CN117689417A - Optimization method and system applied to site selection of logistics distribution center - Google Patents

Abstract

The disclosure provides an optimization method applied to site selection of a logistics distribution center, comprising the following steps: s1, constructing a site selection model of a logistics distribution center; s2, solving the logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution; in the mutation stage in the immune algorithm, the antibody is updated by adopting a multiplication and division searching strategy or an addition and subtraction searching strategy in the arithmetic optimization algorithm; in the technical scheme of the disclosure, an arithmetic optimization algorithm is combined with an immune algorithm, a variation updating mode of a population is changed, a multiplication and division method is used for updating the population in an exploration stage, and an addition and subtraction method is used for completing the population updating in a development stage, so that the convergence speed can be effectively increased, and the obtained result is better.

Description

Optimization method and system applied to site selection of logistics distribution center

Technical Field

The disclosure relates to the technical field of site selection of logistics distribution centers, in particular to an optimization method and system applied to site selection of logistics distribution centers.

Background

The Location-Allocation Problem (LAP) problem of logistics distribution centers is an important planning problem in modern logistics distribution settings. The logistics distribution center is a core node and an important infrastructure in a logistics system network, and plays a pivotal role in the whole logistics system network planning. In the research aspect of the addressing problem, the method mainly comprises mixed integer programming solution, large-scale group decision solution, two-stage random programming solution, a multi-objective network optimization model with random fuzzy coefficients, genetic algorithm addressing solution with multi-cost factors and the like. However, as the scale of the problem increases, the efficiency and accuracy of model solving also need to be improved, so that a new efficient solving method is needed to solve the problem.

Disclosure of Invention

The disclosure aims to at least solve one of the technical problems in the prior art, and provides an optimization method and system applied to site selection of a logistics distribution center.

In a first aspect, an embodiment of the present disclosure provides an optimization method applied to site selection of a logistics distribution center, which is characterized by including:

s1, constructing a site selection model of a logistics distribution center;

the logistics distribution center site selection model aims at: selecting and starting p logistics distribution centers from n alternative logistics distribution centers, wherein the sum of the products of the distances from m demand points to the logistics distribution centers corresponding to the goods and the demand of the goods is minimum; an enabling parameter h for characterizing whether the j-th alternative logistics distribution center is enabled _j ；

S2, solving the logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution comprises each enabling parameter h _j Is the optimum value of (2); the method specifically comprises the following steps:

step S201, carrying out an initialization stage in an immune algorithm, enabling iteration times Iter to be 1, generating an initial antibody population containing q antibodies, and taking the initial antibody population as an original antibody population corresponding to the Iter iteration treatment, wherein each antibody comprises p dimensions, the p dimensions represent p logistics distribution centers which are selected and started from n alternative logistics distribution centers, the value of each dimension in the p dimensions in the antibody is an integer, and the value range is [1, n ];

Step S202, judging whether the original antibody population of the Iter iteration meets the iteration termination condition;

if it is determined that the original antibody population of the Iter iteration satisfies the iteration termination condition, step S207 is executed; if it is determined that the original antibody population of the Iter iteration does not meet the iteration termination condition, executing step S203;

step S203, selecting k antibodies from the original antibody population processed by the Iter iteration to form a current memory bank, wherein k is a positive integer and k is less than q;

step S204, in the crossing stage in the immune algorithm, q-k parent antibodies are selected from the original antibody population subjected to the Iter iteration treatment, and the q-k child antibodies are obtained through the crossing treatment, so that the child antibody population subjected to the Iter iteration treatment is formed;

step S205, performing a mutation stage in an immune algorithm, wherein at least part of offspring antibodies in the offspring antibody population processed by the Iter iteration are used as target offspring antibodies, and performing mutation updating on the target offspring antibodies; the method specifically comprises the following steps:

step S2051, entering a mathematical optimization acceleration stage of an arithmetic optimization algorithm, and determining a mathematical optimization acceleration coefficient MOA (Iter) corresponding to the Iter iteration process;

Step S2052 of comparing the pre-generated random number r between 0 and 1 ₁ Size with MOA (Iter);

if r ₁ < MOA (Iter), then step S2053 is performed; if r ₁ > MOA (Iter), then step S2054 is performed;

step S2053, entering an exploration stage of an arithmetic optimization algorithm, and carrying out mutation updating on a target offspring antibody in the offspring antibody population processed by the Iter iteration based on a multiplication and division searching strategy;

step S2054, entering a development stage of an arithmetic optimization algorithm, and carrying out mutation updating on a target offspring antibody in the offspring antibody population processed by the Iter iteration based on an addition and subtraction searching strategy;

step S206, the k antibodies in the current memory bank of the Iter iteration process and q-k antibodies in the offspring antibody population after the mutation updating process are combined to form an original antibody population corresponding to the Iter+1st iteration process, and 1-adding process is carried out on the Iter to update;

after the end of step S206, step S202 is executed.

And S207, outputting the optimal affinity antibody in the original antibody population of the Iter iteration to obtain the current optimal solution.

In some embodiments, the objective function in the logistics distribution center site selection model is:

F represents the product of the distance from m demand points to the logistics distribution center of corresponding goods supply and the demand quantity of the logistics distribution center, d _ij Represents the distance from the ith demand point to the jth alternative logistics distribution center, w _i Indicating the material demand of the ith demand point, Z _ij For characterizing whether the ith demand point is delivered by the jth alternative logistics delivery center;

the value of each of the p dimensions in the antibody is for Z _ij Is encoded again; for any ith demand point, if the value of the current selected antibody is j in p dimensions, and the distance between the ith demand point and the jth logistics distribution center is smaller than or equal to the distance between the ith demand point and the logistics distribution center shown by other p-1 dimensions except the value of the current selected antibody, at the moment, Z in the objective function _ij The value is 1; otherwise Z _ij The value is 0;

the value of each of the p dimensions in the antibody is for Z _ij Is encoded again; for any ith demand point, if the value of the current selected antibody is j in p dimensions, and the distance between the ith demand point and the jth logistics distribution center is smaller than or equal to the distance between the ith demand point and the logistics distribution center shown by other p-1 dimensions except the value of the current selected antibody, at the moment, Z in the objective function _ij The value is 1; otherwise Z _ij The value is 0;

the constraint conditions in the logistics distribution center site selection model comprise:

condition 1, a demand point can only be distributed by one logistics distribution center, a plurality of demand points can be distributed by one logistics distribution center, and the distribution radius of the logistics distribution center is not limited:

only p of the condition 2, n alternative logistics distribution centers are enabled:

condition 3, only the activated logistics distribution center can distribute to the demand point, and the non-activated logistics distribution center cannot distribute to the demand point:

in some embodiments, in step S205, before step S2051, further comprising:

step S2050a, determining the affinity of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t.epsilon.1, q-k]

