Delayed acceptance memetic search method for solving minimum linear sorting problem

Abstract

The invention relates to a delayed acceptance memetic search method for solving a minimum linear sorting problem, which comprises the following steps of: (1) recording an optimal solution through an initial population P containing eta individuals generated by a population initialization program; (2) randomly selecting two parent solutions in the population, and generating a child solution by using a crossover operator based on local greedy; step (3), using a delayed acceptance hill-climbing algorithm and a classic hill-climbing algorithm to carry out local search on the filial generation solution, and updating the optimal solution; step (4), performing population updating based on a population updating strategy of diversity perception; step (5), repeating the step (2) to the step (4) until a set stop condition is met, and obtaining an optimal solution of the problem; according to the method, four efficient modules including a population initialization program, delayed acceptance of hill-climbing search, local greedy crossover operation and a population updating strategy considering population diversity are integrated, and the method has the advantages of being high in solving quality, high in robustness, wide in application range and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of logistics system design and planning, and in particular to a delayed acceptance meme search method for solving a minimum linear sorting problem. Background Art

[0002] The Minimum Linear Arrangement (MinLA) problem is a well-known graph layout problem. Its goal is to linearly order the vertices of an undirected graph so that the sum of the edge lengths is minimized, where the edge length is defined as the distance between the two vertices of the edge in the sequence position. MinLA has been widely used in many fields since it was first proposed by Harper in 1964 for the design of error-correcting codes. MinLA naturally appears in many practical and theoretical applications. For example, MinLA can be used as a model placement in very large-scale integrated circuit layout, where the vertices of the graph represent modules and the edges represent the connections between modules. MinLA can also be used as a simplified mathematical model of certain neural activities in the cerebral cortex. Other potential applications of MinLA include graph drawing, software graph layout, reordering of large sparse matrices, single-machine job scheduling, structural engineering, and software testing.

[0003] MinLA can be used as a model for the logistics facility location problem, where the vertices of the graph represent facilities, the edges represent the relationships between facilities, the serial numbers represent the location labels assigned to the facilities, and the edge length is the distance between the locations assigned to the two facilities at the edge endpoints. By sorting the facilities with the minimum total edge length as the goal, facilities with closer relationships are brought closer to each other.

[0004] In industrial logistics scenarios, in order to achieve efficient transportation, sorting, processing and storage of materials, it is necessary to establish a fully automated workshop warehousing solution. The reasonable layout and coordinated operation of a large number of processing, sorting, handling, warehousing and other facilities in the workshop are related to the overall operation efficiency of the workshop. The solution to the minimum linear sorting problem helps to layout these facilities and machines more reasonably.

[0005] In addition, this method can also be applied to other scenarios, such as the planning and layout of new energy vehicle charging facilities, the location arrangement of aircraft and boarding gates in airports, the layout of hospital rooms, the arrangement of office building departments, and the arrangement of goods in warehouses.

[0006] MinLA is a challenging graph layout problem in combinatorial optimization. The graph layout problem is a special type of combinatorial optimization problem, whose goal is to find consecutive different integer labels for the vertices of the graph, so as to optimize a certain objective function. MinLA can be formally described as follows. Let G = (V, E) be an undirected graph, where V (|V| = n) is the set of vertices and E (|E| = m) is the set of edges. Given an ordering, π:V→{1,2,...,n}, called a linear permutation, the total edge length of G relative to the permutation π is found according to the following formula:

[0007] f(π)=∑ (u,v)∈E |π(u)―π(v)|

[0008] Where π(u) and π(v) represent the labels assigned to facilities u and v, respectively. The goal of MinLA is to find a linear permutation π for a given graph G such that the target value f(π) is minimized. Figure 1 (a) shows a MinLA example with 6 points and 7 edges. Figure 1 (b) gives a feasible solution with a cost of 12. Figure 1 (c) describes an optimal solution with a cost of 7.

