Two-dimensional boxing vehicle path planning method based on improved distribution estimation algorithm

Abstract

The invention discloses a two-dimensional boxing vehicle path planning method based on an improved distribution estimation algorithm, which combines a mileage saving method and an insertion method to realize population initialization based on a heuristic rule, improves the quality of an initial population, accelerates the convergence speed of the algorithm, and improves the reliability of the algorithm. The search performance of a cargo boxing part is improved by fusing taboo search and a skyline algorithm, the calculation of population individual fitness is completed, the cargo boxing effect is improved, the utilization rate of a carriage loading surface is improved, and finally, by establishing a vehicle and customer distribution relation probability model and an inter-customer scheduling relation probability model, the cargo boxing efficiency is improved. The probability that the search process falls into local optimum is reduced, the cargo transportation efficiency is improved, the logistics transportation cost is reduced, and research on a logistics resource allocation theoretical framework is deepened.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent decision-making and control technology, and specifically relates to a two-dimensional packing vehicle path planning method based on an improved distribution estimation algorithm. Background Art

[0002] In the contemporary business ecology where the digital economy and cross-border trade are deeply integrated, the logistics system is undergoing profound changes in its business model. In complex cargo transportation scenarios, cargo loading methods and path planning have significant space for collaborative optimization. In response to new problems, the operations research community has proposed the Capacitated Vehicle Routing Problem with Two-dimensional Loading Constraints (2L-CVRP). Its core lies in establishing a two-way constraint model between cargo packing and vehicle transportation routes: it is necessary to ensure that the spatial arrangement of cargo in the two-dimensional plane meets the restrictions of the transport compartment, and the dynamic consistency of the loading sequence and the distribution path must be maintained. The research on 2L-CVRP provides a quantitative decision-making tool for solving the problem of resource waste in the last mile of distribution, especially in the fields of refined operations such as cold chain logistics and hazardous chemicals transportation, showing significant application potential. Among them, the vehicle path planning problem under two-dimensional loading constraints is as follows: Figure 1 shown.

[0003] The field of traditional 2L-CVRP has attracted considerable attention in recent years, resulting in numerous remarkable research achievements. The following section will introduce the research background of this problem from three perspectives: exact algorithms, heuristic algorithms based on individual search, and heuristic algorithms based on swarm intelligence.

[0004] In the study of exact solution algorithms, Iori et al. first established a mathematical model for 2L-CVRP and proposed an exact solution algorithm that combines a branch-and-cut algorithm with a branch-and-bound method. To check the feasibility of item packing, the exact solution algorithm iteratively applies a branch-and-bound procedure, which can provide a solution for a 2L-CVRP instance with 30 customers and 90 items. Zhang et al. developed a branch-and-cut algorithm for 2L-CVRP and proposed a separation algorithm to simultaneously identify infeasible set inequalities and weak capacity inequalities for fractional solutions. The algorithm first achieved optimal solutions on six instances.

[0005] Although exact solution algorithms can yield optimal solutions for 2L-CVRP, they are limited in efficiency and scale, preventing their application to large-scale 2L-CVRP instances. In contrast, heuristic algorithms have become an effective approach for rapidly solving 2L-CVRP. Due to the numerous constraints, small number of feasible solutions, and sparse distribution of feasible regions in 2L-CVRP, heuristic algorithms based on individual search have been widely used in this field.

[0006] Gendreau proposed a tabu search algorithm for solving the 2L-CVRP problem, in which the packing strategy is determined through a branch-and-bound procedure with heuristics, lower bounds, and truncation. Building on this, Zachariadis proposed an algorithm that combines tabu search and guided local search, namely the Guided Tabu Search algorithm. To accelerate the search process, the Guided Tabu Search algorithm reduces the intensity of the search in the neighborhood and stores the packing strategy of each solution during the iteration, facilitating its rapid recall and subsequent packing solution development. Leung used a simulated annealing algorithm to solve the 2L-CVRP problem, employing a set of heuristic rules to determine the feasibility of two-dimensional packing solutions. Building on this, Leung et al. developed another efficient individual search method, the Extended Guided Tabu Search algorithm, which combines the advantages of tabu search and extended guided local search (EGLS), effectively escaping local optima during the search process. Zachariadis summarized previous work and proposed a novel metaheuristic algorithm with a simple design, a small number of parameters, and ease of implementation. For cargo packing, this algorithm uses a hash table to store partial cargo loading information, guiding the subsequent generation of diverse loading plans.