B1 _t Represents the affinity of the t th generation antibody in the offspring antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the(s) th dimension in the (t) th sub-generation antibody in the sub-generation antibody population, D1 _i,t Indicating the ith demand point and offspring reactanceThe minimum value of the distance between the logistics distribution centers shown in each dimension in the t-th sub-generation antibody in the body population;

step S2050b, determining the mutation probability of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

P1 _t Representing variation probability of t-th generation antibody in offspring antibody population, wherein alpha 1 is a first preset probability value, alpha 2 is a second preset probability value, alpha 1 epsilon (0, 1), alpha 2 epsilon (0, 1) and alpha 1 < alpha 2, and mu 1 is a first preset coefficient and mu 1 epsilon [0.8,1 ]]，B1 _best Representing the maximum of affinities of all progeny antibodies within the population of progeny antibodies;

step S2050c, generating random numbers for mutation between 0 and 1 corresponding to each child antibody aiming at each child antibody in the child antibody population processed by the Iter iteration, and screening child antibodies with the corresponding random numbers for mutation larger than the corresponding mutation probability as target child antibodies.

In some embodiments, step S204 includes:

step S2041, determining the affinity of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,representing the point of the ith demand to the s-th dimension of the t' th antibody in the original antibody populationDistance between hearts, D2 _i,t' Representing the minimum value of the distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population;

Step S2042, determining the cross probability of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

P2 _t' representing the cross probability of the t' th antibody in the original antibody population, wherein alpha 3 is a third preset probability value, alpha 4 is a fourth preset probability value, alpha 3 epsilon (0, 1), alpha 4 epsilon (0, 1) and alpha 3 < alpha 4, mu 2 is a second preset coefficient and mu 2 epsilon [0.8,1 ]]，B2 _best Representing the maximum of affinities of all antibodies within the original antibody population;

s2043, screening the first q-k antibodies with the highest cross probability from the original antibody population processed by the Iter iteration as parent antibodies;

and S2044, performing cross treatment based on q-k parent antibodies to obtain corresponding q-k child antibodies to form a child antibody population.

In some embodiments, step S203 includes:

step S2031, determining the affinity of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,representing the ith point of demand to the original antibodyDistance between logistics distribution centers shown in the s-th dimension in t' th antibody in population, D2 _i,t' Representing the minimum value of the distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population;

Step S2032, determining the association force between antibodies in the original antibody population processed by the Iter iteration based on the following formula;

wherein s is _t',t” Representing the association force between the set corresponding to the t 'th antibody and the set corresponding to the t' th antibody in the original antibody population; k (K) _t',t” Representing the number of identical elements in the set corresponding to the t 'th antibody and the set corresponding to the t' th antibody in the original antibody population, wherein t 'is a positive integer and t' is E [1, q ]]T 'is a positive integer and t' is [1, q ]]；

Step S2033, determining the concentration of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

wherein C is _t' Is the concentration of the t' th antibody in the original antibody population,is the association force S between the t 'th antibody corresponding set and the t' th antibody corresponding set in the original antibody population _t',t” Mapping results of mapping to 0 or 1, wherein T is a preset threshold constant;

step S2034, determining expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

wherein P is _t' For the expected reproduction rate of the t' th antibody in the original antibody population, lambda is a preset weight coefficient, lambda epsilon (0, 1), theta is a variable parameter, maxIter is a preset maximum iteration number, beta is a preset adjustment coefficient, and beta epsilon [0,1 ] ]；

Step S2035, selecting k antibodies from the original antibody population according to the roulette selection mechanism by taking the expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration as the probability of each antibody being selected.

In some embodiments, the mathematically optimized acceleration coefficient MOA (Iter) is derived based on the following equation:

Min_MOP and Max_MOP are respectively a preset minimum optimization probability and a preset maximum optimization probability, and MaxIter is a preset maximum iteration number.

In some embodiments, in step S2053, variant updates are made to the t th sub-generation antibody as the target sub-antibody within the population of progeny antibodies processed by the first iteration based on the following formula:

xam _t,s (Iter) means that the inside of the offspring antibody population treated by the Iter's iteration is the target offspringThe value of the s-th dimension after mutation update of the t-th sub-antibody of the antibody, MOP (Iter) represents the mathematical optimization probability corresponding to the Iter iteration process, best (xa) _s Iter) represents the value of the optimal affinity antibody in the s-dimension of the population of offspring antibodies processed at the Iter iteration, round () represents a rounding function, ε is a predetermined constant, α is a predetermined sensitivity parameter, LB _s And UB _s Representing the lower and upper bounds of the s-th dimension in the antibody, wherein the lower bound has a value of 1, the upper bound has a value of n, μ is a constant having a value between 0 and 1, r ₂ To take on random numbers between 0 and 1.

In some embodiments, in step S2054, variant updates are made to the t th sub-generation antibody as the target sub-antibody within the population of progeny antibodies processed by the first iteration based on the following formula:

xam _t,s (Iter) represents the value of the s-th dimension after mutation update of the t-th child antibody as the target child antibody in the child antibody population subjected to the Iter iteration process, MOP (Iter) represents the mathematical optimization probability corresponding to the Iter iteration process, best (xa) _s Iter) represents the value of the optimal affinity antibody in the s-th dimension of the population of offspring antibodies processed by the Iter iteration, round () represents the rounding function, alpha is a preset sensitivity parameter, LB _s And UB _s Representing the lower and upper bounds of the s-th dimension in the antibody, wherein the lower bound has a value of 1, the upper bound has a value of n, μ is a constant having a value between 0 and 1, r ₃ To take on random numbers between 0 and 1.

