Optimization method and system for joint replenishment and distribution considering capacity constraints

Abstract

The present invention discloses an optimization method and system for joint replenishment and distribution considering capacity constraints, belonging to the field of optimization algorithms. The method includes: constructing a JRD model considering capacity constraints during transportation in the joint replenishment stage and the distribution stage; optimizing the JRD model considering capacity constraints to obtain the current optimal solution of the JRD model considering capacity constraints; and performing replenishment and distribution based on the current optimal solution. The adaptive Boosting optimization algorithm proposed in the present invention integrates the theoretical basis of machine learning to ensure search performance and stability; by establishing a large number of targets and introducing randomness, it helps the search individual to conduct extensive exploration in the early stage of iteration and reduce the number of targets in the later stage of iteration; using the greedy idea to enhance the development ability of the search individual and improve the accuracy of the optimal solution; by adaptively decreasing the greedy factor, the probability threshold is controlled to ensure that there is a possibility of jumping out of the local optimum at any time, thereby improving the solution effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimization algorithms, and in particular relates to an optimization method and system for joint replenishment and distribution taking into account capacity constraints. 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 based on JRP, considering the distribution, site selection and other links in the supply chain. The integrated optimization model of Joint Replenishment-Delivery (JRD) has been verified to be an NP-hard problem, and the JRD model considering capacity constraints is more complicated. Currently, 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.

[0003] Metaheuristic algorithms are algorithms that imitate various operating mechanisms in nature and are widely used in engineering, computer science, economics and other fields. At present, more and more metaheuristic algorithms have been proposed, which can be mainly divided into five categories: population-based algorithms, evolution-based algorithms, physics-based algorithms, human society-based algorithms and other algorithms. Population-based algorithms mainly simulate the behavior of animals and other organisms. For example, the Seahorse Optimizer (SHO) imitates the movement and predation mechanism of seahorses. Evolution-based algorithms are inspired by the natural selection mechanism of "survival of the fittest" and the law of gene transmission in the process of biological evolution, mainly including differential evolution algorithms (DE). Physics-based algorithms mainly establish mathematical models based on various phenomena, concepts and laws in physics. For example, Hashim et al. proposed Fick's Law Algorithm (FLA) based on Fick's first law. Human society-based algorithms mainly simulate human behavior and interaction in social life. For example, Zhang et al. simulated the combat methods of special forces and proposed the Special Forces Algorithm (SFA). Other algorithms are inspired by other phenomena. For example, the Arithmetic Optimization Algorithm (AOA) is a meta-heuristic optimization algorithm designed based on the idea of ​​mixed operations of four arithmetic operations. Existing meta-heuristic algorithms have the following advantages: ① simple operation and easy to understand; ② strong versatility and can be widely used in practical optimization problems. Although existing meta-heuristic algorithms have shown the above advantages in solving some optimization problems, they still have shortcomings such as weak theoretical foundation, poor balance between global search and local search, and easy to fall into local optimality when facing large-scale complex optimization problems.

[0004] First, existing metaheuristic algorithms lack theoretical basis. Existing metaheuristic algorithms usually draw inspiration from certain phenomena in nature, especially extracting strategies from animal behavior patterns, such as ant colony algorithms simulating the behavior of ants looking for food, and particle swarm optimization algorithms simulating the foraging behavior of bird flocks. This method does provide an intuitive and effective way to solve complex optimization problems, but such algorithms often lack scientific basis and theoretical support.

[0005] The second problem is the poor balance between global search and local search. Traditional metaheuristic algorithms usually do not introduce greedy strategies, and have strong global search capabilities, but also result in low accuracy of the optimal solution obtained. On the contrary, some recently proposed metaheuristic algorithms introduce greedy strategies, which strengthen local search capabilities, but also significantly reduce global search capabilities. The simple addition or removal of greedy strategies does not necessarily improve algorithm performance, and may even lead to performance degradation.