[0009] Researchers have found that for general graphs, MinLA is an NP-hard combinatorial optimization problem, and a heuristic algorithm is required to obtain a near-optimal solution within a reasonable running time. Based on the above analysis, the present invention mainly studies the minimum linear sorting problem. In view of the high complexity and long solution time of this problem, a delayed acceptance memetic search method (LAMS) is proposed. This method can effectively optimize the arrangement of facility locations, thereby minimizing logistics costs and transportation distances, and can meet the optimization needs in the site selection of logistics facilities. Summary of the invention

[0010] The technical problem to be solved by the present invention is to provide a delayed acceptance meme search method for solving the minimum linear sorting problem, so as to achieve high robustness and high quality solution.

[0011] In order to solve the above technical problems, the technical solution of the present invention is: a delayed acceptance meme search method for solving the minimum linear sorting problem, the innovation of which is: comprising the following steps:

[0012] Step (1), generate an initial population P containing n individuals through a population initialization program, and record the optimal solution;

[0013] Step (2), randomly select two parent solutions in the population, and use a local greedy crossover operator to generate a child solution;

[0014] Step (3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to perform local search on the offspring solution and update the optimal solution;

[0015] Step (4), updating the population based on the diversity-aware population update strategy;

[0016] Step (5): Repeat steps (2) to (4) until the set stop condition is reached and the optimal solution to the problem is obtained.

[0017] Furthermore, the specific steps of the population initialization procedure in step (1) include:

[0018] Step (1.1), randomly select a starting vertex and assign it label 1;

[0019] Step (1.2), for each remaining label 2 to n, select an unassigned vertex and assign it to label i through the Frontal Increase Minimization (FIM) strategy. Assume that to assign label i, P i represents the set of vertices that have currently been assigned labels, U i represents the set of vertices that are not currently assigned a label. The basic idea of ​​the FIM strategy is to select an adjacent U for label i. i ―F i The vertex with the least vertices, where F i = {u∈U i ,v∈P i ,(u,v)∈E}, represents the set of edge vertices that have been assigned vertices when assigning label i;

[0020] Step (1.3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to optimize the obtained initial solution;

[0021] Step (1.4), repeat steps (1.1) to (1.3) until the population P is filled with η high-quality solutions.

[0022] Furthermore, the step (1.2) heuristically defines an evaluation function (v)=d(v)-2|{(u,v)∈E,u∈P i}| to evaluate F i , where d(v) is the degree of vertex v. For each label i, select a vertex with the minimum The value of the vertex v∈F i , and assign it to its label i.

[0023] Furthermore, the crossover operator in step (2) specifically includes:

[0024] Step (2.1), randomly select two parent solutions g F and g M The common label assignment of vertex i in is directly inherited to the descendant solution π 0 And set these vertices to taboo state, that is, T[i] = 1;

[0025] Step (2.2), use the greedy mechanism to locally minimize the objective function f(π) =

[0026] ∑ (u,v)∈E |π(u)―π(v)| to find π 0 The labels of the adjacent vertices of the assigned vertices in ;

[0027] Step (2.3), for each remaining unassigned vertex, randomly assign it an unassigned label on the vertex from the two parent solutions;

[0028] Step (2.4) obtains a feasible sub-solution by randomly assigning the remaining labels to the remaining vertices.

[0029] Furthermore, the specific steps of the delayed acceptance hill climbing algorithm in step (3) include:

[0030] Step (3.1), solve π for the children generated in step (2) 0 Conduct a hill-climbing search with delayed acceptance;

[0031] Step (3.2), use the classical hill climbing algorithm (CHC) to solve π 0 Perform optimization again and update the optimal solution to the problem.

[0032] Furthermore, the specific steps of population updating described in step (4) include:

[0033] Step (4.1), tentatively put the newly generated solution S into the population P to obtain p′

[0034] = p∪(S);

[0035] Step (4.2), calculate the fitness score F(S) of each solution in p′ according to the following formula i ,P′);

[0036] F(S i ,P′)=λ*f′(S i )+(1―λ)*D′(S i ,P′)

[0037] In the formula, λ represents the weight factor;

[0038] Step (4.3), find the solution S with the largest fitness score w ;

[0039] Step (4.4), if the improved offspring solution S and S w Not the same, replace S with S w , otherwise discard S.