In a second aspect, an embodiment of the present disclosure further provides an optimization system applied to site selection of a logistics distribution center, wherein the optimization method as provided in the first aspect can be implemented, and the optimization system includes:

the component module is used for constructing a logistics distribution center site selection model;

The logistics distribution center site selection model aims at: selecting and starting p logistics distribution centers from n alternative logistics distribution centers, wherein the sum of the products of the distances from m demand points to the logistics distribution centers corresponding to the goods and the demand of the goods is minimum; an enabling parameter h for characterizing whether the j-th alternative logistics distribution center is enabled _j ；

The arithmetic-immune optimization module is used for solving the logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution comprises each enabling parameter h _j Is set to the optimum value of (2).

In a third aspect, an embodiment of the present disclosure further provides an electronic device, including:

one or more processors;

a memory for storing one or more programs;

the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the optimization method as provided in the first aspect.

Drawings

Fig. 1 is a flowchart of an optimization method applied to site selection of a logistics distribution center according to an embodiment of the present disclosure.

FIG. 2 is a schematic diagram showing comparison between the arithmetic-immune optimization algorithm according to the present disclosure and the solution results of the conventional immune algorithm and the simulated annealing algorithm in the related art;

FIG. 3 is a block diagram of an optimization system for site selection in a logistics distribution center according to an embodiment of the present disclosure;

fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the disclosure.

Detailed Description

In order that those skilled in the art will better understand the technical solutions of the present disclosure, the present disclosure will be described in further detail with reference to the accompanying drawings and detailed description.

Unless defined otherwise, technical or scientific terms used in this disclosure should be given the ordinary meaning as understood by one of ordinary skill in the art to which this disclosure belongs. The terms "first," "second," and the like, as used in this disclosure, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Likewise, the terms "a," "an," or "the" and similar terms do not denote a limitation of quantity, but rather denote the presence of at least one. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate relative positional relationships, which may also change accordingly when the absolute position of the object being described changes.

Like elements are denoted by like reference numerals throughout the various figures. For purposes of clarity, the various features of the drawings are not drawn to scale. Furthermore, some well-known portions may not be shown in the drawings.

Numerous specific details of the disclosure are set forth below in order to provide a more thorough understanding of the disclosure. However, as will be understood by those skilled in the art, the present disclosure may be practiced without these specific details.

The Immune Algorithm (IA) belongs to a genetic Algorithm, and imitates the deriving rule and other characteristic information of organisms in an Immune system through an Immune operator, so that the Immune Algorithm has the learning capability of the genetic Algorithm and certain updating, exciting, calculating, memorizing and global searching capabilities. The algorithm is mainly divided into three stages, namely an initialization stage: at this stage, the immune algorithm will randomly generate a certain number of antibodies (also called individuals) based on the characteristics and parameter settings of the problem; and secondly, a clone selection stage: at this stage, a portion from each antibody is randomly selected for cloning operations based on fitness values; third, the variant evolution stage: at this stage, a crossover and mutation mechanism is introduced, i.e. two different antibodies are crossed and mutated to obtain a new antibody. Cross variation can increase antibody diversity and improve searching ability. Through the continuous iteration of the three stages, the evolution process of the biological immune system is simulated, so that the optimal solution is found. IA has the following advantages: (1) the self-adaptive capacity is strong, the IA can adapt to different problem environments and parameter changes, and the robustness is strong; (2) the method has strong flexibility, and the immune algorithm can adapt to different types of optimization problems by adjusting parameters and strategies, so that the method has higher flexibility. Although IA exhibits the above advantages well when solving a partial optimization problem, IA is prone to be trapped in a local optimal solution when facing a complex optimization problem, and a problem that a global optimal solution cannot be found easily occurs because it is susceptible to the local optimal solution during the search. In view of this, many scholars at home and abroad have improved on the IA algorithm. For example, in terms of search strategies and convergence, one of the related technologies proposes a group immune optimization algorithm to improve convergence by performing a solution space search by mimicking the rapid propagation and death update of viruses; in the aspects of individual updating mode and population diversity, a second related technology provides a discrete coronavirus immune algorithm, introduces a discrete individual updating mode and provides a population updating mechanism of multi-scale joint search to quickly and uniformly search a solution space; in the aspect of the preservation and utilization of the population, the third related technology combines an immune algorithm and a genetic algorithm and improves the immune algorithm, so that elite population is preserved and utilized, loss of good individuals is avoided, and the accuracy of an optimal solution is improved; in the aspect of immune operation, a hybrid immune algorithm is proposed in the fourth related technology, and the feasible solution is improved by adopting the crossover and variation of immune operation, so that the accuracy of the feasible solution is further improved. Although the above-described improved IA algorithm achieves better results in solving some optimization problems. However, for the difficult problem of locating the logistics distribution center, although the IA algorithm can solve the LAP problem to a certain extent, the following disadvantages still exist:

First, the update method adopted by the conventional IA algorithm in the cross mutation stage is too simple, resulting in insufficient population diversity. Population diversity is an important factor of algorithm performance, and can help the algorithm to explore a wider problem space, so that a better solution can be found with a higher probability. In the cross mutation process of the IA algorithm, the clone selection operation can lead to mass propagation of excellent individuals, and worse individuals are eliminated, so that population diversity is reduced; in addition, affinity maturation may also lead to reduced population diversity, as individuals with high similarity compete with each other, resulting in the elimination of some individuals. The deficiencies of the prior art methods in this respect can lead to reduced convergence of the algorithm and difficulty in achieving a globally optimal solution.

Secondly, the problem of slow convergence speed is solved, specifically, the IA algorithm regards the search space as an antigen space, and optimizes the antigen by simulating cloning, mutation and other processes in the human immune system. However, these processes consume significant computational resources and time, and when dealing with complex problems, the search space is very large, and millions of iterations may be required to find a satisfactory solution.

In addition, the search process of the IA algorithm may be affected by other factors, such as setting parameters of cloning efficiency, mutation rate, etc., selection of an initial solution, etc. If these factors are not reasonably controlled, a slower convergence rate may result. This is particularly true when dealing with large-scale optimization problems such as the location of a logistics distribution center.

The arithmetic optimization algorithm (Arithmetic Optimization Algorithm, AOA for short) is a meta-heuristic optimization algorithm designed based on the idea of four-rule mixed operation. The algorithm is divided into three parts, namely, an optimization strategy is selected through a mathematical optimizer accelerating function; the second is that the searching stage uses multiplication strategy and division strategy to make global searching, so as to raise the dispersion of solution, enhance the global optimizing and overcoming the convergence ability of premature, and implement global searching optimizing; and in the development stage, the dispersion of the solution is reduced by utilizing an addition strategy and a subtraction strategy, so that the population is fully developed in a local range, and the local optimizing capability of an algorithm is enhanced. AOA has the following advantages: (1) the operation is simple, and the universality is strong; (2) the self-adaptive learning capability is strong, and the searching precision and the convergence speed can be balanced; (3) global and local searches may be balanced.

