 0 and 0' represent the warehouse that the vehicle leaves and the same warehouse that the vehicle arrives at when it returns, Indicates that the vehicle arrives at the hth customer node i on the vehicle path h Time and client node i h Service start time r is the total number of customer nodes in the vehicle path; Client node i h The lower bound of the feasible arrival time for: is client node i h The earliest service time, For client node i h The maximum residence time, Represents customer node i h-1 The lower limit of the feasible service start time, Represents customer node i h-1 Service time, is the travel time of the vehicle from customer node i to customer node j; Client node i h The upper limit of the feasible arrival time for: is client node i h The latest service time, For client node i h-1 The upper limit of the feasible service start time; among which, The feasible arrival time window is The feasible service start time window is The backward adjustment algorithm further optimizes the feasibility time window by propagating constraints forward from subsequent client nodes: For the last customer node i in the vehicle path r : For client node i h , h=1,…,r-1:

7. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The feasibility time window of the node to be assigned is calculated based on the feasibility time windows of all customer nodes on the current path, and it is determined whether the vehicle can arrive and complete the service within the feasibility time window of the node to be assigned. If so, the node to be assigned is added to the current path; If not, the vehicle path from the warehouse to the node to be assigned is used as the new current path, specifically including: For each current client node i r , evaluate the subsequent customer node i h Whether it is possible to insert it to the end of the current vehicle path to form a longer feasible loop: Through the current client node i r Feasible service start time window Calculate customer node i h Feasibility reaches the time window are client nodes i h The feasibility reaches the lower and upper limits of the time window; are client nodes i r The lower and upper limits of the feasible service start time window; Determine whether: or is client node i h The earliest service time, For client node i h The maximum residence time, is client node i h The latest service time of client node i; if so, the subsequent client node i h It cannot form a loop with the current vehicle path; if not, the subsequent customer node i h Ability to insert at the end of the current vehicle path.

8. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The selective destruction operator deletes the client node in the current solution, specifically including: The destruction operator is used to remove client nodes from the current solution to expand the search space. When the destruction operator is applied, a certain number of client nodes are removed from the vehicle path corresponding to the current solution and added to the deleted node set R. The destruction operator includes: Random customer deletion: Randomly select and delete a specified number of customer nodes, and add the deleted customer nodes to R. Each customer node has an equal probability of being selected until the required number of customer nodes are deleted. Continuous customer deletion: delete multiple consecutive customer nodes and add the deleted customer nodes to R; Minimum customer path deletion: Identify the minimum customer node paths in the current solution and delete all customer nodes in these paths, adding the deleted customer nodes to the deleted node set R; Most customer paths deleted: Identify the paths with the most customer nodes in the current solution, delete all customer nodes in these paths, and add the deleted customer nodes to the deleted node set R; Path deletion: randomly select and completely delete several paths in the current solution, and add the deleted client nodes to the deleted node set R; Partial path deletion: Randomly select a path in the current solution, then randomly select a customer node on the path, and add the deleted customer node to the deleted node set R.

9. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The selection repair operator inserts the client node into the current solution, specifically including: After deleting a client node, the repair operator reinserts each client node in the deleted node set R into the current solution in a specific order. The repair operator includes: Random insertion: insert the customer nodes in the deleted node set R into the path corresponding to the current solution in random order; Greedy insertion: For each customer node in the deleted node set R, traverse the path to find a suitable insertion position, satisfy the problem constraints and form a new path. Customer nodes that cannot be inserted into the existing path will be added to the beginning or end of the path corresponding to the current solution; End insertion: Randomly disrupt the order of the client nodes in the deleted node set R, and insert all client nodes consecutively to the end of the path corresponding to the current solution; Insert at the beginning: Randomly disrupt the order of the client nodes in the deleted node set R, and insert all client nodes consecutively to the beginning of the path corresponding to the current solution.

10. The adaptive large neighborhood search method based on a feasibility time window and a forward-backward adjustment algorithm according to claim 1, characterized in that: The weights of the destruction operator and the repair operator are updated based on whether the new solution is better than the current solution in terms of total travel cost, specifically including: Each destruction operator and repair operator has a fraction π k and a probability measure ω k ; In each iteration, we first calculate the probability metric ω of each destruction operator based on k The destruction operator is selected according to the roulette wheel, and the probability of each destruction operator being selected is Delete the client node from the current solution; then again based on the probability ω of each repair operator k The repair operator is selected according to the roulette wheel, and the probability of each repair operator being selected is The deleted client nodes are reinserted into the current solution to form a new solution; h is the total number of destruction operators or repair operators; Then the total driving cost of the new solution is evaluated, and π is updated according to the performance of the new solution. k and ω k The value of If the new solution performs better than the optimal solution, the fraction of destruction and repair operators that are selected is π k The first score σ1 is increased and the new solution is taken as the new optimal solution; If the new solution performs better than the current solution but worse than the optimal solution, the fraction of the destruction and repair operators selected is π k Both increase the second fraction σ2; If the new solution performs worse than the current solution, the simulated annealing algorithm is used to decide whether to accept the new solution; if the new solution is accepted, the fraction of the selected destruction operator and repair operator is π k Both increase the third fraction σ3; According to the fraction π k Update the probability measure of the destruction operator and the repair operator: u k Indicates whether the destruction operator or repair operator is used in the current iteration, u k =0 means that the destruction operator or repair operator is not used; u k =1 means that the destruction operator or repair operator is used; ρ represents the smoothing parameter, which is used to control the learning speed of the operator weight; In the current iteration, if the new solution performs better than the optimal solution, the temperature of the simulated annealing algorithm will increase; otherwise, the current temperature will decrease at a cooling rate of 0.9.

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