[0040] Furthermore, the specific steps of the delayed acceptance meme search method include:

[0041] Step (1), generate an initial population P containing n individuals through a population initialization program, and record the optimal solution;

[0042] Step (1.1), randomly select a starting facility and assign it label 1;

[0043] Step (1.2), for each remaining label 2 to n, through the frontal increase minimization (FIM) strategy, this FIM strategy represents the facility location selection process in the logistics facility location problem, where label assignment corresponds to facility location selection, select an unassigned facility and assign it to its label i. Assume that to assign label i, P i Represents the set of facilities that have currently been assigned labels, U i represents the set of facilities that are not currently assigned a label. The basic idea of ​​the FIM strategy is to select an adjacent U for label i. i ―F i The facility with the least facilities, among which F i = {u∈U i :v∈P i ,(u,v)∈E}, represents the set of unallocated facilities adjacent to the allocated facility when label i is assigned;

[0044] Heuristically define an evaluation function φ i (v)=d(v)-2|{(u,v)∈E,u∈P i}| to evaluate F i facilities in the set, where d(v) is the degree of facility v. For each label i, select a facility with the minimum φ i (v) facility v∈F i , and assign it to its label i;

[0045] Step (1.3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to optimize the obtained initial solution;

[0046] Step (1.4), repeat steps (1.1) to (1.3) until the population P is filled with η high-quality solutions;

[0047] Step (2), randomly select two parent solutions in the population, and use a local greedy crossover operator to generate a child solution;

[0048] Step (2.1), randomly select two parent solutions g F and g M The common label assignments of facility i in π are directly inherited to the descendant solutions π 0 And set these facilities to taboo state, that is, T[i] = 1;

[0049] Step (2.2), use the greedy mechanism to locally minimize the objective function f(π) =

[0050] ∑ (u,v)∈E |π(u)―π(v)| to find π 0 The labels of the neighboring facilities of the allocated facilities;

[0051] Step (2.3), for each remaining unassigned facility, randomly assign to it one of the unassigned labels on the facility from the two parent solutions;

[0052] Step (2.4), by randomly assigning the remaining labels to the remaining facilities, a feasible sub-generation solution is obtained;

[0053] Step (3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to perform local search on the offspring solution and update the optimal solution;

[0054] Step (3.1), solve π for the children generated in step (2) 0 Conduct a hill-climbing search with delayed acceptance;

[0055] Step (3.2), use the Classic Hill Climbing algorithm (CHC) to calculate π 0 Perform optimization again and update the optimal solution of the problem;

[0056] Step (4), updating the population based on the diversity-aware population update strategy;

[0057] Step (4.1), tentatively put the newly generated solution S into the population P to obtain p′

[0058] = p∪(S);

[0059] Step (4.2), calculate the fitness score F(S) of each solution in p′ according to the following formula i ,P′);

[0060] F(S i ,P′)=λ*f′(S i )+(1―λ)*D′(S i ,P′)

[0061] In the formula, λ represents the weight factor;

[0062] Step (4.3), find the solution S with the largest fitness score w ;

[0063] Step (4.4), if the improved offspring solution S and S w Not the same, replace S with S w , otherwise discard S;

[0064] Step (5), repeat step (2) to step (4) until the set stop condition is reached, and the best solution found in the problem solving process is obtained, that is, the best arrangement of the locations of logistics facilities.

[0065] The advantages of the present invention are:

[0066] (1) The delayed acceptance meme search method for solving the minimum linear sorting problem of the present invention integrates four efficient modules: a population initialization procedure, a delayed acceptance hill climbing search, a local greedy crossover operation, and a population update strategy that considers population diversity. It has the advantages of high solution quality, strong robustness, and a wide range of applications.