In order to effectively improve at least one technical problem existing in the related technology, the technical scheme of the present disclosure provides an optimization method applied to site selection of a logistics distribution center based on a combination of an IA algorithm and an AOA algorithm.

Fig. 1 is a flowchart of an optimization method applied to site selection of a logistics distribution center according to an embodiment of the present disclosure. As shown in fig. 1, the optimization method includes:

s1, constructing a logistics distribution center site selection model.

The following assumptions are made in this disclosure for the logistics distribution center site selection problem:

(1) The logistics distribution center is sized to support demand supplies at demand points and is determined by the demand in its distribution radiation range.

(2) One demand point can only meet the distribution demand by one logistics distribution center, and one logistics distribution center can radiate a plurality of demand points.

(3) Regardless of the service radius of the logistics distribution center.

The logistics distribution center site selection model aims at: selecting and starting p logistics distribution centers from n alternative logistics distribution centers, wherein the sum of the products of the distances from m demand points to the logistics distribution centers corresponding to the goods and the demand of the goods is minimum; an enabling parameter h for characterizing whether the j-th alternative logistics distribution center is enabled _j ；

S2, solving a logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution; wherein, the current optimal unpackingIncluding each enabling parameter h _j Is set to the optimum value of (2).

The step S2 specifically includes:

step S201, carrying out an initialization stage in an immune algorithm, enabling iteration times Iter to be 1, generating an initial antibody population containing q antibodies, and taking the initial antibody population as an original antibody population corresponding to Iter iteration treatment, wherein each antibody comprises p dimensions, and the p dimensions represent p logistics distribution centers which are selected and started from n alternative logistics distribution centers; wherein the value of each of the p dimensions in the antibody is an integer and the range of values is [1, n ].

The process of generating an initial population of antibodies in the IA algorithm is well within the routine skill in the art and will not be described in detail herein.

Step S202, judging whether the original antibody population of the Iter iteration meets the iteration termination condition.

If it is determined that the original antibody population of the Iter iteration satisfies the iteration termination condition, step S207 is executed; if it is determined that the original antibody population of the ith iteration does not meet the iteration termination condition, step S203 is performed.

In practical application, the iteration termination condition can be preset according to practical requirements; for example, the iterative process ends when the original antibody population of the ith iteration satisfies at least one of the following iteration termination conditions:

1) The iteration number Iter is larger than the preset maximum iteration number MaxIter.

2) The affinity (affinity), which may also be referred to as fitness) value of the optimal affinity antibody in the original antibody population of the ith iteration is greater than a preset affinity threshold.

The optimal affinity antibody in the original antibody population refers to the antibody with the largest affinity value corresponding to the original antibody population. For calculation of affinity of antibodies, see examples below.

Step S203, selecting k antibodies from the original antibody population processed by the Iter iteration to form a current memory bank, wherein k is a positive integer and k is less than q.

Step S204, in the crossing stage in the immune algorithm, q-k parent antibodies are selected from the original antibody population subjected to the Iter iteration treatment, and the q-k child antibodies are obtained through the crossing treatment, so that the child antibody population subjected to the Iter iteration treatment is formed.

Step S205, performing a mutation stage in an immune algorithm, taking at least part of offspring antibodies in the offspring antibody population processed by the Iter iteration as target offspring antibodies, and performing mutation updating on the target offspring antibodies.

The step S205 specifically includes:

Step S2051, entering a mathematical optimization acceleration stage of an arithmetic optimization algorithm, and determining a mathematical optimization acceleration coefficient MOA (Iter) corresponding to the Iter iteration process.

In some embodiments, the mathematically optimized acceleration coefficient MOA (Iter) is derived based on the following equation:

Min_MOP and Max_MOP are respectively a preset minimum optimization probability (for example, the value is 0.2) and a maximum optimization probability (for example, the value is 1), and MaxIter is a preset maximum iteration number (for example, the value is 200).

Step S2052 of comparing the pre-generated random number r between 0 and 1 ₁ And MOA (Iter).

If r ₁ < MOA (Iter), then step S2053 is performed; if r ₁ > MOA (Iter), step S2054 is performed.

Step S2053, entering an exploration stage of an arithmetic optimization algorithm, and carrying out mutation updating on the target offspring antibody in the offspring antibody population processed by the Iter iteration based on a multiplication and division searching strategy.

Step S2054, entering a development stage of an arithmetic optimization algorithm, and carrying out mutation updating on the target offspring antibody in the offspring antibody population processed by the Iter iteration based on an addition and subtraction searching strategy.

In some embodiments, the variation update is performed during the exploration phase (multiplier-divider search strategy) on the t-th sub-generation antibody that is the target sub-antibody within the population of sub-antibodies processed by the first iteration using the following formula:

In some embodiments, variation updates are performed in the development phase (addition and subtraction search strategy) on the t-th sub-generation antibody as the target sub-antibody within the sub-antibody population processed by the first iteration based on the following formula:

xam _t,s (Iter) represents the value of the s-th dimension after mutation update of the t-th child antibody as the target child antibody in the child antibody population subjected to the Iter iteration process, MOP (Iter) represents the mathematical optimization probability corresponding to the Iter iteration process, best (xa) _s Iter) represents the value of the optimal affinity antibody in the s-dimension of the population of offspring antibodies processed at the Iter iteration, round () represents a rounding function, ε is a predetermined constant, α is a predetermined sensitivity parameter, LB _s And UB _s Representing the lower and upper bounds of the s-th dimension in an antibody, where the lower bound is 1, the upper bound is n, μ is a constant (e.g., 0.499) between 0 and 1, r ₂ To take a random number between 0 and 1, r ₃ To take on random numbers between 0 and 1.

In the process of performing mutation updating based on the multiplication-division searching strategy or the addition-subtraction searching strategy, if xam is generated _t,s (Iter) has a value greater than UB _s Xam then _t,s (Iter) final value UB _s If xam is produced _t,s The value of (Iter) is less than LB _s Xam then _t,s (Iter) final value LB _s 。

Of course, the multiplication and division search strategy adopted by the exploration stage and the addition and subtraction search strategy adopted by the development stage in the present disclosure may also take other forms, which are not exemplified herein.

