Optimization method and system for joint replenishment and distribution

Abstract

The present disclosure provides an optimization method and system for joint replenishment and distribution, belonging to the technical field of joint replenishment and distribution; wherein the optimization method comprises: after obtaining a preliminary update population corresponding to the current iterative processing in the exploration stage or development stage of an arithmetic optimization algorithm, creating a newly introduced population corresponding to the current iterative processing, and then selecting half of the individuals with the largest fitness from the preliminary update population and the newly introduced population as the final update population corresponding to the current iterative processing, and using them as the original population for the next iterative processing to perform the next iterative processing; by introducing new individuals in each iterative processing process, the global optimization capability can be improved, thereby improving the solution effect of the joint replenishment and distribution problem.

Description

Technical Field

[0001] The present disclosure relates to the technical field of joint replenishment and distribution, and in particular to an optimization method and system applied to joint replenishment and distribution. Background Art

[0002] The Joint Replenishment Problem (JRP) refers to the process of reducing the total cost by sharing the ordering costs of multiple products through group purchasing strategies. In recent years, some scholars have conducted integrated optimization research on the distribution and site selection of the supply chain based on JRP. The integrated optimization model of Joint Replenishment-Delivery (JRD) has been verified to be an NP-hard problem; the commonly used solution methods are genetic algorithms, differential evolution algorithms, and some heuristic methods. However, as the scale of the problem increases, the solution efficiency also needs to be improved, and it is necessary to design new efficient solution methods. Summary of the invention

[0003] In a first aspect, an embodiment of the present disclosure provides an optimization method for joint replenishment and distribution, including:

[0004] Step S1: construct a joint replenishment and distribution model. The goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution. The decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity. The replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is f i , i∈[1,N] and is an integer, N represents the number of goods;

[0005] Step S2: Solving the joint replenishment and distribution model based on an improved arithmetic optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution includes an optimal value of a replenishment cycle multiplier of each commodity and an optimal value of a distribution frequency of each commodity; specifically, including:

[0006] Step S201, initializing the parameters of the improved arithmetic optimization algorithm;

[0007] Step S202: Generate an initialization population including P individuals as the original population corresponding to the first iteration process, each individual includes D dimensions, D=2*N, the first N dimensions in each individual represent the replenishment cycle multipliers of the N commodities, and the last N dimensions represent the delivery frequencies of the N commodities;

[0008] Step S203, determine whether the current number of iterations iter is greater than the maximum number of iterations Miter;

[0009] If it is determined that the current number of iterations iter is greater than the maximum number of iterations Miter, step S209 is executed;

[0010] If it is determined that the current number of iterations iter is less than or equal to the maximum number of iterations Miter, step S204 is executed;

[0011] Step S204, mathematical optimization acceleration stage, determining the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process;

[0012] Step S205, compare the pre-generated random number r1 between 0 and 1 with MOA(iter), if r1>MOA(iter), then enter the exploration phase to update the original population processed by the iter-th iteration based on the multiplication and division search method to obtain the preliminary updated population processed by the iter-th iteration; if r1≤MOA(iter), then enter the development phase to update the original population processed by the iter-th iteration based on the addition and subtraction search method to obtain the preliminary updated population processed by the iter-th iteration;

[0013] Step S206: Create a newly introduced population corresponding to the iter-th iteration process, wherein the newly introduced population includes P individuals:

[0014]

[0015] Among them, xan p,j (iter) represents the value of the jth dimension of the pth individual in the newly introduced population corresponding to the iterth iteration, round() represents the rounding function, xa p,j (iter) represents the value of the jth dimension of the pth individual in the original population processed by the iterth iteration, rand(1) represents the generation of a random number between 0 and 1, rr1 represents a random number between 0 and 2π, rr2 represents a random number between 0 and 2, rr3 represents a random number between 0 and 1, best(xa j ) represents the value of the jth dimension of the best fitness individual in the original population processed by the iterth iteration; p∈[1,P] and is an integer, j∈[1,D] and is an integer;

[0016] Step S207, from the preliminary updated population of the iter-th iterative processing and the 2*P individuals included in the newly introduced population, select the first P individuals with the smallest fitness to form the final updated population corresponding to the iter-th iterative processing;

[0017] Step S208: The final updated population corresponding to the iter-th iteration is used as the original population corresponding to the iter+1-th iteration, and the current iteration number iter is incremented by 1 for updating, and step S203 is executed again;

[0018] Step S209: output the individual with the best fitness in the final updated population corresponding to the Miterth iteration to obtain the current optimal solution.

[0019] In some embodiments, the combined replenishment and delivery total cost TC is:

[0020] TC=C s,w +C h,w +C o,w +C h,R

[0021]

[0022]

[0023]

[0024]

[0025] Among them, C s,w represents the ordering cost, C h,w represents the central warehouse inventory cost, C o,w represents the delivery cost, C h,R represents the retailer's inventory cost; d i represents the annual demand for the ith commodity (unit / year), S w represents the fixed ordering cost generated by the ordering behavior of the central warehouse, s i w The additional ordering cost for ordering the i-th item for the central warehouse, s i R represents the delivery cost of the ith product, h i w represents the unit inventory maintenance cost of the i-th commodity in the central warehouse, Represents the unit inventory maintenance cost of the retailer's inventory of the i-th item.