[0007] Inspired by the above work, Wei improved the cargo packing algorithm, using a heuristic rule-based skyline algorithm to determine the feasibility of vehicle paths, and also used an improved variable neighborhood search algorithm to solve the 2L-CVRP. Wei considered both unconstrained and first-in, last-out 2L-CVRP problems, using tabu search to search for the cargo packing order for each transport vehicle, thereby obtaining the cargo loading and unloading solution with the highest utilization rate. Building on this, Wei further proposed a 2L-CVRP solution based on simulated annealing (SA), and used a heuristic packing algorithm based on open space to determine the feasibility of item packing. In this work, Wei considered four constraints of 2L-CVRP, including that items can be rotated without restrictions in the packing order, that items cannot be rotated without restrictions in the packing order, that items can be rotated as long as the packing order satisfies the first-in-last-out constraint, and that items cannot be rotated as long as the packing order satisfies the first-in-last-out constraint. A variety of neighborhood structures were used to complete the search of the solution space. The algorithm obtained a better path planning solution in solving 2L-CVRP.

[0008] Individual-based heuristic algorithms are prone to falling into local optimal solutions during the search process, while heuristic algorithms based on swarm intelligence better compensate for this shortcoming. Fuellerer et al. first used the ant colony algorithm to solve 2L-CVRP. On small-scale instances, the algorithm achieved the currently known optimal solution, and on large-scale instances, the ant colony algorithm was significantly superior to other heuristic algorithms. For infeasible solutions that may appear in the population, Fuellerer designed a penalty function to guide the search process towards the feasible domain. Sbai used a genetic algorithm to solve 2L-CVRP, retaining the convergence of the optimal individual enhancement algorithm in each generation during the iterative process. Dahmani used the adaptive chemical reaction optimization algorithm (ACRO) to generate potential solutions. During the optimization process, the algorithm can adjust its parameters according to the characteristics of 2L-CVRP, thereby better exploring new areas of the search space.

[0009] The aforementioned solution frameworks, based on exact algorithms or heuristic rules, suffer from drawbacks such as difficulty guaranteeing optimality and insufficient timeliness. Specifically, exact solution algorithms are limited by the scale of the problem and cannot solve large-scale 2L-CVRP instances. Individual-based heuristic algorithms are prone to falling into local optimal solutions during the search process. While swarm intelligence-based heuristic algorithms can somewhat avoid this drawback, they often use random generation to construct the initial population. For this strictly constrained problem with a sparsely distributed feasible domain, using random initialization can generate a large number of infeasible solutions, thereby reducing the quality of the population.

[0010] Similarly, existing methods for handling cargo packing are not perfect. Most packing methods use easy-to-implement heuristic packing rules, but these methods suffer from low cargo loading and unloading utilization rates. Furthermore, for a specific transport vehicle, the order in which the cargo is loaded into the carriage will also affect the packing effect. Therefore, in order to improve the optimization effect of the vehicle path planning problem under two-dimensional loading constraints, in the cargo loading strategy, on the one hand, it is necessary to improve the packing rules and adopt algorithms with higher loading efficiency; on the other hand, it is necessary to determine the optimal cargo packing order. Regarding the definition of packing constraints in 2L-CVRP, traditional solutions only consider whether the cargo satisfies the Last In First Out (LIFO) constraint. However, for cargo to be transported, which is abstracted into a two-dimensional rectangle, the cargo can also be orthogonally rotated 90 degrees to change the packing scheme, thereby further optimizing cargo packing efficiency. Summary of the Invention

[0011] In view of this, the present invention provides a two-dimensional packing vehicle path planning method based on an improved distribution estimation algorithm, which realizes the synchronous decision-making of cargo packing and vehicle transportation route planning schemes.

[0012] The present invention provides a two-dimensional containerized vehicle path planning method based on an improved distribution estimation algorithm, comprising the following steps:

[0013] Step 1: Calculate the distance initialization data between customers and initialize the improved distribution estimation algorithm;

[0014] Step 2: Assign transportation routes to customers and merge routes based on the mileage saved. Arrange all routes in descending order based on the vehicle's current load capacity, cancel routes that exceed the number of vehicles, save the customers corresponding to the canceled routes in the list of unserved customers, and use an insertion rule-based algorithm to insert the unserved customers into the remaining routes. The resulting set of routes is used as an individual, and the initial population is composed of multiple individuals.

[0015] Step 3: The skyline packing strategy based on tabu search calculates whether there is a cargo arrangement that can accommodate all the cargo. If so, it is a feasible solution; otherwise, it is an infeasible solution. The fitness of the feasible solution is the inverse of the sum of the route lengths, and the fitness of the infeasible solution is the set value. The individual with the larger fitness value is the dominant individual.