Step S206, the k antibodies in the current memory bank of the Iter iteration process and q-k antibodies in the offspring antibody population after the mutation updating process are combined to form an original antibody population corresponding to the Iter+1st iteration process, and 1 adding process is carried out on the Iter to update.

After the end of step S206, step S202 is executed;

and S207, outputting the optimal affinity antibody in the original antibody population of the Iter iteration to obtain the current optimal solution.

In the embodiment of the disclosure, by the p-dimensional value of the optimal affinity antibody output in step S207, it is possible to know which p of the n candidate logistics distribution centers are enabled, i.e. obtain the enabling parameters h corresponding to the n candidate logistics distribution centers _j . Correspondingly, m demand points can respectively determine the nearest one from the p logistics distribution centers output in step S207 as the logistics distribution center for distributing the materials to itself (Z described later _ij And the value of (2) is also determined), namely the logistics distribution center corresponding to the demand point.

In the technical scheme of the disclosure, an arithmetic optimization algorithm is combined with an immune algorithm, a variation updating mode of a population is changed, a multiplication and division method is used for updating the population in an exploration stage, and an addition and subtraction method is used for completing the population updating in a development stage, so that the convergence speed can be effectively increased, and the obtained result is better.

In some embodiments, in step S1, the objective function in the logistics distribution center site selection model is:

f represents the product of the distance from m demand points to the logistics distribution center of corresponding goods supply and the demand quantity of the logistics distribution center, d _ij Represents the distance from the ith demand point to the jth alternative logistics distribution center, w _i Indicating the material demand of the ith demand point, Z _ij For characterizing whether the ith demand point is being delivered by the jth alternative logistics delivery center.

The value of each of the p dimensions in the antibody is for Z _ij Is encoded again; for any ith demand point, if the value of the current selected antibody is j in p dimensions, and the distance between the ith demand point and the jth logistics distribution center is smaller than or equal to the distance between the ith demand point and the logistics distribution center shown by other p-1 dimensions except the value of the current selected antibody, at the moment, Z in the objective function _ij The value is 1; otherwise Z _ij The value is 0.

Constraints in the logistics distribution center site selection model include:

condition 1, a demand point can only be distributed by one logistics distribution center, a plurality of demand points can be distributed by one logistics distribution center, and the distribution radius of the logistics distribution center is not limited:

only p of the condition 2, n alternative logistics distribution centers are enabled:

condition 3, only the activated logistics distribution center can distribute to the demand point, and the non-activated logistics distribution center cannot distribute to the demand point:

in some embodiments, step S203 includes:

step S2031, determining the affinity of each antibody in the original antibody population processed by the ith iteration based on the following formula.

s∈[1,p]And t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the s dimension of the t' th antibody in the original antibody population, D2 _i,t' Representing the minimum distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population.

Step S2032, determining the association force between antibodies in the original antibody population processed by the ith iteration based on the following formula.

Wherein S is _t',t” Representing the association force between the corresponding set of t 'th antibodies and t' th antibodies in the original antibody population; k (K) _t',t” Representing the number of identical elements in the set corresponding to the t 'th antibody and the set corresponding to the t' th antibody in the original antibody population, wherein t 'is a positive integer and t' is E [1, q ]]T 'is a positive integer and t' is [1, q ]]。

Step S2033, determining the concentration of each antibody in the original antibody population processed by the ith iteration based on the following formula.

Wherein C is _t' Is the concentration of the t' th antibody in the original antibody population,and (3) mapping the association force between the T 'antibody corresponding set and the T' antibody corresponding set in the original antibody population to be a mapping result of 0 or 1, wherein T is a preset threshold constant.

Step S2034, determining expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

wherein P is _t' For the expected reproduction rate of the t' th antibody in the original antibody population, lambda is a preset weight coefficient, lambda epsilon (0, 1), theta is a variable parameter, maxIter is a preset maximum iteration number, beta is a preset adjustment coefficient, and beta epsilon [0,1 ]]。

Step S2035, selecting k antibodies from the original antibody population according to the roulette selection mechanism by taking the expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration as the probability of each antibody being selected.

In the embodiment of the disclosure, when the propagation expectation rate of the function is calculated, the global search can be better realized at the beginning of iteration by introducing the variable parameter theta, and convergence is accelerated when the maximum iteration number is reached. And the value of theta gradually decreases along with the increase of the iteration times, so that the propagation expectation rate of individuals with high antibody concentration can be effectively reduced at the beginning of the iteration, and the expected propagation probability gradually increases for accelerating convergence when the maximum iteration times are reached.

In some embodiments, step S204 includes:

step S2041, determining the affinity of each antibody in the original antibody population processed by the Iter iteration based on the following formula.

s∈[1,p]And t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the s dimension of the t' th antibody in the original antibody population, D2 _i,t' Representing the minimum distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population.

Step S2042, determining the cross probability of each antibody in the original antibody population processed by the Iter iteration based on the following formula.

P2 _t Representing the cross probability of the t' th antibody in the original antibody population, wherein alpha 3 is a third preset probability value, alpha 4 is a fourth preset probability value, alpha 3 epsilon (0, 1), alpha 4 epsilon (0, 1) and alpha 3 < alpha 4, mu 2 is a second preset coefficient and mu 2 epsilon [0.8,1 ] ]，B1 _best Representing the maximum of affinities of all antibodies within the original antibody population;

and S2043, screening the first q-k antibodies with the highest crossover probability from the original antibody population processed by the Iter iteration as parent antibodies.

And S2044, performing cross treatment based on q-k parent antibodies to obtain corresponding q-k child antibodies to form a child antibody population.

As an example, 2 parent antibodies may be randomly selected from q-k parent antibodies as a set of parent antibodies, and then the set of parent antibodies is cross-treated to obtain the corresponding 2 child antibodies (or alternatively, 2 child antibodies may be cross-treated to obtain the child antibodies). By cycling through the above operations until q-k sub-generation antibodies are obtained.

Where a set of parent antibodies is cross-processed, a single point cross-processing or a multi-point cross-processing may be employed.