[0026] In some embodiments, step S201 includes:

[0027] Step S2011, setting the upper and lower bounds of the value range of the replenishment cycle multiplier of each commodity;

[0028] Step S2012: Set the upper and lower bounds of the value range of the delivery frequency of each product, where the upper bound of the replenishment cycle multiplier of the ith product is for:

[0029]

[0030] in, It is the upper bound of the replenishment cycle multiplier of the i-th commodity set in step S2011.

[0031] In some embodiments, the current optimal solution also includes: an optimal value of the unit time for commodity replenishment;

[0032] Step S208 includes:

[0033] Step S2081: Obtain the optimal value of the replenishment cycle multiplier of each commodity and the optimal value of the delivery frequency of each commodity from the individuals with the best fitness in the final updated population corresponding to the Miterth iteration, where the optimal value of the delivery frequency of the ith commodity is f i * , the optimal value of the replenishment period multiplier of the i-th commodity is k i * ;

[0034] Step S2082: Determine the optimal value of the unit time for replenishment of the product T according to the optimal value of the replenishment cycle multiplier of each product and the optimal value of the delivery frequency of each product. * :

[0035]

[0036] In some embodiments, in step S205, the step of entering the exploration phase to update the original population processed for the iterth iteration based on the multiplication and division search method to obtain the preliminary updated population processed for the iterth iteration specifically includes:

[0037] The P individuals included in the initial update population are determined based on the following formula:

[0038]

[0039]

[0040] Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, MOP(iter) represents the mathematical optimization probability coefficient corresponding to the iterth iteration, α is the preset sensitive parameter, LB j represents the lower bound of the j-th dimension in the individual, μ is a constant between 0 and 1, and r2 is a random number between 0 and 1.

[0041] In some embodiments, in step S205, the step of entering the development exploration phase to update the original population processed for the iterth iteration based on the addition and subtraction search method to obtain the preliminary updated population processed for the iterth iteration specifically includes:

[0042] The P individuals included in the initial update population are determined based on the following formula:

[0043]

[0044] Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, mean(xa j ) represents the average value of the j-th dimension of all individuals in the original population processed in the iter-th iteration.

[0045] In some embodiments, in step S202, the P individuals included in the initialization population are determined based on the following formula:

[0046] x p,j (1) = round(rand(1) × (UB j -LB j )+LB j )

[0047] Among them, x p,j (1) represents the value of the jth dimension of the pth individual in the initial population, UB j represents the upper bound of the j-th dimension in an individual, LB j represents the lower bound of the j-th dimension in an individual.

[0048] In some embodiments, in step S204, the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process is:

[0049]

[0050] Among them, miniter and maxiter are the minimum and maximum values ​​of the preset acceleration function respectively.

[0051] In a second aspect, the embodiment of the present disclosure further provides an optimization system for joint replenishment and distribution, which can be used to implement the optimization method provided in the first aspect, and the optimization system includes:

[0052] A construction module is configured to construct a joint replenishment and distribution model, wherein the goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution, and the decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity, wherein the replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is f i , i∈[1,N] and is an integer, N represents the number of goods;

[0053] The arithmetic optimization module is configured to solve the joint replenishment and distribution model based on an improved arithmetic optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution includes an optimal value of a replenishment cycle multiplier of each commodity and an optimal value of a distribution frequency of each commodity.

[0054] In a third aspect, an embodiment of the present disclosure further provides an electronic device, comprising:

[0055] one or more processors;

[0056] A memory for storing one or more programs;

[0057] When the one or more programs are executed by the one or more processors, the one or more processors implement the optimization method provided in the first aspect.

[0058] The technical solution disclosed in this disclosure has the following beneficial technical effects:

[0059] 1) Narrow the range of individual initial solutions (corresponding to step S2012). i The upper bound of Set to Replace related technologies Designed as a random maximum value, this can effectively narrow the initial search range of the optimal solution and improve the efficiency of the algorithm.

[0060] 2) Innovative population update method (corresponding to step S205). By designing a new population update method, the population diversity of the improved arithmetic optimization algorithm can be improved. Population diversity is one of the key factors in algorithm performance. By increasing the diversity of the population, the global optimization ability of the algorithm can be improved. Compared with related technologies, the population generation method of the present invention can better explore the problem space and find a better solution.

[0061] 3) Further optimize the updated population of the AOA algorithm (corresponding to step S206 and step S207). By generating new individuals, the optimal solution can be better searched. By further optimizing the search and adjusting the one-to-one selection operation to select the top 50% of individuals from all individuals as the next generation of individuals, the global optimization ability can be further improved and the solution effect can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flowchart of an optimization method for combined replenishment and distribution provided in an embodiment of the present disclosure.