[0067] (2) The delayed acceptance meme search method of the present invention can effectively reduce logistics costs and improve service efficiency by optimizing the arrangement of facility locations in the application of logistics facility site selection problems. It has the advantages of high solution quality, strong robustness, and a wide range of applications. Especially in the face of complex logistics networks and changing demand conditions, the method exhibits strong adaptability and stability, and provides an efficient solution to the logistics facility site selection problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0069] Figure 1 The figure is a feasible MinLA example and the corresponding solution diagram of the present invention.

[0070] Figure 2 A schematic diagram of domain relations of neighborhood search based on delayed acceptance in the present invention.

[0071] Figure 3 Schematic diagram of three state changes of the state matrix of the classic hill climbing algorithm in the present invention.

[0072] Figure 4 For LAMS1 (disabled neighborhood N) in the present invention 1 ), LAMS2 (disable neighborhood N 2 ), LAMS3 (disable neighborhood N 3 ) and LAMS. DETAILED DESCRIPTION

[0073] The following embodiments can enable those skilled in the art to more fully understand the present invention, but the present invention is not limited to the scope of the embodiments.

[0074] The present invention provides a delayed acceptance meme search method for solving a minimum linear sorting problem, comprising the following steps:

[0075] Step (1), generate an initial population P containing n individuals through a population initialization program, and record the optimal solution;

[0076] Among them, the specific steps of the population initialization program include:

[0077] Step (1.1), randomly select a starting facility and assign it label 1;

[0078] Step (1.2), for each remaining label 2 to n, through the frontal increase minimization (FIM) strategy, this FIM strategy represents the facility location selection process in the logistics facility location problem, where label assignment corresponds to facility location selection. Select an unassigned facility and assign it to its label i. Suppose to assign label i, P i Represents the set of facilities that have currently been assigned labels, U i Represents a collection of facilities that are not currently assigned a label;

[0079] The basic idea of ​​the FIM strategy is to select a neighboring U for label i. i ―F i The facility with the least facilities, among which F i = {u∈U i ,v∈P i ,(u,v)∈E} represents the set of unallocated facilities adjacent to the allocated facility when label i is assigned;

[0080] Heuristically define an evaluation function φ i (v)=d(v)-2|{(u,v)∈E,u∈P i}| to evaluate F i facilities in the set, where d(v) is the degree of facility v. For each label i, select a facility with the minimum φ i (v) facility v∈F i , and assign it to its label i;

[0081] Step (1.3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to optimize the obtained initial solution;

[0082] Step (1.4), repeat steps (1.1) to (1.3) until the population P is filled with η high-quality solutions.

[0083] Step (2), randomly select two parent solutions in the population, and use a local greedy crossover operator to generate a child solution;

[0084] Among them, the specific steps of the crossover operator include:

[0085] Step (2.1), randomly select two parent solutions g F and g M The common label assignments of facility i in π are directly inherited to the descendant solutions π 0 And set these facilities to taboo state, that is, T[i] = 1;

[0086] Step (2.2), use the greedy mechanism to locally minimize the objective function f(π) =

[0087] ∑ (u,v)∈E |π(u)―π(v)|Find π 0 The labels of the neighboring facilities of the allocated facilities;

[0088] Step (2.3), for each remaining unassigned facility, randomly assign to it one of the unassigned labels on the facility from the two parent solutions;

[0089] In step (2.4), a feasible offspring solution is obtained by randomly assigning the remaining labels to the remaining facilities.

[0090] Step (3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to perform local search on the offspring solution and update the optimal solution;

[0091] like Figure 2 and Figure 3 As shown, the specific steps of the delayed acceptance hill climbing algorithm include:

[0092] Step (3.1), solve π for the children generated in step (2) 0 Perform delayed acceptance hill climbing search (LAHC);

[0093] LAHC includes two neighborhood operations: Random Swap Neighborhood 1 The solution π′ is obtained from a given candidate solution π by exchanging the labels of two randomly selected non-taboo facilities u and v; and the constrained swap neighborhood N 2 The solution π′ is obtained by exchanging a randomly selected non-taboo facility u with a non-taboo facility v that is close to its assigned label given a candidate solution π; in LAHC, we use the neighborhood N with probability ρ 1 Generate new candidate solutions and select N with a probability of 1-ρ2 Generate new candidate solutions;