[0016] Step 4: Based on the dominant individual, the probability model of the vehicle-customer allocation relationship and the probability model of the inter-customer scheduling relationship are updated. The probability model of the vehicle-customer allocation relationship is sampled to obtain the customer-vehicle allocation relationship. The probability model of the inter-customer scheduling relationship is sampled to obtain the visit order of different customers in the route.

[0017] Step 5: If the distribution estimation algorithm reaches the maximum number of iterations, the individual with the highest fitness among all populations is taken as the historical optimal solution, and the process ends; otherwise, execute step 3.

[0018] Furthermore, the data in step 1 includes the number of transport vehicles, vehicle load and compartment specifications, distribution center coordinates, customer coordinates, total weight of customer cargo and customer cargo specifications.

[0019] Furthermore, the method of merging the routes according to the mileage saved in allocating transportation routes to customers in step 2 is as follows: an initial route set is established with the distribution center as the starting point and the end point and the customer as the intermediate node; under the condition that the vehicle load constraint and the two-dimensional cargo loading constraint are satisfied, the original routes in the initial route set are merged into a new route, the mileage difference between the new route and the original route is calculated, and the new route that saves the most mileage compared to the original route is selected as the merged route.

[0020] Furthermore, in step 2, all routes are arranged in descending order according to the existing vehicle load, and routes that exceed the number of vehicles are eliminated in the following manner: the routes in the merged route set are sorted in descending order of vehicle space utilization, and a set number of routes with lower vehicle space utilization are deleted according to the route quantity constraint.

[0021] Furthermore, the method of inserting the unserved customer into the remaining routes using the insertion rule-based algorithm described in step 2 is as follows: let the customer with the largest cargo area ratio in the unserved customer list be the target customer; if there is a route in the current route set that can accommodate the target customer's cargo, then add the route to the third route set, insert the target customer into the route with the lowest incremental cost in the third route set, and update the third route set; if it does not exist, select a route from the current route set, delete the customers on the route one by one until the target customer's cargo can be accommodated, update the second route set, and save the deleted customers to the unserved customer list, and repeat the above process until all customers in the unserved customer list are inserted into the routes.

[0022] Furthermore, the method for calculating whether there is a cargo ordering that can accommodate all cargoes in the skyline packing strategy based on tabu search in step 3 is:

[0023] Step 4.1: Sort the goods to be transported by the individuals according to different heuristic rules to obtain multiple initial goods sequences;

[0024] Step 4.2: Use the skyline algorithm to calculate the packing feasibility of the cargo lists of multiple initial cargo sequences. If there is an initial cargo sequence that can load all the cargo in the route into the carriage, then the tabu search process ends. Otherwise, proceed to step 4.3.

[0025] Step 4.3: Perform a swap sequence operation on the initial cargo sequence to generate a new cargo packing sequence. This swap sequence operation is added to the taboo table until the swap sequence operation is performed a number of times equal to the length of the taboo table, at which point the swap sequence operation is released from the taboo table.

[0026] Step 4.4: Use the skyline algorithm to calculate the packing feasibility of the cargo list in the new cargo packing sequence. If all cargo can be packed, proceed to step 4.5; otherwise, randomly select a sequence permutation operation that is not in the taboo table and proceed to step 4.3.

[0027] Step 4.5: When a sequence that successfully loads all goods into the carriage is found, or the maximum number of iterations of the tabu search algorithm is reached, the tabu search process ends.

[0028] Furthermore, when the cargo is a two-dimensional rectangular cargo, the skyline algorithm is used to calculate the packing feasibility of the cargo list of the new cargo packing sequence. The coverage area of ​​the new skyline under the cargo rotation and non-rotation placement schemes is calculated respectively, and the cargo packing sequence with the smaller coverage area is selected.

[0029] Furthermore, in step 3, a local search is performed on the dominant individuals based on the variable neighborhood descent method to obtain the optimal scheduling order of the customers in the individual routes.

[0030] Furthermore, the vehicle-customer allocation relationship probability model P1 is updated as follows:

[0031]

[0032] Among them, g and g+1 represent the generations of the original population and the new population respectively, p1 kj represents the (k, j)th element of the probability matrix P1 of the vehicle-customer allocation relationship, α is the learning rate, Ind ep represents the epth dominant individual in the original population, for:

[0033] Furthermore, the updating method of the inter-customer scheduling relationship probability model P2 is:

[0034]

[0035] Among them, p2 ij represents the (i, j)th element of the probability matrix P2 for scheduling relationships between customers, α is the learning rate, Ind ep represents the epth dominant individual in the original population, for:

[0036]

[0037] Beneficial effects:

[0038] 1. This invention combines the mileage saving method with the insertion method to implement population initialization based on heuristic rules, thereby improving the quality of the initial population and accelerating the algorithm convergence speed. By integrating the tabu search and skyline algorithms, the search performance of the cargo packing part is improved, the fitness of the individual population is calculated, the cargo packing effect is improved, and the utilization rate of the carriage loading surface is increased. Finally, by establishing a probability model of the vehicle-customer allocation relationship and a probability model of the scheduling relationship between customers, the probability of the search process falling into a local optimum is reduced, the cargo transportation efficiency is improved, the logistics transportation cost is reduced, and the research on the theoretical framework of logistics resource allocation is deepened.