As known from the conventional IA algorithm, population updating mainly depends on crossover and mutation. For example, if the crossover probability is greater, the faster new individuals can be generated, while the population has more significant diversity. However, if the crossover probability is too large, the previously inherited superior genes are easily disrupted, which directly results in the entire population becoming a random search; in addition, the probability is too small, which is unfavorable for generating new individuals, so that all individuals are trapped in local optimum. For this reason, the disclosure proposes bidirectional interleaving, and the specific implementation manner is as follows: for antibodies with higher affinity, a lower crossover probability is adopted, so that their excellent genes can be transmitted to the next generation with a larger probability, while for antibodies with lower affinity, a larger crossover probability is adopted, so that the antibodies can be eliminated as soon as possible, new individuals are generated, and thus, the population has diversity.

In some embodiments, in step S205, before step S2051, further comprising:

step S2050a, determining the affinity of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t.epsilon.1, q-k]

B1 _t Represents the affinity of the t th generation antibody in the offspring antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the(s) th dimension in the (t) th sub-generation antibody in the sub-generation antibody population, D1 _i,t Representing the minimum value of the distance between the ith demand point and the logistics distribution center shown in each dimension of the t th sub-generation antibody in the population of the offspring antibodies;

step S2050b, determining the mutation probability of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

P1 _t representing variation probability of t-th generation antibody in offspring antibody population, wherein alpha 1 is a first preset probability value, alpha 2 is a second preset probability value, alpha 1 epsilon (0, 1), alpha 2 epsilon (0, 1) and alpha 1 < alpha 2, and mu 1 is a first preset coefficient and mu 1 epsilon [0.8,1 ]]，B1 _best Representing the maximum of affinities of all progeny antibodies within the population of progeny antibodies;

step S2050c, generating random numbers for mutation between 0 and 1 corresponding to each child antibody aiming at each child antibody in the child antibody population processed by the Iter iteration, and screening child antibodies with the corresponding random numbers for mutation larger than the corresponding mutation probability as target child antibodies.

In an embodiment of the present disclosure, based on the principle of the foregoing bi-directional interleaving, the present disclosure also provides a bi-directional mutation mechanism. The specific implementation mode is as follows: for antibodies with higher affinity, a lower mutation probability is adopted, so that excellent genes of the antibodies can be transmitted to the next generation with a higher probability, while for antibodies with lower affinity, a higher mutation probability is adopted, so that the antibodies can be eliminated as soon as possible, new individuals are generated, and the population is diversified.

The technical scheme of the present disclosure has the following advantages and beneficial effects:

firstly, aiming at the problem that a conventional immune algorithm is easy to fall into local optimum, when the propagation expectation rate of a function is calculated, the technical scheme can be used for increasing individuals with high fitness values and simultaneously inhibiting individuals with high concentration, the introduction of the parameter theta can be used for better realizing global search at the beginning of iteration, and accelerating convergence when the maximum iteration times are reached, so that the solving effect is improved. Meanwhile, the technical scheme of the invention further optimizes the variation mode of the population in the algorithm, changes the variation updating mode of the population by combining an immune algorithm and an arithmetic optimization algorithm, and updates the population by respectively applying the modes of multiplication and division and addition and subtraction in the exploration stage and the development stage, thereby helping the algorithm to better jump out of local optimum and accelerating the convergence speed in the running process.

Secondly, in the aspect of diversity of the population, the technical scheme of the present disclosure adopts a bidirectional cross mutation method in the cross mutation process, so that the effect is that individuals with better affinity can be better reserved, individuals with worse affinity are eliminated, the convergence speed is increased, the diversity of the population is further improved, and the adaptability and generalization capability of the algorithm are improved.

Finally, the technical scheme of the present disclosure can solve the LAP solving problem more effectively. The technical scheme of the disclosure further combines an immune algorithm with an arithmetic optimization algorithm and applies the immune algorithm and the arithmetic optimization algorithm to the LAP solution problem. The comparative experiments of the solving results of different algorithms show that: the method accelerates the convergence rate and the obtained result is better.

Fig. 2 is a schematic diagram showing comparison between the arithmetic-immune optimization algorithm according to the present disclosure and the solution results of the conventional immune algorithm and the simulated annealing algorithm in the related art. As shown in fig. 2, n=20, p=8, m=40, d are set _ij ∈[0，100]，w _i ∈[0,1000]D in the actual simulation process _ij 、w _i Randomly taking values in the corresponding interval, and carrying out maximum iterationThe number maxiter=200, and each of the three algorithms is run 5 times. The solving result shows that compared with the traditional immune algorithm and simulated annealing algorithm, the arithmetic-immune optimization algorithm provided by the present disclosure has better obtained result.

Based on the same inventive concept, the embodiment of the disclosure also provides an optimization system applied to site selection of the logistics distribution center. Fig. 3 is a block diagram of a system for optimizing a site selection of a logistics distribution center according to an embodiment of the present disclosure. As shown in fig. 3, the optimization system includes: building block and arithmetic-immune optimization module.

The component module is used for constructing a logistics distribution center site selection model. Specifically, the method can be used to implement step S1 in the previous embodiment.

The arithmetic-immune optimization module is used for solving the addressing model of the logistics distribution center based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution, and the current optimal solution comprises each enabling parameter h _j Is set to the optimum value of (2). Specifically, the method can be used to implement step S2 in the previous embodiment.

For a specific description of the construction module and the arithmetic-immune optimization module, reference may be made to the corresponding contents in the previous embodiments, and this will not be repeated.

Based on the same inventive concept, the embodiment of the disclosure also provides electronic equipment. Fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the disclosure. As shown in fig. 4, an embodiment of the present disclosure provides an electronic device including: one or more processors 101, memory 102, one or more I/O interfaces 103. The memory 102 has one or more programs stored thereon that, when executed by the one or more processors, cause the one or more processors to implement the optimization method according to any of the above embodiments; one or more I/O interfaces 103 are coupled between the processor and the memory and are configured to enable information interaction between the processor and the memory.

Wherein the processor 101 is a device having data processing capabilities, including but not limited to a Central Processing Unit (CPU) or the like; memory 102 is a device having data storage capability including, but not limited to, random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically charged erasable programmable read-only memory (EEPROM), FLASH memory (FLASH); an I/O interface (read/write interface) 103 is connected between the processor 101 and the memory 102 to enable information interaction between the processor 101 and the memory 102, including but not limited to a data Bus (Bus) or the like.

In some embodiments, processor 101, memory 102, and I/O interface 103 are connected to each other via bus 104, and thus to other components of the computing device.

In some embodiments, the one or more processors 101 comprise a field programmable gate array.