[0094] The main idea of ​​LAHC is based on an array of size θ (i.e., history length), which is used to memorize the function values ​​of previously visited solutions. Initially, all elements of this array are assigned the function values ​​of the initial solution S. In each iteration ζ, a candidate solution S′ is generated; then, based on the comparison between the two, the target value of the candidate solution S′ is compared with the target value of the previous iteration solution stored in position v in the array (the virtual starting point of the array, v←ζmodθ) to decide whether to accept S′. Specifically, if the target value of the candidate solution S′ is not worse than the value fv in position v of the array, then we accept it. Then, we update the value of position v of the array, i.e., f v ←f(S′). This process is repeated until the stopping condition is met;

[0095] Step (3.2), use the Classic Hill Climbing algorithm (CHC) to calculate π 0 Perform optimization again and update the optimal solution of the problem;

[0096] CHC includes 1 neighborhood operation: Sequential Swap Neighborhood 3 Given a candidate solution π, two sequentially selected facilities u and v are exchanged in sequence and satisfy u <v的标签得到的解π′组成,邻域N 1 、N 2 and N 3 The relationship is as Figure 2 As shown, where rd is a random number between 0 and 1, and ρ is a parameter representing the neighborhood N in LAHC. 1 In the search process, firstly, the neighborhood N 3 is decomposed into n×n exchange neighborhoods, where n is the number of facilities; then, the search is concentrated on promising neighborhoods, skipping neighborhoods that have been checked without hope in previous searches. Initially, all N 3 (π,u,v) are all promising. During the search process, if a neighborhood N 3 (π,u,v) is judged to be valid, then all neighborhoods including facilities u, v and their adjacent facilities become promising. To indicate whether the exchange neighborhood has been checked during the search process, we construct an n×n binary state matrix M. If the neighborhood N that has been checked before 3 (π,u,v), no improved solution is found, then M uv =0, otherwise 1. Figure 3 The three state changes of the state matrix are shown. Initially, all neighbors are promising neighbors, and the corresponding state matrix values ​​are all 1, such as Figure 3 (a). During the search process, if the facility v is checked i 、v j If no improved solution is found after the exchange operation between them, M(i,j)=0 is adjusted. Otherwise, M(i,j)=1. Figure 3 (b) shows the state matrix M at time t, Figure 3 (c) shows the updated state matrix M at time t+1, where facility v 3 and v 4 The exchange operations between them can improve the solution. Once the exchange operation is performed, all 3 、v 4 The exchange operations associated with and its neighboring facilities will become promising exchange operations. Accordingly, their state matrix values ​​are set to 1, such as Figure 3 (c) as shown.

[0097] Step (4), updating the population based on the diversity-aware population update strategy;

[0098] Among them, the specific steps of population update include:

[0099] Step (4.1), tentatively put the newly generated solution S into the population P to obtain p′

[0100] = p∪(S);

[0101] Step (4.2), calculate the fitness score F(S) of each solution in p′ according to the following formula i ,P′);

[0102] F(S i ,P′)=λ*f′(S i )+(1―λ)*D′(S i ,P′)

[0103] In the formula, λ represents the weight factor;

[0104] Step (4.3), find the solution S with the largest fitness score w ;

[0105] Step (4.4), if the improved offspring solution S and S w Not the same, replace S with S w , otherwise discard S.

[0106] Step (5), repeat step (2) to step (4) until the set stop condition is reached, and the best solution found in the problem solving process is obtained, that is, the best arrangement of the locations of logistics facilities.

[0107] Combination Figure 4 Further explanation of neighborhood N 1 、N2 and N 3 effectiveness.