[0063] Figure 2 for Figure 1 A flow chart of a specific implementation method of step S2.

[0064] Figure 3 It is a schematic diagram of the changes in inventory in the central warehouse and the changes in the volume of goods transported during distribution in the joint replenishment and distribution model in the embodiment of the present disclosure.

[0065] Figure 4 Schematic diagram of a single individual in a population in an embodiment of the present disclosure.

[0066] Figure 5 It is a schematic diagram comparing the solution effects of the EAOA algorithm involved in the present disclosure with the GA algorithm, DE algorithm and original AOA algorithm in related technologies.

[0067] Figure 6 A structural block diagram of an optimization system for combined replenishment and distribution provided in an embodiment of the present disclosure.

[0068] Figure 7 The figure is a schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0069] In order to enable those skilled in the art to better understand the technical solution of the present disclosure, the present disclosure is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0070] Unless otherwise defined, the technical terms or scientific terms used in the present disclosure should be understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, similar words such as "one", "one" or "the" do not indicate quantity restrictions, but indicate that there is at least one. Similar words such as "include" or "comprise" mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Similar words such as "connect" or "connected" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described target changes, the relative positional relationship may also change accordingly.

[0071] In each of the accompanying drawings, identical elements are represented by similar reference numerals. For the sake of clarity, the various parts in the accompanying drawings are not all drawn to scale. In addition, some well-known parts may not be shown in the drawings.

[0072] Many specific details of the present disclosure are described below to provide a clearer understanding of the present disclosure. However, as those skilled in the art will appreciate, the present disclosure may be implemented without following these specific details.

[0073] Arithmetic Optimization Algorithm (AOA) is a meta-heuristic optimization algorithm designed based on the idea of ​​four mixed operations. The algorithm is divided into three parts. The first is to select the optimization strategy through the mathematical optimizer acceleration function; the second is the exploration stage, using the multiplication strategy and the division strategy to perform global search, improve the dispersion of the solution, enhance the global optimization of the algorithm and overcome premature convergence, and realize global exploration optimization; the third is the development stage, using the addition strategy and the subtraction strategy to reduce the dispersion of the solution, which is conducive to the full development of the population in the local range and strengthen the local optimization ability of the algorithm. AOA has the following advantages: ① simple operation and strong versatility; ② strong adaptive learning ability, which can balance the search accuracy and convergence speed; ③ can balance global and local search. Although AOA shows the above advantages in solving some optimization problems, it is also easy to fall into local optimality when facing large-scale complex optimization problems. Many scholars have made improvements to the AOA algorithm.

[0074] In terms of population optimization or search strategy, as one of the related technologies, the Gaussian distribution function is used to change the new population generation rules of the AOA algorithm to improve population diversity and achieve faster convergence speed; as the second related technology, the Levy flight strategy is used to change the movement step of the AOA algorithm population; as the third related technology, an improved AOA based on elementary function perturbation is proposed, and the perturbations generated by 6 elementary functions are added to the original parameters, which can effectively enhance the global search capability of AOA and improve the convergence speed of AOA. As the fourth related technology, a forced switching mechanism is used to jump out of the local optimum of the AOA algorithm, and a random optimization factor is used to increase population diversity. As the fifth related technology, a new population of the AOA algorithm is generated based on the adversarial learning mechanism to jump out of the local optimum.

[0075] In terms of hybridization with other intelligent algorithms, as one of the related technologies, AOA is hybridized with the slime mold algorithm. The local optimal value and global optimal value of the slime mold algorithm are used to initialize the search process of AOA, and then the best individual obtained by AOA is used to initialize the slime mold algorithm to further expand the search space.

[0076] Although the improved AOA method involved in the relevant technology has achieved good results in solving some optimization problems; however, it is still necessary to design an improved AOA method specifically for the difficulty of integrated optimization of joint replenishment and distribution.

[0077] At present, the AOA algorithm involved in related technologies can find relatively good solutions in a local range, but it is difficult to guarantee the global optimal solution, that is, there are certain limitations in the global optimization ability. This will lead to the low efficiency of the AOA algorithm in solving complex problems of joint replenishment and distribution, and it is impossible to obtain a lower-cost optimal solution.

[0078] Figure 1 A flowchart of an optimization method for combined replenishment and distribution provided in an embodiment of the present disclosure. Figure 2 for Figure 1 A flow chart of a specific implementation method of step S2. Figure 3 It is a schematic diagram of the changes in inventory in the central warehouse and the changes in the volume of goods transported during distribution in the joint replenishment and distribution model in the embodiment of the present disclosure. Figure 4 Schematic diagram of a single individual in a population in the embodiment of the present disclosure. Figures 1 to 4 As shown in FIG. 1 , the optimization method for joint replenishment and distribution includes:

[0079] Step S1: construct a joint replenishment and distribution model.