According to an embodiment of the present disclosure, there is also provided a computer-readable medium. The computer readable medium has stored thereon a computer program, wherein the program when executed by a processor realizes the steps of the optimization method according to any of the above embodiments.

In particular, according to embodiments of the present disclosure, the processes described above with reference to flowcharts may be implemented as computer software programs. For example, embodiments of the present disclosure include a computer program product comprising a computer program embodied on a machine-readable medium, the computer program comprising program code for performing the method shown in the flow chart. In such embodiments, the computer program may be downloaded and installed from a network via a communication portion, and/or installed from a removable medium. The above-described functions defined in the system of the present disclosure are performed when the computer program is executed by a Central Processing Unit (CPU).

It should be noted that the computer readable medium shown in the present disclosure may be a computer readable signal medium or a computer readable storage medium, or any combination of the two. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this disclosure, a computer-readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In the present disclosure, however, the computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, with the computer-readable program code embodied therein. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.

The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

It is to be understood that the above embodiments are merely exemplary embodiments employed to illustrate the principles of the present disclosure, however, the present disclosure is not limited thereto. Various modifications and improvements may be made by those skilled in the art without departing from the spirit and substance of the disclosure, and are also considered to be within the scope of the disclosure.

Claims (10)

1. An optimization method applied to site selection of a logistics distribution center is characterized by comprising the following steps:

s1, constructing a site selection model of a logistics distribution center;

the logistics distribution center site selection model aims at: selecting and starting p logistics distribution centers from n alternative logistics distribution centers, wherein the sum of the products of the distances from m demand points to the logistics distribution centers corresponding to the goods and the demand of the goods is minimum; an enabling parameter h for characterizing whether the j-th alternative logistics distribution center is enabled _j ；

S2, solving the logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution comprises each enabling parameter h _j Is the optimum value of (2); the method specifically comprises the following steps:

step S201, carrying out an initialization stage in an immune algorithm, enabling iteration times Iter to be 1, generating an initial antibody population containing q antibodies, and taking the initial antibody population as an original antibody population corresponding to the Iter iteration treatment, wherein each antibody comprises p dimensions, the p dimensions represent p logistics distribution centers which are selected and started from n alternative logistics distribution centers, the value of each dimension in the p dimensions in the antibody is an integer, and the value range is [1, n ];

Step S202, judging whether the original antibody population of the Iter iteration meets the iteration termination condition;

if it is determined that the original antibody population of the Iter iteration satisfies the iteration termination condition, step S207 is executed; if it is determined that the original antibody population of the Iter iteration does not meet the iteration termination condition, executing step S203;

step S203, selecting k antibodies from the original antibody population processed by the Iter iteration to form a current memory bank, wherein k is a positive integer and k is less than q;

step S204, in the crossing stage in the immune algorithm, q-k parent antibodies are selected from the original antibody population subjected to the Iter iteration treatment, and the q-k child antibodies are obtained through the crossing treatment, so that the child antibody population subjected to the Iter iteration treatment is formed;

step S205, performing a mutation stage in an immune algorithm, wherein at least part of offspring antibodies in the offspring antibody population processed by the Iter iteration are used as target offspring antibodies, and performing mutation updating on the target offspring antibodies; the method specifically comprises the following steps:

step S2051, entering a mathematical optimization acceleration stage of an arithmetic optimization algorithm, and determining a mathematical optimization acceleration coefficient MOA (Iter) corresponding to the Iter iteration process;

Step S2052 of comparing the pre-generated random number r between 0 and 1 ₁ Size with MOA (Iter);

if r ₁ < MOA (Iter), then step S2053 is performed; if r ₁ > MOA (Iter), then step S2054 is performed;

step S2053, entering an exploration stage of an arithmetic optimization algorithm, and carrying out mutation updating on a target offspring antibody in the offspring antibody population processed by the Iter iteration based on a multiplication and division searching strategy;

step S2054, entering a development stage of an arithmetic optimization algorithm, and carrying out mutation updating on a target offspring antibody in the offspring antibody population processed by the Iter iteration based on an addition and subtraction searching strategy;

step S206, the k antibodies in the current memory bank of the Iter iteration process and q-k antibodies in the offspring antibody population after the mutation updating process are combined to form an original antibody population corresponding to the Iter+1st iteration process, and 1-adding process is carried out on the Iter to update;

after the end of step S206, step S202 is executed.

And S207, outputting the optimal affinity antibody in the original antibody population of the Iter iteration to obtain the current optimal solution.

2. The method of claim 1, wherein the objective function in the logistics distribution center site selection model is:

F represents the product of the distance from m demand points to the logistics distribution center of corresponding goods supply and the demand quantity of the logistics distribution center, d _ij Represents the distance from the ith demand point to the jth alternative logistics distribution center, w _i Indicating the material demand of the ith demand point, Z _ij For characterizing whether the ith demand point is delivered by the jth alternative logistics delivery center;

the value of each of the p dimensions in the antibody is for Z _ij Is encoded again; for any ith demand point, if the value of the current selected antibody is j in p dimensions, and the distance between the ith demand point and the jth logistics distribution center is smaller than or equal to the distance between the ith demand point and the logistics distribution center shown by other p-1 dimensions except the value of the current selected antibody, at the moment, Z in the objective function _ij The value is 1; otherwise Z _ij The value is 0;

the constraint conditions in the logistics distribution center site selection model comprise:

condition 1, a demand point can only be distributed by one logistics distribution center, a plurality of demand points can be distributed by one logistics distribution center, and the distribution radius of the logistics distribution center is not limited:

only p of the condition 2, n alternative logistics distribution centers are enabled:

Condition 3, only the activated logistics distribution center can distribute to the demand point, and the non-activated logistics distribution center cannot distribute to the demand point:

3. the method according to claim 1, characterized in that in step S205, before step S2051, it further comprises:

step S2050a, determining the affinity of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t.epsilon.1, q-k]

B1 _t Represents the affinity of the t th generation antibody in the offspring antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the(s) th dimension in the (t) th sub-generation antibody in the sub-generation antibody population, D1 _i,t Represent the firstThe minimum value of the distance between the i demand points and the logistics distribution center shown in each dimension of the t th subantibody in the offspring antibody population;

step S2050b, determining the mutation probability of each offspring antibody in the offspring antibody population processed by the Iter iteration based on the following formula;

P1 _t representing variation probability of t-th generation antibody in offspring antibody population, wherein alpha 1 is a first preset probability value, alpha 2 is a second preset probability value, alpha 1 epsilon (0, 1), alpha 2 epsilon (0, 1) and alpha 1 < alpha 2, and mu 1 is a first preset coefficient and mu 1 epsilon [0.8,1 ]]，B1 _best Representing the maximum of affinities of all progeny antibodies within the population of progeny antibodies;

Step S2050c, generating random numbers for mutation between 0 and 1 corresponding to each child antibody aiming at each child antibody in the child antibody population processed by the Iter iteration, and screening child antibodies with the corresponding random numbers for mutation larger than the corresponding mutation probability as target child antibodies.