[0006] Finally, it is easy to fall into local optimality. Many current metaheuristic algorithms lack an effective mechanism to escape from local optimality, which causes them to often fall into local optimality and fail to obtain the global optimal solution. The main reason for this problem is that metaheuristic algorithms often rely on random search and heuristic rules. Although these methods can explore the solution space to a certain extent, when faced with complex or multi-peak optimization problems, the algorithm may converge to a local optimal solution too early. Joint replenishment and distribution integrated optimization is a complex problem that requires targeted design solutions. Summary of the invention

[0007] The present invention aims to solve the shortcomings of the prior art and proposes an optimization method for joint replenishment and distribution considering capacity constraints. For the JRD model considering capacity constraints, an adaptive Boosting optimization algorithm (ABOA) is proposed by drawing on the Boosting idea in machine learning. The algorithm continuously reduces the distance (error) between the search individual and the optimal value (target) to find the approximate optimal solution. At the same time, randomness is introduced to help the search individual to conduct extensive exploration in the early stage of iteration, and the number of targets is reduced in the later stage of iteration. The greedy idea is used to enhance the development ability of the search individual, thereby improving the accuracy of the optimal solution. Finally, an adaptive greedy factor is designed to enable it to have the possibility of accepting a poor solution and ensure its ability to jump out of the local optimal solution.

[0008] To achieve the above object, the present invention provides the following solution: an optimization method for combined replenishment and distribution considering capacity constraints, comprising the following steps:

[0009] S1. Construct a JRD model that considers capacity constraints during transportation in the joint replenishment and distribution stages;

[0010] S2. Optimizing the JRD model considering capacity constraints to obtain a current optimal solution of the JRD model considering capacity constraints; and performing replenishment and delivery based on the current optimal solution.

[0011] Preferably, the JRD model considering capacity constraints includes:

[0012]

[0013]

[0014]

[0015] In the formula, TC represents the total cost; C s,w represents the ordering cost; C h,w represents the inventory cost of the central warehouse; C o,w represents the delivery cost; C h,R represents the retailer's inventory cost; S w represents the main ordering cost; represents the delivery cost; T represents the unit time for product replenishment; N represents the number of products; i represents the product number; represents the secondary ordering cost; k i represents the replenishment cycle multiplier of commodity i; f i represents the delivery frequency of product i; D i represents the demand rate of commodity i; represents the unit inventory maintenance cost of item i in the central warehouse; b represents the unit inventory maintenance cost of commodity i at the retailer; i represents the unit mass of commodity i; B w It represents the maximum carrying capacity of the goods in the joint replenishment phase; It represents the maximum carrying capacity for commodity i during the distribution stage.

[0016] Preferably, based on the JRD model considering capacity constraints, the optimal k i 、f i and T, where T is represented as follows:

[0017]

[0018] Preferably, in S2, an adaptive Boosting optimization algorithm is used to optimize the JRD model considering capacity constraints;

[0019] The adaptive Boosting optimization algorithm includes:

[0020] Step 1: Set hyperparameters and generate initial individuals; the dimensions of the initial individuals correspond to the decision variables k to be optimized. i and f i ;

[0021] Step 2, calculate the target number of individuals; when the current iteration number is 1, sort the individuals in the population according to the fitness value, and keep the first tar_num individuals as the target; when the iteration number is greater than 1, merge the previous generation population and the current population, sort the individuals in the population according to the fitness value, and keep the first tar_num individuals as the target;

[0022] Step 3, calculate the potential position of the next generation population; and determine whether the potential position is better than the current position; if it is better than the current position, update the current position to the potential position; otherwise, calculate the greedy factor and the probability threshold, and determine whether to update the position based on the probability threshold;

[0023] Step 4: Calculate the fitness value of each individual in the updated population to obtain the current optimal individual; the updated fitness value is the total cost value;

[0024] Step 5: Determine whether the maximum number of iterations has been reached. When the maximum number of iterations has been reached, obtain the total cost value and the current optimal k i 、f i and T value.

[0025] Preferably, the method for calculating the target quantity includes:

[0026]

[0027] In the formula, iter represents the current number of iterations; NP represents the number of individuals; floor represents the floor function; Miter represents the maximum number of iterations.