[0108] We experimentally compare LAMS with its three variants, LAMS1, LAMS2, and LAMS3. LAMS1 can be disabled by 1 Obtained from LAMS, LAMS2 can be obtained by disabling the neighborhood N 2 Obtained from LAMS, LAMS3 can be obtained by disabling the neighborhood N 3 Obtained from LAMS. Use line graphs to compare performance. Figure 4 The optimal solution f of LAMS1, LAMS2, LAMS3 and LAMS is shown min and the average solution f avg Performance comparison. Figure 4 In the example, the x-axis represents the specific example, and the y-axis represents the performance gap relative to BKS (known optimal solution). By taking BKS as the benchmark, the performance gap between them is calculated as (f―f 0 ) / f 0 × 100%, where f is the result, f 0 is the value of the benchmark BKS. Figure 4 LAMS outperforms LAMS1, LAMS2, and LAMS3. In terms of optimal solution, LAMS outperforms its three variants in 5 out of 6 cases, and outperforms BKS in 2 of them. Overall, LAMS3 is slightly worse than LAMS, while LAMS1 is significantly worse than LAMS. Similarly, the same results can be obtained from the figure in terms of average solution. These results show that the neighborhood N 1 、N 2 and N 3 The has a clear role in LAMS.

[0109] In the application of the delayed acceptance meme search method in the logistics facility location selection problem, by optimizing the arrangement of facility locations, it can effectively reduce logistics costs and improve service efficiency. It has the advantages of high solution quality, strong robustness, and a wide range of applications. Especially in the face of complex logistics networks and changing demand conditions, this method shows strong adaptability and stability, and provides an efficient solution to the logistics facility location selection problem.

[0110] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A delayed acceptance meme search method for solving the minimum linear sorting problem, characterized by: The following steps are involved: Step (1), generate an initial population P containing n individuals through a population initialization program, and record the optimal solution; Step (2), randomly select two parent solutions in the population, and use a local greedy crossover operator to generate a child solution; Step (3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to perform local search on the offspring solution and update the optimal solution; Step (4), updating the population based on the diversity-aware population update strategy; Step (5): Repeat steps (2) to (4) until the set stop condition is reached and the optimal solution to the problem is obtained.

2. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 1, characterized in that: The specific steps of the population initialization procedure in step (1) include: Step (1.1), randomly select a starting vertex and assign it label 1; Step (1.2), for each remaining label 2 to n, select an unassigned vertex and assign it to label i through the Frontal Increase Minimization (FIM) strategy. Assume that to assign label i, P i represents the set of vertices that have currently been assigned labels, U i represents the set of vertices that are not currently assigned a label. The basic idea of ​​the FIM strategy is to select an adjacent U for label i. i ―F i The vertex with the least vertices, where F i = {u∈U i ,v∈P i ,(u,v)∈E}, represents the set of edge vertices that have been assigned vertices when assigning label i; Step (1.3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to optimize the obtained initial solution; Step (1.4), repeat steps (1.1) to (1.3) until the population P is filled with η high-quality solutions.

3. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 2, characterized in that: In step (1.2), a heuristic evaluation function φ is defined i (v)=d(v)-2|{(u,v)∈E,u∈P i }| to evaluate F i where d(v) is the degree of vertex v. For each label i, select a vertex with the minimum φ i (v) value of vertex v∈F i , and assign it to its label i.

4. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 1, characterized in that: The specific steps of the crossover operator in step (2) include: Step (2.1), randomly select two parent solutions g F and g M The common label assignment of vertex i in is directly inherited to the descendant solution π0, and these vertices are set to taboo state, that is, T[i] = 1; Step (2.2), use the greedy mechanism to locally minimize the objective function f(π) = ∑ (u,v)∈E |π(u)―π(v)| to find the labels of the adjacent vertices of the assigned vertices in π0; Step (2.3), for each remaining unassigned vertex, randomly assign it an unassigned label on the vertex from the two parent solutions; Step (2.4) obtains a feasible sub-solution by randomly assigning the remaining labels to the remaining vertices.

5. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 1, characterized in that: The specific steps of the delayed acceptance hill climbing algorithm in step (3) include: Step (3.1), perform delayed acceptance hill climbing search on the offspring solution π0 generated in step (2); Step (3.2), use the classical hill climbing algorithm (CHC) to optimize π0 again and update the optimal solution of the problem.

6. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 1, characterized in that: The specific steps of population updating described in step (4) include: Step (4.1), tentatively put the newly generated solution S into the population P to obtain p ′ = p∪(S); Step (4.2), calculate p according to the following formula ′ The fitness score F(S i ,P ′ ); F(S i ,P ′ )=λ*f ′ (S i )+(1―λ)*D ′ (S i ,P ′ ) In the formula, λ represents the weight factor; Step (4.3), find the solution S with the largest fitness score w ; Step (4.4), if the improved offspring solution S and S w Not the same, replace S with S w , otherwise discard S.

7. The delayed acceptance meme search method for solving the minimum linear sorting problem according to claim 1, characterized in that: The specific steps of the delayed acceptance meme search method include: Step (1), generate an initial population P containing n individuals through a population initialization program, and record the optimal solution; Step (1.1), randomly select a starting facility and assign it label 1; Step (1.2), for each remaining label 2 to n, through the frontal increase minimization (FIM) strategy, this FIM strategy represents the facility location selection process in the logistics facility location problem, where label assignment corresponds to facility location selection, select an unassigned facility and assign it to its label i. Assume that to assign label i, P i Represents the set of facilities that have currently been assigned labels, U i represents the set of facilities that are not currently assigned a label. The basic idea of ​​the FIM strategy is to select an adjacent U for label i. i ―F i The facility with the least facilities, among which F i = {u∈U i :v∈P i ,(u,v)∈E}, represents the set of unallocated facilities adjacent to the allocated facility when label i is assigned; Heuristically define an evaluation function φ i (v)=d(v)-2|{(u,v)∈E,u∈P i }| to evaluate F i facilities in the set, where d(v) is the degree of facility v. For each label i, select a facility with the minimum φ i (v) facility v∈F i , and assign it to its label i; Step (1.3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to optimize the obtained initial solution; Step (1.4), repeat steps (1.1) to (1.3) until the population P is filled with η high-quality solutions; Step (2), randomly select two parent solutions in the population, and use a local greedy crossover operator to generate a child solution; Step (2.1), randomly select two parent solutions g F and g M The common label assignment of facility i is directly inherited to the child solution π0, and these facilities are set to the taboo state, that is, T[i] = 1; Step (2.2), use the greedy mechanism to locally minimize the objective function f(π) = ∑ (u,v)∈E |π(u)―π(v)| to find the labels of the neighboring facilities of the allocated facilities in π0; Step (2.3), for each remaining unassigned facility, randomly assign to it one of the unassigned labels on the facility from the two parent solutions; Step (2.4), by randomly assigning the remaining labels to the remaining facilities, a feasible sub-generation solution is obtained; Step (3), use the delayed acceptance hill climbing algorithm and the classical hill climbing algorithm to perform local search on the offspring solution and update the optimal solution; Step (3.1), perform delayed acceptance hill climbing search on the offspring solution π0 generated in step (2); Step (3.2), use the Classic Hill Climbing algorithm (CHC) to optimize π0 again and update the optimal solution of the problem; Step (4), updating the population based on the diversity-aware population update strategy; Step (4.1), tentatively put the newly generated solution S into the population P to obtain p ′ = p∪(S); Step (4.2), calculate p according to the following formula ′ The fitness score F(S i ,P ′ ); F(S i ,P ′ )=λ*f ′ (S i )+(1―λ)*D ′ (S i ,P ′ ) In the formula, λ represents the weight factor; Step (4.3), find the solution S with the largest fitness score w ; Step (4.4), if the improved offspring solution S and S w Not the same, replace S with S w , otherwise discard S; Step (5), repeat step (2) to step (4) until the set stop condition is reached, and the best solution found in the problem solving process is obtained, that is, the best arrangement of the locations of logistics facilities.

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