[0080] The goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution. The decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity. The replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is f i , i∈[1,N] is an integer, and N represents the number of products.

[0081] Step S2: Solve the joint replenishment and distribution model based on the improved arithmetic optimization algorithm to obtain the corresponding current optimal solution.

[0082] The current optimal solution includes the optimal value of the replenishment cycle multiplier of each commodity and the optimal value of the delivery frequency of each commodity; step S2 specifically includes:

[0083] Step S201: Initialize the parameters of the improved arithmetic optimization algorithm.

[0084] Step S202: Generate an initialization population of P individuals as the original population corresponding to the first iterative processing. Each individual includes D dimensions, D=2*N. The first N dimensions of each individual represent the replenishment cycle multipliers of the N commodities, and the last N dimensions represent the delivery frequencies of the N commodities.

[0085] Step S203: Determine whether the current number of iterations iter is greater than the maximum number of iterations Miter.

[0086] If it is determined that the current number of iterations iter is greater than the maximum number of iterations Miter, step S209 is executed.

[0087] If it is determined that the current number of iterations iter is less than or equal to the maximum number of iterations Miter, step S204 is executed.

[0088] Step S204, mathematical optimization acceleration stage, determining the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process.

[0089] Step S205, compare the pre-generated random number r1 between 0 and 1 with the size of MOA(iter). If r1>MOA(iter), enter the exploration phase to update the original population processed by the iter-th iteration based on the multiplication and division search method to obtain the preliminary updated population processed by the iter-th iteration; if r1≤MOA(iter), enter the development phase to update the original population processed by the iter-th iteration based on the addition and subtraction search method to obtain the preliminary updated population processed by the iter-th iteration.

[0090] Step S206: Create a newly introduced population corresponding to the iter-th iteration process, where the newly introduced population includes P individuals.

[0091]

[0092] Among them, xan p,j (iter) represents the value of the jth dimension of the pth individual in the newly introduced population corresponding to the iterth iteration, round() represents the rounding function, xa p,j (iter) represents the value of the jth dimension of the pth individual in the original population processed by the iterth iteration, rand(1) represents the generation of a random number between 0 and 1, rr1 represents a random number between 0 and 2π, rr2 represents a random number between 0 and 2, rr3 represents a random number between 0 and 1, best(xa j ) represents the value of the j-th dimension of the individual with the best fitness in the original population processed in the iter-th iteration; p∈[1,P] is an integer, j∈[1,D] is an integer.

[0093] It should be noted that when generating individuals in the newly introduced population in step S206, if a dimension of the generated new individual exceeds the upper and lower bounds of the corresponding decision variable, the value of the corresponding individual on the dimension can be adjusted (for example, if the value of the j-th dimension of the p-th individual in the newly introduced population obtained based on rr1 and rr2 exceeds the upper and lower bounds of the j-th dimension, the adjusted value of the j-th dimension of the p-th individual in the newly introduced population is as follows:

[0094] xan p,j (iter) = round(rand(1)×(UB j -LB j )+LB j )

[0095] Among them, UB j represents the upper bound of the j-th dimension in an individual, LB j represents the lower bound of the j-th dimension in an individual.

[0096] It should be noted that in the embodiment of the present disclosure, the fitness of each individual in the population (i.e., the total cost of joint replenishment and distribution obtained after the corresponding individual is input into the objective function) can be obtained based on the objective function of the joint replenishment and distribution model (the function of the total cost of joint replenishment and distribution with respect to the decision variables), wherein the smaller the total cost of joint replenishment and distribution, the better the fitness of the individual. The individual with the best fitness in the population is the optimal fitness individual (i.e., the individual with the smallest corresponding fitness).

[0097] Step S207: From the 2*P individuals included in the preliminary updated population of the iter-th iterative processing and the newly introduced population, select the first P individuals with the largest fitness to form the final updated population corresponding to the iter-th iterative processing.

[0098] Step S208: Use the final updated population corresponding to the iter-th iteration as the original population corresponding to the iter+1-th iteration, add 1 to the current iteration number iter for updating, and execute step S203 again.

[0099] Step S209: output the individual with the best fitness in the final updated population corresponding to the Miterth iteration to obtain the current optimal solution.

[0100] Different from the conventional AOA algorithm, in which the updated population obtained through the exploration stage or development phase is directly used as the original population corresponding to the iter+1th iteration, in the present disclosure, after the preliminary updated population obtained through the exploration stage or development phase is obtained through step S205, a newly introduced population corresponding to the iterth iteration is created through step S206, and then the first P individuals with the largest fitness are selected from the 2*P individuals included in the preliminary updated population and the newly introduced population of the iterth iteration through step S207 to form the final updated population corresponding to the iterth iteration, and used as the original population corresponding to the iter+1th iteration. By generating new individuals (individuals in the newly introduced population) after the exploration stage or development phase, the optimal solution can be better searched. Through further search optimization and adjusting the one-to-one selection operation used in the conventional AOA algorithm (taking P individuals in the initial update population as the P individuals in the original population for the next iterative update) to selecting the top 50% of individuals from all individuals (P individuals in the initial update population and P individuals in the newly introduced population, a total of 2*P individuals) as the next generation of individuals, the global optimization capability can be further improved, and the solution effect of the joint replenishment and distribution problem can be improved.