[0039] 2. The present invention takes into account the rotation constraint of rectangular cargo in the case of orthogonal rotation, further improves the cargo packing effect, and enhances the utilization of the carriage loading surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of the vehicle routing problem under existing two-dimensional loading constraints.

[0041] Figure 2 A schematic diagram of the processing flow of a two-dimensional packing vehicle path planning method based on an improved distribution estimation algorithm provided by the present invention.

[0042] Figure 3 This is a schematic diagram of the effect of using the mileage-saving method to merge routes in a two-dimensional container vehicle path planning method based on an improved distribution estimation algorithm provided by the present invention.

[0043] Figure 4 A schematic diagram of inserting unserved customers into allowed routes in a two-dimensional box vehicle path planning method based on an improved distribution estimation algorithm provided by the present invention.

[0044] Figure 5 A schematic diagram of the processing flow of a skyline packing strategy based on tabu search in a two-dimensional packing vehicle path planning method based on an improved distribution estimation algorithm provided by the present invention.

[0045] Figure 6 This is a schematic diagram of the execution of the Swap operator in a two-dimensional boxed vehicle path planning method based on an improved distribution estimation algorithm provided by the present invention. DETAILED DESCRIPTION

[0046] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0047] The constraints of the vehicle path planning problem under two-dimensional loading constraints related to the present invention are as follows:

[0048] (1) The total weight of cargo on each transport route cannot exceed the vehicle load;

[0049] (2) The vehicle departs from the distribution center and eventually returns to the distribution center;

[0050] (3) Any customer point can only be served by one transport vehicle once, and the vehicle must complete the transportation of all goods for the customer point;

[0051] (4) Any side of a two-dimensional rectangular cargo in a carriage can only be parallel or perpendicular to the rectangular carriage;

[0052] (5) Two-dimensional rectangular goods cannot overlap;

[0053] (6) Two-dimensional rectangular cargo cannot exceed the scope of the carriage.

[0054] The symbol definition is as follows:

[0055]

[0056]

[0057]

[0058] For the vehicle path planning problem under two-dimensional packing constraints, the following formula can be used to construct a mathematical model. The objective function is as follows:

[0059]

[0060] The constraints are as follows:

[0061]

[0062] f mn +f nm +ρ mn +ρ nm ≥y ik +y jk -1

[0063]

[0064] m≠n,k∈K

[0065]

[0066]

[0067]

[0068] x ijk ,y ik ,f mn ,ρmn ∈{0,1}

[0069]

[0070] The present invention provides a two-dimensional container vehicle path planning method based on an improved distribution estimation algorithm, the processing flow is as follows: Figure 2 As shown, the specific steps include:

[0071] Step 1: Read in the 2L-CVRP data and perform data preprocessing to obtain initial data, including: the number of transport vehicles, vehicle load and compartment specifications, distribution center coordinates, customer coordinates, total weight of customer cargo, and customer cargo specifications. Among them, customer cargo specifications can be expressed in width and length.

[0072] Step 2: Initialize customer distance data and calculate the distance c between each customer ij , i and j are both customer numbers; at the same time, the improved estimation of distribution algorithm (IEDA) is initialized, and the population size pop, the maximum number of iterations Mg, the probability matrix learning rate α and the proportion of dominant individuals β are set.

[0073] Step 3: Using the heuristic rules of the mileage saving method, a set of routes is generated as the initial population, provided that the routes satisfy the vehicle load constraints and the two-dimensional cargo loading constraints. The individuals in the population are the set of routes that complete the transportation services for all customers. That is, first, transportation routes are assigned to customers according to the mileage saving method, and routes are merged according to the amount of mileage saved. Then, all routes are sorted in descending order according to the current vehicle load, and routes that exceed the number of vehicles are cancelled. The customers corresponding to the cancelled routes are saved in the list of unserved customers. The unserved customers are inserted one by one into the remaining routes using an insertion rule-based algorithm. The resulting set of routes serves as the individuals in the initial population, and the initial population is composed of multiple different individuals.