4. The method according to claim 1, wherein step S204 comprises:

step S2041, determining the affinity of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the s dimension of the t' th antibody in the original antibody population, D2 _i,t' Representing the minimum value of the distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population;

step S2042, determining the cross probability of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

P2 _t' representing the cross probability of the t' th antibody in the original antibody population, wherein alpha 3 is a third preset probability value, alpha 4 is a fourth preset probability value, alpha 3 epsilon (0, 1), alpha 4 epsilon (0, 1) and alpha 3 < alpha 4, mu 2 is a second preset coefficient and mu 2 epsilon [0.8,1 ] ]，B2 _best Representing the maximum of affinities of all antibodies within the original antibody population;

s2043, screening the first q-k antibodies with the highest cross probability from the original antibody population processed by the Iter iteration as parent antibodies;

and S2044, performing cross treatment based on q-k parent antibodies to obtain corresponding q-k child antibodies to form a child antibody population.

5. The method according to claim 1, wherein step S203 comprises:

step S2031, determining the affinity of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

s∈[1,p]and t'. Epsilon.1, q]

B2 _t' Represents the affinity of the t' th antibody within the original antibody population,represents the distance between the ith demand point and the logistics distribution center shown in the s dimension of the t' th antibody in the original antibody population, D2 _i,t' Representing the minimum value of the distance between the ith demand point and the logistics distribution center shown in each dimension of the t' th antibody in the original antibody population;

step S2032, determining the association force between antibodies in the original antibody population processed by the Iter iteration based on the following formula;

wherein s is _t',t” Representing the association force between the set corresponding to the t 'th antibody and the set corresponding to the t' th antibody in the original antibody population; k (K) _t',t” Representing the number of identical elements in the set corresponding to the t 'th antibody and the set corresponding to the t' th antibody in the original antibody population, wherein t 'is a positive integer and t' is E [1, q ]]T 'is a positive integer and t' is [1, q ]]；

Step S2033, determining the concentration of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

wherein C is _t' Is the concentration of the t' th antibody in the original antibody population,is the association force S between the t 'th antibody corresponding set and the t' th antibody corresponding set in the original antibody population _t',t” Mapping results of mapping to 0 or 1, wherein T is a preset threshold constant;

step S2034, determining expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration based on the following formula;

wherein P is _t' For the expected reproduction rate of the t' th antibody in the original antibody population, lambda is a preset weight coefficient, lambda epsilon (0, 1), theta is a variable parameter, maxIter is a preset maximum iteration number, beta is a preset adjustment coefficient, and beta epsilon [0,1 ]]；

Step S2035, selecting k antibodies from the original antibody population according to the roulette selection mechanism by taking the expected reproduction rate of each antibody in the original antibody population processed by the Iter iteration as the probability of each antibody being selected.

6. The method according to claim 1, characterized in that the mathematical optimized acceleration coefficient MOA (Iter) is obtained based on the following formula:

Min_MOP and Max_MOP are respectively a preset minimum optimization probability and a preset maximum optimization probability, and MaxIter is a preset maximum iteration number.

7. The method according to claim 1, wherein in step S2053, the t-th sub-generation antibody as the target sub-antibody within the sub-antibody population processed by the first iteration is subjected to mutation update based on the following formula:

xam _t,s (Iter) represents the value of the s-th dimension after mutation update of the t-th child antibody as the target child antibody in the child antibody population subjected to the Iter iteration process, MOP (Iter) represents the mathematical optimization probability corresponding to the Iter iteration process, best (xa) _s Iter) represents the value of the optimal affinity antibody in the s-dimension of the population of offspring antibodies processed at the Iter iteration, round () represents a rounding function, ε is a predetermined constant, α is a predetermined sensitivity parameter, LB _s And UB _s Representing the lower and upper bounds of the s-th dimension in the antibody, wherein the lower bound has a value of 1, the upper bound has a value of n, μ is a constant having a value between 0 and 1, r ₂ To take on random numbers between 0 and 1.

8. The method of claim 1, wherein in step S2054, the t-th sub-generation antibody as the target sub-antibody within the population of child antibodies treated by the first iteration is subjected to mutation update based on the following formula:

xam _t,s (Iter) means the s-th dimension after mutation update of the t-th child antibody as the target child antibody in the child antibody population treated by the Iter iterationThe value MOP (Iter) represents the mathematical optimization probability corresponding to the Iter-th iteration process, best (xa) _s Iter) represents the value of the optimal affinity antibody in the s-th dimension of the population of offspring antibodies processed by the Iter iteration, round () represents the rounding function, alpha is a preset sensitivity parameter, LB _s And UB _s Representing the lower and upper bounds of the s-th dimension in the antibody, wherein the lower bound has a value of 1, the upper bound has a value of n, μ is a constant having a value between 0 and 1, r ₃ To take on random numbers between 0 and 1.

9. An optimisation system for use in the site selection of a logistics distribution centre, characterised in that it is capable of implementing a method according to any one of claims 1 to 8, said system comprising:

the component module is used for constructing a logistics distribution center site selection model;

the logistics distribution center site selection model aims at: selecting and starting p logistics distribution centers from n alternative logistics distribution centers, wherein the sum of the products of the distances from m demand points to the logistics distribution centers corresponding to the goods and the demand of the goods is minimum; an enabling parameter h for characterizing whether the j-th alternative logistics distribution center is enabled _j ；

The arithmetic-immune optimization module is used for solving the logistics distribution center site selection model based on an arithmetic-immune optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution comprises each enabling parameter h _j Is set to the optimum value of (2).

10. An electronic device, comprising:

one or more processors;

a memory for storing one or more programs;

when executed by the one or more processors, causes the one or more processors to implement the method of any of claims 1 to 8.