[0101] In some embodiments, in step S1, the combined replenishment and delivery total cost TC is:

[0102] TC=C s,w +C h,w +C o,w +C h,R

[0103]

[0104]

[0105]

[0106]

[0107] Among them, C s,w represents the ordering cost, C h,w represents the central warehouse inventory cost, C o,w represents the delivery cost, C h,R represents the retailer's inventory cost; d i represents the annual demand for the ith commodity, S w It represents the fixed ordering cost generated by the ordering behavior of the central warehouse (also called "main ordering cost", which represents a fixed cost that will be generated when ordering behavior occurs). i w The additional ordering cost incurred when ordering the i-th product for the central warehouse (also called “secondary ordering cost”, representing the additional cost incurred when ordering the corresponding product), s i R represents the delivery cost of the ith product, h i w represents the unit inventory maintenance cost of the ith commodity in the central warehouse, h i R Represents the unit inventory maintenance cost of the retailer's inventory of the i-th item.

[0108] In some embodiments, the parameters of the Enhanced Arithmetic Optimization Algorithm (EAOA) initialized in step S201 include: the size of the population (i.e., the number of individuals P included in the population), the dimension D of the individual (D=2*N), the maximum number of iterations Miter, the minimum value miniter and the maximum value maxiter of the acceleration function, the upper and lower bounds of the value range of the replenishment cycle multiplier of each commodity (i.e., the upper and lower bounds of each dimension in the first N dimensions of the individual), the upper and lower bounds of the value range of each delivery frequency (i.e., the upper and lower bounds of each dimension in the last N dimensions of the individual), etc.

[0109] Optionally, step S201 includes:

[0110] Step S2011, setting the upper and lower bounds of the value range of the replenishment cycle multiplier of each commodity;

[0111] Step S2012: Set the upper and lower bounds of the value range of the delivery frequency of each product, where the upper bound of the replenishment cycle multiplier of the ith product is for:

[0112]

[0113] in, It is the upper bound of the replenishment cycle multiplier of the i-th commodity set in step S2011.

[0114] In this disclosure, for T and any given k i , the corresponding f i Optimal value f i * Need to meet TC(f i * )≤TC(f i * -1) and TC(f i * )≤TC(f i * +1), where TC(f i * ) indicates that in f i The value is f i * The TC value corresponding to the time, TC(f i * -1) indicates that at f i The value is f i * The TC value corresponding to -1, TC(f i * +1) indicates that in f i The value is f i * +1 corresponds to the TC value.

[0115] Further, it can be deduced that Therefore, it can be found that the corresponding f i * satisfy: in Denoted as k i The upper bound of T is 0<T≤1, so f i The upper bound of Can be set to:

[0116] In the related technology, the delivery frequency f of the product is set i When the upper and lower bounds of the product are set, the lower bound is often set to 1, and the upper bound is often designed to be a manually specified larger value (for example, greater than 20). At this time, the value range of the replenishment cycle multiplier of the product is larger (the difference between the upper and lower bounds). When the initialization population is generated in step S202, the individuals in the initialization population are often randomly generated within a larger range, which will lead to a lower efficiency of the AOA algorithm (the size of the initial search range directly affects the search efficiency of the AOA algorithm). In the present disclosure, according to the product d i , and To reasonably set the delivery frequency f i The upper bound of can effectively and reasonably reduce the delivery frequency f i The initial search range of the optimal solution can improve the search effect and the solving efficiency of the AOA algorithm.

[0117] In some embodiments, in step S202, the P individuals included in the initialization population are determined based on the following formula:

[0118] xan p,j (iter) = round(rand(1)×(UB j -LB j )+LB j )

[0119] Among them, x p,j (1) represents the value of the jth dimension of the pth individual in the initial population, UB j represents the upper bound of the j-th dimension in an individual, LB j represents the lower bound of the j-th dimension in an individual.

[0120] The initial population can be expressed as:

[0121]

[0122] In some embodiments, in step S204, the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process is:

[0123]

[0124] In some embodiments, in step S205, the step of entering the exploration phase to update the original population processed for the iterth iteration based on the multiplication and division search method to obtain the preliminary updated population processed for the iterth iteration specifically includes:

[0125] The P individuals included in the initial update population are determined based on the following formula:

[0126]

[0127]

[0128] Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, MOP(iter) represents the mathematical optimization probability coefficient corresponding to the iterth iteration, α is the preset sensitive parameter, LB jrepresents the lower bound of the jth dimension in the individual, μ is a constant between 0 and 1 (generally, it is 0.5), and r2 is a random number between 0 and 1.