[0074] In the prior art, the initial population is usually generated randomly. The present invention uses the heuristic rule of the mileage saving method to generate the initial population, which can effectively improve the fitness of the population and accelerate the convergence speed. Specifically, the present invention uses the heuristic rule of the mileage saving method to generate the initial population, including the following process:

[0075] Step 3.1: Create an initial route set with the distribution center as the starting and ending point and the customer as the intermediate node. Under the conditions of satisfying the vehicle load constraint and the two-dimensional cargo loading constraint, merge the original routes in the initial route set into a new route. Calculate the mileage difference between the new route and the original route, and obtain the route set consisting of the new routes that save the most mileage compared to the original routes. This is recorded as the first route set.

[0076] Specifically, the following formula can be used to determine whether the route meets the vehicle load constraint:

[0077]

[0078] The two-dimensional packing constraints of goods are described as follows:

[0079]

[0080]

[0081] f mn +f nm +ρ mn +ρ nm ≥y ik +y jk -1

[0082]

[0083] m≠n,k∈K

[0084]

[0085] x ijk ,y ik ,f mn ,ρ mn ∈{0,1}

[0086]

[0087] Suppose there are two cities labeled i and j, and the distribution center labeled 0. Initially, two routes are obtained: 0→i→0 and 0→j→0. The new route after merging the two routes is 0→i→j→0. The mileage saved by the new route compared to the original two routes is s(i,j)=2c. 0i +2c 0j -(c 0i +c 0j +c ij )=c 0i +c 0j -c ij Merge routes one by one until they are close to the vehicle load constraint and the cargo two-dimensional loading constraint. The effect of merging routes is as follows: Figure 3 shown.

[0088] Step 3.2: Sort the routes in the first route set in descending order of vehicle space utilization. Then, based on the route quantity constraint, delete a certain number of routes with low vehicle space utilization. The deleted routes form a deleted route set, and the remaining routes form a second route set. Select the customer with the largest cargo area ratio from the deleted route set as the target customer. Search the second route set to see if there is a route that can accommodate the target customer's cargo. If so, form a third route set with the routes that can accommodate the target customer's cargo. Select the route with the lowest incremental cost after inserting the target customer from the third route set as the route to be modified. Insert the target customer into the corresponding position of the route. Update the third route set with the modified route, and use the third route set as the initial population. If not, select a route from the second route set and delete customers on the route one by one until the target customer's cargo can be accommodated. Update the second route set with the modified route, and save the deleted customers to the unserved customer list. Repeat the above process to insert the customers in the unserved customer list into the routes selected from the second route set to complete the update of the second route set. Use the second route set as the initial population and insert the unserved customers into the allowed routes. Figure 4 shown.

[0089] Step 4: In order to screen out the shortest distance, define the fitness of each individual (solution) in the initial population established in step 3. Based on the skyline packing strategy of taboo search, sort all the goods that need to be transported in the individual's corresponding route to obtain a cargo packing sequence, and screen out the packing sequence that can accommodate all the goods in the route. Among them, the individual with such a packing sequence is a feasible solution, and the individual without such a packing sequence is an infeasible solution; assign the fitness of the infeasible solution to the set value, and calculate the fitness of the feasible solution. The value of the fitness of the feasible solution is the sum of the distances of all routes in the individual route set, Z 2l-cvrp The reciprocal of is as follows:

[0090]

[0091] Among them, c ij is the Euclidean distance from customer i to customer j; x ijk is a variable that takes the value 0 or 1. When it takes the value 1, it means that vehicle k has passed through arc (i, j). When it takes the value 0, it means that vehicle k has not passed through arc (i, j). The set value can be set to 0.

[0092] In order to further improve the selection efficiency of dominant individuals, the present invention can also remove the screened infeasible solutions from the initial population.

[0093] For a certain transport route, the packing situation of all the goods is not only related to the packing algorithm used, but also has a coupling relationship with the packing order of the input algorithm. Therefore, the present invention combines the tabu search and skyline packing algorithms, and adopts the skyline packing strategy based on tabu search to establish the individual route set. Specifically, the present invention sorts all the goods that need to be transported in the individual corresponding route based on the skyline packing strategy of tabu search to form the corresponding individual route set. The calculation process is as follows: Figure 5 As shown, the specific method is:

[0094] Step 4.1: Sort all the goods that need to be transported in the individual corresponding routes according to the set different heuristic rules to obtain multiple initial goods sequences.

[0095] For example, the three heuristic rules can be used for arrangement, including: arranging in descending order based on the longest side of rectangular goods, arranging in descending order based on the area of ​​rectangular goods, and arranging in descending order based on the perimeter of rectangular goods, thereby obtaining three initial goods sequences seq1, seq2, and seq3.