[0129] In step S205, the steps of entering the development exploration phase and updating the original population processed by the iter-th iteration based on the addition and subtraction search method to obtain the preliminary updated population processed by the iter-th iteration specifically include:

[0130] The P individuals included in the initial update population are determined based on the following formula:

[0131]

[0132] Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, mean(xa j ) represents the average value of the j-th dimension of all individuals in the original population processed in the iter-th iteration.

[0133] Population diversity is an important factor in algorithm performance, which can help the algorithm explore a wider problem space and have a greater probability of finding a better solution. The AOA algorithm involved in the related technology has a relatively simple population generation method and cannot effectively improve the population diversity of the AOA algorithm, which will reduce the convergence of the algorithm and make it difficult to reach the global optimal solution.

[0134] In view of the above technical problems, the present disclosure provides a new population update method, which can improve the population diversity of the improved arithmetic optimization algorithm. Specifically, in the exploration phase, the value of the jth dimension of the best fitness individual in the original population processed by the iterth iteration is used. j ), replacing the upper bound UB of the jth dimension of the individual in the existing AOA algorithm j ; In addition, in the development stage, the average value mean(xa) of the j-th dimension of the individuals in the original population processed by the iter-th iteration is used j ) and the value of the jth dimension of the optimal fitness individual best(xa j ), replacing the lower bound LB of the jth dimension of the individual in the existing AOA algorithm j and upper bound UB j Such a design can increase the diversity of the updated population obtained by iterative processing, thereby improving the global optimization ability of the algorithm.

[0135] In some embodiments, the current optimal solution also includes: an optimal value of the unit time for commodity replenishment;

[0136] Step S208 includes:

[0137] Step S2081: Obtain the optimal value of the replenishment cycle multiplier of each commodity and the optimal value of the delivery frequency of each commodity from the individuals with the best fitness in the final updated population corresponding to the Miterth iteration, where the optimal value of the delivery frequency of the ith commodity is f i * , the optimal value of the replenishment period multiplier of the i-th commodity is k i * ;

[0138] Step S2082: Determine the optimal value of the unit time for replenishment of the product T according to the optimal value of the replenishment cycle multiplier of each product and the optimal value of the delivery frequency of each product. * :

[0139]

[0140] The technical solution disclosed in this disclosure has the following beneficial technical effects:

[0141] 1) Narrow the range of individual initial solutions (corresponding to step S2012). i The upper bound of Set to Replace related technologies Designed as a random maximum value, this can effectively narrow the initial search range of the optimal solution and improve the efficiency of the algorithm.

[0142] 2) Innovative population update method (corresponding to step S205). By designing a new population update method, the population diversity of the improved arithmetic optimization algorithm can be improved. Population diversity is one of the key factors in algorithm performance. By increasing the diversity of the population, the global optimization ability of the algorithm can be improved. Compared with related technologies, the population generation method of the present invention can better explore the problem space and find a better solution.

[0143] 3) Further optimize the updated population of the AOA algorithm (corresponding to step S206 and step S207). By generating new individuals, the global optimal solution can be better searched. By further optimizing the search and adjusting the one-to-one selection operation to select the top 50% of individuals from all individuals as the next generation of individuals, the global optimization ability can be further improved and the solution effect can be improved.

[0144] Figure 5 The figure is a schematic diagram comparing the solution effects of the EAOA algorithm involved in the present disclosure with the GA algorithm, DE algorithm and original AOA algorithm in the related art. Figure 5 As shown, set d i ∈[500,5000], S i w ∈[40,100], h iw ∈[0.5,3], S i R ∈[0.1S i w ,0.3S i w ],h i R ∈[1.2h i w ,2h i w ], in the actual simulation process d i , S i w 、h i w , S i R and h i R Randomly select a value in the corresponding interval.

[0145] In order to verify the effect of the improved arithmetic optimization algorithm (EAOA) to be adopted in this invention to optimize the integrated optimization problem of joint replenishment and distribution, three comparative schemes are designed: the original arithmetic optimization algorithm (AOA), differential evolution algorithm (DE) and genetic algorithm (GA). The number of goods is set to 30, 50 and 100 respectively. w They are set to 0.5 and 1.0 times of the secondary ordering cost, that is, V = 0.5 and V = 1.0, respectively. The maximum number of iterations is set to 300, and each case is run 20 times. Figure 5 The results of solving the JRD problem with four solutions are shown. Figure 5 It can be seen that the average value, minimum value and maximum value of the total cost obtained by the EAOA algorithm are better than those of the AOA algorithm, the DE algorithm and the GA algorithm.

[0146] Based on the same inventive concept, the disclosed embodiment also provides an optimization system for combined replenishment and distribution. Figure 6 FIG. 1 is a structural block diagram of an optimization system for joint replenishment and distribution provided in an embodiment of the present disclosure. Figure 6 As shown, the optimization system can be used to implement the optimization method provided by any of the previous embodiments. The optimization system includes: a construction module and an arithmetic optimization module.