[0096] Step 4.2: Use the skyline algorithm to calculate the packing feasibility of the cargo lists of multiple initial cargo sequences. If there is an initial cargo sequence that can load all the cargo in the route into the carriage, it means that the individual solution is feasible. Otherwise, execute step 4.3 and use the tabu search algorithm to adjust the cargo packing order.

[0097] Step 4.3: Perform the swap sequence operation on the initial cargo sequence to generate a new cargo packing sequence. That is, for a certain initial cargo sequence R, i and b j Two goods execute Swap(b i ,b j ) Swap b in the sequence i and b j The position order of Swap is the neighborhood operator that generates a new packing order. The schematic diagram of the Swap operator is as follows Figure 6 shown.

[0098] Step 4.4, the operator Swap(b i ,b j ) is added to the taboo table, the length of the taboo table is Tabu_size, and the operator Swap(b) is not swapped until the Tabu_sizeth sequence operation. i ,b j ) is released from the taboo list to ensure that the operators added to the taboo list cannot be applied again within a certain period of time.

[0099] Step 4.5: Use the skyline algorithm to calculate the packing feasibility of the cargo list in the new cargo packing sequence. If all the cargo can be completely packed, the packing is successful, indicating that the individual is a feasible solution, and proceed to step 4.6; otherwise, randomly select a swap operation that is not in the taboo table and proceed to step 4.3.

[0100] Step 4.6: When a sequence that successfully loads all goods into the carriage is found, or the maximum number of iterations of the tabu search algorithm, Pack_iter, is reached, the tabu search process ends, and a successful cargo packing sequence or cargo packing failure information is obtained, completing the screening of whether the individual is a feasible solution.

[0101] The cargo packing steps of the skyline algorithm include:

[0102] (1) Generating skyline: The skyline algorithm defines a sequence of T consecutive horizontal line segments (s1, s2, ..., s T ) to represent the skyline, where the skyline must satisfy the following properties:

[0103] For any t∈{1,2,…,T}, the skyline s t The y-axis coordinate value of its adjacent skyline is different;

[0104] For any t∈{1,2,…,T}, the skyline s t The x-axis coordinate value of the right endpoint is the same as s t+1 The x-axis coordinate values ​​of the left endpoints are the same.

[0105] (2) Generate candidate point set: define a series of candidate points at both ends of the skyline as the coordinate point set for placing matrix cargo. First, the left end point of the leftmost skyline s1 and the rightmost skyline s T The right endpoint of is always used as a candidate point for placing rectangular cargo; for the middle skyline s t , when a skyline t-1 Higher than s t When the skyline t The left endpoint is taken as the candidate point; similarly, when the next skyline s t+1 Higher than s t When the skyline t The right endpoint of is selected as a candidate point.

[0106] (3) Select feasible (candidate) points for the rectangular cargo r to be placed: traverse the existing skyline candidate points and form a feasible point set of candidate points where a rectangular cargo r can be placed. The placement method is as follows: the lower left corner of the rectangle touches the skyline s t The left end candidate point, or its lower right corner touches the line segment s in the skyline t The right end candidate point of .

[0107] (4) Select the best placement point: If there is only one feasible candidate point, then that candidate point is the best placement point. If there are multiple feasible candidate points, the space usage of the rectangular cargo r at each placement point is calculated, and the location with the smallest skyline coverage area after the rectangular cargo r is placed is selected as the best placement point. If there are multiple candidate points, that is, the updated skyline coverage area after the rectangular cargo r is placed is the same, then the candidate point with the lowest y-axis coordinate is selected as the best candidate point.

[0108] (5) Update the affected skyline: The upper edge of the placed rectangular cargo r is regarded as a new skyline segment, and the affected skyline segments are updated. This process includes the deletion of the skyline and the change of the skyline length.

[0109] (6) Update the global skyline. Traverse each skyline segment and merge adjacent skylines with the same height.

[0110] This invention addresses the issue of two-dimensional rectangular cargo rotation. For a given rectangular cargo, the authors consider both rotated and non-rotated scenarios. They calculate the optimal candidate points for each scenario. They then compare the coverage areas of the new skylines under the two placement options and select the one with the smallest coverage area, thereby improving the utilization of the carriage's loading surface.

[0111] Step 5: Sort the individuals in the population in descending order of fitness value, and select EP_size dominant individuals with larger fitness values, where EP_size = Pop × β, Pop is the number of individuals in the population, and β is the percentage of dominant individuals.

[0112] Step 6: Perform a local search on the dominant individuals based on the variable neighborhood descent method (VND) to obtain the optimal scheduling order of customers in the individual routes.

[0113] To address the complexity of the solution space of the path planning problem, the present invention integrates multiple neighborhood structures and applies the variable neighborhood descent method to perform a local search for dominant individuals in the population. The process of updating the initial solution Sol0 based on the variable neighborhood descent method includes:

[0114] Step 6.1: Let q = 0, Sol * =Sol0.

[0115] Step 6.2, search for the solution Sol′ in the neighborhood NS q All neighborhood solutions of , if there exists a better solution Sol * The neighboring solution Sol′ with a higher fitness value, namely Fitness(Sol * )>Fitness(Sol′), then let Sol *=Sol′, and execute step 6.2 again; if there is no solution Sol * If the fitness value of the neighboring solution is lower, set q = q + 1; if q < |NS|, re-execute 6.2; if q = |NS|, execute step 6.3.

[0116] Step 6.3: Return the optimal solution Sol obtained by the variable neighborhood descent method * .

[0117] The present invention employs two types of neighborhood structures for the variable neighborhood descent search method: single-path neighborhood actions and paired-path neighborhood actions. Single-path neighborhood actions include single-path client position movement, single-path client exchange, and partial single-path client sequence reversal. Paired-path neighborhood actions include inter-path client position movement, inter-path client exchange, and path crossing.

[0118] Step 7: Update the probability model of the distribution estimation algorithm based on the dominant individual, including the probability model of the vehicle-customer allocation relationship and the probability model of the scheduling relationship between customers.

[0119] Among them, the vehicle-customer allocation relationship probability model is used to construct the allocation relationship between vehicles and customers. The vehicle-customer allocation probability model is a two-dimensional matrix P1 of size num_vehicles × num_customers. The matrix element p1(k,j) represents the probability of assigning customer j to vehicle k. Sampling the probability matrix P1 can obtain the vehicle-customer allocation relationship. num_vehicles is the total number of vehicles, and num_customers is the total number of customers.

[0120] The inter-customer scheduling relationship probability model represents the service order of vehicles for different customers in the route. The inter-customer scheduling relationship probability model is a two-dimensional matrix P2 of size num_customers×num_customers. The matrix element p2(i,j) represents the probability that customer i in the route is served before customer j.

[0121] Both of the above probability models follow the Population-Based Incremental Learning (PBIL) algorithm. The update method of the vehicle-customer assignment relationship probability model P1 is:

[0122]

[0123] Among them, g and g+1 represent the generations of the original population and the new population respectively, p1 kj represents the (k, j)th element of the probability matrix P1 of the vehicle-customer allocation relationship, α is the learning rate, Ind ep represents the epth dominant individual in the original population, where The values ​​and descriptions are as follows:

[0124]

[0125] The update method of the scheduling relationship probability model P2 between customers is:

[0126]

[0127] where p2 ij represents the (i, j)th element of the probability matrix P2 for scheduling relationships between customers, α is the learning rate, Ind ep represents the epth dominant individual in the original population, where The values ​​and descriptions are as follows:

[0128]

[0129] Step 8: Sample the updated probability model to obtain a new population. First, sample the probability model of the vehicle-customer allocation relationship to obtain the customer-vehicle allocation relationship, that is, which route the customer is on. Then sample the probability model of the inter-customer scheduling relationship to obtain the visit order of different customers on a certain route.

[0130] Step 9: Repeat steps 4 to 8 until the distribution estimation algorithm reaches the maximum number of iterations Mg.

[0131] Step 10: From all individuals in all populations of all generations, select the individual with the highest fitness as the historical optimal solution, which is the optimal solution of 2L-CVRP, including the customer visit sequence of each path, the corresponding rectangular cargo packing solution and the shortest vehicle distance Z 2l-cvrp , ending this process.

[0132] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A two-dimensional containerized vehicle path planning method based on an improved distribution estimation algorithm, characterized in that: The following steps are involved: Step 1: Calculate the distance initialization data between customers and initialize the improved distribution estimation algorithm; Step 2: Assign transportation routes to customers and merge routes based on the mileage saved. Arrange all routes in descending order based on the vehicle's current load capacity, cancel routes that exceed the number of vehicles, save the customers corresponding to the canceled routes in the list of unserved customers, and use an insertion rule-based algorithm to insert the unserved customers into the remaining routes. The resulting set of routes is used as an individual, and the initial population is composed of multiple individuals. Step 3: The skyline packing strategy based on tabu search calculates whether there is a cargo ordering that can accommodate all the cargoes. If so, it is a feasible solution; otherwise, it is an infeasible solution. The fitness of a feasible solution is the inverse of the sum of the route lengths, and the fitness of an infeasible solution is the set value; the individual with the larger fitness value is the dominant individual; Step 4: Based on the dominant individual, the probability model of the vehicle-customer allocation relationship and the probability model of the inter-customer scheduling relationship are updated. The probability model of the vehicle-customer allocation relationship is sampled to obtain the customer-vehicle allocation relationship. The probability model of the inter-customer scheduling relationship is sampled to obtain the visit order of different customers in the route. Step 5: If the distribution estimation algorithm reaches the maximum number of iterations, the individual with the highest fitness among all populations is taken as the historical optimal solution, and the process ends; otherwise, execute step 3.