[0147] The construction module is configured to construct a joint replenishment and distribution model. The goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution. The decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity. The replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is fi , i∈[1,N] and is an integer, N represents the number of goods;

[0148] The arithmetic optimization module is configured to solve the joint replenishment and distribution model based on an improved arithmetic optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution includes an optimal value of a replenishment cycle multiplier of each commodity and an optimal value of a distribution frequency of each commodity.

[0149] For the detailed description of the construction module and the arithmetic optimization module, please refer to the corresponding content in the previous embodiments, which will not be repeated here.

[0150] Based on the same inventive concept, an embodiment of the present disclosure also provides an electronic device. Figure 7 FIG. 1 is a schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure. Figure 7 As shown, an embodiment of the present disclosure provides an electronic device including: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors implement any optimization method in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, and are configured to implement information interaction between the processor and the memory.

[0151] Among them, the processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU), etc.; the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory (FLASH); the I / O interface (read-write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus), etc.

[0152] In some embodiments, the processor 101 , the memory 102 , and the I / O interface 103 are connected to each other via a bus 104 , and further connected to other components of the computing device.

[0153] In some embodiments, the one or more processors 101 include a field programmable gate array.

[0154] According to an embodiment of the present disclosure, a computer-readable medium is further provided, wherein a computer program is stored on the computer-readable medium, wherein when the program is executed by a processor, the steps in any optimization method in the above-mentioned embodiment are implemented.

[0155] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, including a computer program carried on a machine-readable medium, the computer program containing a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication part, and / or installed from a removable medium. When the computer program is executed by a central processing unit (CPU), the above-mentioned functions defined in the system of the present disclosure are executed.

[0156] 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 above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, 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 disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0157] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a module, a program segment or a part of the code, and the aforementioned module, program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0158] It is to be understood that the above embodiments are merely exemplary embodiments used to illustrate the principles of the present disclosure, but the present disclosure is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and substance of the present disclosure, and these modifications and improvements are also considered to be within the scope of protection of the present disclosure.

Claims

1. An optimization method for joint replenishment and distribution, It is characterized in that include: Step S1: construct a joint replenishment and distribution model. The goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution. The decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity. The replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is f i , i∈[1,N] and is an integer, N represents the number of goods; Step S2: Solving the joint replenishment and distribution model based on an improved arithmetic optimization algorithm to obtain the corresponding current optimal individual, wherein the current optimal individual includes the optimal value of the replenishment cycle multiplier of each commodity and the optimal value of the distribution frequency of each commodity; specifically including: Step S201, initializing the parameters of the improved arithmetic optimization algorithm; Step S202: Generate an initialization population including P individuals as the original population corresponding to the first iteration process, each individual includes D dimensions, D=2*N, the first N dimensions in each individual represent the replenishment cycle multipliers of the N commodities, and the last N dimensions represent the delivery frequencies of the N commodities; Step S203, determine whether the current number of iterations iter is greater than the maximum number of iterations Miter; If it is determined that the current number of iterations iter is greater than the maximum number of iterations Miter, step S209 is executed; If it is determined that the current number of iterations iter is less than or equal to the maximum number of iterations Miter, step S204 is executed; Step S204, mathematical optimization acceleration stage, determining the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process; Step S205: Compare the pre-generated random number r between 0 and 1 1 and the size of MOA(iter), if r 1 >MOA(iter), then enter the exploration phase and update the original population processed by the iter-th iteration based on the multiplication and division search method to obtain the preliminary updated population processed by the iter-th iteration; if r 1 ≤MOA(iter), then enter the development phase to update the original population processed by the iter-th iteration based on the addition and subtraction search method to obtain the preliminary updated population processed by the iter-th iteration; Step S206: Create a newly introduced population corresponding to the iter-th iteration process, wherein the newly introduced population includes P individuals: Among them, xan p,j (iter) represents the value of the jth dimension of the pth individual in the newly introduced population corresponding to the iterth iteration, round() represents the rounding function, xa p,j (iter) represents the value of the jth dimension of the pth individual in the original population processed by the iterth iteration, rand(1) represents the generation of a random number between 0 and 1, and rr 1 Represents a random number between 0 and 2π, rr 2 Represents a random number between 0 and 2, rr 3 represents a random number between 0 and 1 generated in advance before executing step S206, best(xa j ) represents the value of the jth dimension of the best fitness individual in the original population processed by the iterth iteration; p∈[1,P] and is an integer, j∈[1,D] and is an integer; Step S207, from the preliminary updated population of the iter-th iterative processing and the 2*P individuals included in the newly introduced population, select the first P individuals with the smallest fitness value to form the final updated population corresponding to the iter-th iterative processing; Step S208: The final updated population corresponding to the iter-th iteration is used as the original population corresponding to the iter+1-th iteration, and the current iteration number iter is incremented by 1 for updating, and step S203 is executed again; Step S209: output the individual with the best fitness in the final updated population corresponding to the Miterth iteration to obtain the current optimal solution.