2. The two-dimensional container vehicle path planning method according to claim 1 is characterized in that: The data in step 1 includes the number of transport vehicles, vehicle load and vehicle compartment specifications, distribution center coordinates, customer coordinates, total weight of customer cargo and customer cargo specifications.

3. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: The method for allocating transportation routes to customers in step 2 and merging routes based on the amount of mileage saved is as follows: an initial route set is established with the distribution center as the starting point and end point and the customer as the intermediate node; under the condition that the vehicle load constraint and the two-dimensional cargo loading constraint are satisfied, the original routes in the initial route set are merged into a new route, the mileage difference between the new route and the original route is calculated, and the new route that saves the most mileage compared to the original route is selected as the merged route.

4. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: In step 2, all routes are sorted in descending order according to the existing vehicle loads, and routes that exceed the number of vehicles are eliminated by sorting the routes in the merged route set in descending order of vehicle space utilization, and deleting a set number of routes with lower vehicle space utilization according to the route quantity constraint.

5. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: The method of inserting the unserved customer into the remaining routes using the insertion rule-based algorithm in step 2 is as follows: the customer with the largest cargo area ratio in the unserved customer list is designated as the target customer; if there is a route in the current route set that can accommodate the cargo of the target customer, then the route is added to the third route set; the target customer is inserted into the route with the lowest incremental cost in the third route set, and the third route set is updated; If it does not exist, a route is selected from the current route set, and customers on the route are deleted one by one until the target customer's goods can be accommodated. The second route set is updated, and the deleted customers are saved in the unserved customer list. The above process is repeated until all customers in the unserved customer list are inserted into the route.

6. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: The way to calculate whether an individual has a cargo sorting that can accommodate all cargoes in the skyline packing strategy based on tabu search in step 3 is: Step 4.1: Sort the goods to be transported by the individuals according to different heuristic rules to obtain multiple initial goods sequences; Step 4.2: Use the skyline algorithm to calculate the packing feasibility of the cargo lists of multiple initial cargo sequences. If there is an initial cargo sequence that can load all the cargo in the route into the carriage, then the tabu search process ends. Otherwise, proceed to step 4.

3. Step 4.3: Perform a swap sequence operation on the initial cargo sequence to generate a new cargo packing sequence. This swap sequence operation is added to the taboo table until the swap sequence operation is performed a number of times equal to the length of the taboo table, at which point the swap sequence operation is released from the taboo table. Step 4.4: Use the skyline algorithm to calculate the packing feasibility of the cargo list in the new cargo packing sequence. If all cargo can be packed, proceed to step 4.5; otherwise, randomly select a sequence permutation operation that is not in the taboo table and proceed to step 4.

3. Step 4.5: When a sequence that successfully loads all goods into the carriage is found, or the maximum number of iterations of the tabu search algorithm is reached, the tabu search process ends.

7. The two-dimensional container vehicle path planning method according to claim 6, characterized in that: When the cargo is a two-dimensional rectangular cargo, the skyline algorithm is used to calculate the packing feasibility of the cargo list of the new cargo packing sequence. The coverage area of ​​the new skyline under the cargo rotation and non-rotation placement schemes is calculated respectively, and the cargo packing sequence with the smaller coverage area is selected.

8. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: In step 3, a local search is performed on the dominant individuals based on the variable neighborhood descent method to obtain the optimal scheduling order of customers in the individual routes.

9. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: The updating method of the vehicle-customer allocation relationship probability model P1 is: Among them, g and g+1 represent the generations of the original population and the new population respectively, p1 kj represents the (k, j)th element of the probability matrix P1 of the vehicle-customer allocation relationship, α is the learning rate, Ind ep represents the epth dominant individual in the original population, for:

10. The two-dimensional container vehicle path planning method according to claim 1, characterized in that: The updating method of the inter-customer scheduling relationship probability model P2 is: Among them, p2 ij represents the (i, j)th element of the probability matrix P2 for scheduling relationships between customers, α is the learning rate, Ind ep represents the epth dominant individual in the original population, for:

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