2. The optimization method according to claim 1, It is characterized in that The total cost of combined replenishment and distribution TC is: TC=C s,w +C h,w +C o,w +C h,R Among them, C s,w represents the ordering cost, C h,w represents the central warehouse inventory cost, C o,w represents the delivery cost, C h,R represents the retailer's inventory cost; d i represents the annual demand for the ith commodity, S w represents the fixed ordering cost generated by the ordering behavior of the central warehouse, s i w The additional ordering cost for ordering the i-th item for the central warehouse, s i R represents the delivery cost of the ith product, h i w represents the unit inventory maintenance cost of the ith commodity in the central warehouse, h i R Represents the unit inventory maintenance cost of the retailer's inventory of the i-th item.

3. The optimization method according to claim 2, It is characterized in that Step S201 includes: Step S2011, setting the upper and lower bounds of the value range of the replenishment cycle multiplier of each commodity; Step S2012: Set the upper and lower bounds of the value range of the delivery frequency of each product, where the upper bound of the replenishment cycle multiplier of the ith product is for: in, It is the upper bound of the replenishment cycle multiplier of the i-th commodity set in step S2011.

4. The optimization method according to claim 2, It is characterized in that The current optimal solution also includes: the optimal value of the unit time for commodity replenishment; Step S208 includes: Step S2081: Obtain the optimal value of the replenishment cycle multiplier of each commodity and the optimal value of the delivery frequency of each commodity from the individuals with the best fitness in the final updated population corresponding to the Miterth iteration, where the optimal value of the delivery frequency of the ith commodity is f i * , the optimal value of the replenishment period multiplier of the i-th commodity is k i * ; Step S2082: Determine the optimal value of the unit time for replenishment of the product T according to the optimal value of the replenishment cycle multiplier of each product and the optimal value of the delivery frequency of each product. * :

5. The optimization method according to claim 1, It is characterized in that In step S205, the steps of entering the exploration phase and updating the original population processed by the iter-th iteration based on the multiplication and division search method to obtain the preliminary updated population processed by the iter-th iteration specifically include: The P individuals included in the initial update population are determined based on the following formula: Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, MOP(iter) represents the mathematical optimization probability coefficient corresponding to the iterth iteration, α is the preset sensitive parameter, LB j represents the lower bound of the jth dimension in an individual, μ is a constant between 0 and 1, and r 2 It is a random number between 0 and 1 that is generated in advance before the step of determining the P individuals included in the preliminary update population in the exploration phase.

6. The optimization method according to claim 1, It is characterized in that In step S205, the development phase enters the step of updating the original population processed by the iter-th iteration based on the addition and subtraction search method to obtain the preliminary updated population processed by the iter-th iteration, which specifically includes: The P individuals included in the initial update population are determined based on the following formula: Among them, xam p,j (iter) represents the value of the jth dimension of the pth individual in the initial update population corresponding to the iterth iteration, mean(xa j ) represents the average value of the j-th dimension of all individuals in the original population processed in the iter-th iteration, r 3 It is a random number between 0 and 1 generated in advance before the step of determining the P individuals included in the preliminary update population in the development phase.

7. The optimization method according to claim 1, It is characterized in that In step S202, the P individuals included in the initialization population are determined based on the following formula: if p,j (1)=round(rand(1)×(UB j -LB j )+LB j ) Among them, x p,j (1) represents the value of the jth dimension of the pth individual in the initial population, UB j represents the upper bound of the j-th dimension in an individual, LB j represents the lower bound of the j-th dimension in an individual.

8. The optimization method according to claim 1, It is characterized in that In step S204, the mathematical optimization acceleration coefficient MOA(iter) corresponding to the iter-th iteration process is: Among them, miniter and maxiter are the minimum and maximum values ​​of the preset acceleration function respectively.

9. An optimization system for joint replenishment and distribution, It is characterized in that The optimization system can be used to implement the optimization method as claimed in any one of claims 1 to 8, wherein the optimization system comprises: A construction module is configured to construct a joint replenishment and distribution model, wherein the goal of the joint replenishment and distribution model is to minimize the total cost of joint replenishment and distribution, and the decision variables in the joint replenishment and distribution model are the unit time T of commodity replenishment, the replenishment cycle multiplier of each commodity, and the distribution frequency of each commodity, wherein the replenishment cycle multiplier of the i-th commodity is k i , the delivery frequency of the i-th product is f i , i∈[1,N] and is an integer, N represents the number of goods; The arithmetic optimization module is configured to solve the joint replenishment and distribution model based on an improved arithmetic optimization algorithm to obtain a corresponding current optimal solution, wherein the current optimal solution includes an optimal value of a replenishment cycle multiplier of each commodity and an optimal value of a distribution frequency of each commodity.

10. An electronic device, in, include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the optimization method according to any one of claims 1 to 8.

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