[0028] Preferably, when or And rand ≥ 0.6, the calculation method of the potential position of the population includes:

[0029]

[0030] distance i，j = abs(sorted_target i，j -xA i，j (iter)),

[0031] t=(δ-1)×rand+1,

[0032]

[0033] In the formula, round(·) represents the rounding function; b is a constant that controls the shape of the logarithmic spiral; the fluctuation range of t changes from [-1, 1] to [-2, 1] as the number of iterations increases; sorted_target represents all targets left after sorting; tar_num represents the number of targets; abs(·) represents the absolute value; xa i,j represents the jth dimension of the i-th individual; δ decreases linearly from -1 to -2 as the number of iterations increases.

[0034] Preferably, when And rand < 0.6, the calculation method of the potential position of the population includes:

[0035] xp i，j =round(Best_P j -(Best_P j -mean(sorted_tar get j ))×rand),

[0036] Where Best_P represents the historical optimal solution; mean(·) represents the mean function.

[0037] Preferably, the calculation method of the greedy factor and the update threshold includes:

[0038] T(iter) = T0 - α,

[0039]

[0040]

[0041] In the formula, T0 represents the initial greedy factor; α represents the update amplitude of the greedy factor; fitness represents the fitness function; p i Indicates the update threshold; xp i represents the potential position of the i-th individual in the population.

[0042] The present invention also provides an optimization system for joint replenishment and distribution considering capacity constraints, comprising: a construction module and an optimization module;

[0043] The building module is used to build a JRD model that considers capacity constraints during transportation in the joint replenishment phase and the distribution phase;

[0044] The optimization module is used to optimize the JRD model considering the capacity limitation to obtain the current optimal solution of the JRD model considering the capacity limitation.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] First of all, it integrates the theoretical basis of machine learning. The Boosting method is a mature and perfect technology in machine learning, and has achieved excellent performance in many fields. The ABOA algorithm proposed in the present invention draws on the Boosting idea and searches for the approximate optimal solution by continuously reducing the distance (error) between the search individual and the optimal value (target). Compared with algorithms designed based on experimental observations or simulations of natural phenomena, the ABOA algorithm has the theoretical support of machine learning, which ensures the search performance and stability of the algorithm.

[0047] Secondly, balance local search and global search. The present invention helps search individuals to conduct extensive exploration in the early stage of iteration by establishing a large number of targets and introducing randomness, reduces the number of targets in the later stage of iteration, and uses greedy thinking to enhance the development ability of search individuals, thereby improving the accuracy of the optimal solution. The balance between local search and global search can not only improve the search efficiency of the algorithm, but also improve the search accuracy of the algorithm.

[0048] Then, we design an adaptive greedy operator to avoid falling into the local optimum. By adaptively decreasing the greedy factor, we can control the probability threshold, so that there is a greater probability of accepting the difference solution in the early stage of iteration, and there is also a certain probability of accepting the difference solution in the later stage of iteration, ensuring that the algorithm has the possibility of jumping out of the local optimum at any time, thus improving the solution effect.

[0049] Finally, the present invention can effectively solve the multi-product JRD problem considering capacity constraints. The adaptive boosting optimization algorithm (ABOA) proposed in the present invention is applied to the multi-product JRD problem considering capacity constraints. In multiple example results, the total cost obtained by the ABOA algorithm is significantly lower than that of the DE algorithm and the AOA algorithm. This shows that the technical solution of the present invention has higher efficiency and better optimization ability in solving the multi-product JRD problem considering capacity constraints.

[0050] In summary, compared with the existing technical solutions, the present invention proposes an adaptive Boosting optimization algorithm by drawing on the Boosting idea in machine learning, which has excellent global optimization ability and solution efficiency. Applied to the multi-product JRD solution problem considering capacity constraints, the ABOA algorithm can obtain a lower total cost. These advantages and beneficial effects make the technical solution of the present invention have broad application prospects and market promotion value in the field of optimization algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0052] Figure 1 It is a schematic diagram of the inventory changes in the central warehouse and the changes in the volume of goods during distribution in the JRD model according to an embodiment of the present invention;

[0053] Figure 2 A schematic diagram of the process flow of the adaptive Boosting optimization algorithm according to an embodiment of the present invention;

[0054] Figure 3 It is a schematic diagram of the meaning of individual dimensions in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] Embodiment 1:

[0058] This embodiment provides an optimization method for joint replenishment and distribution considering capacity constraints, including the following steps:

[0059] S1. Construct a JRD model that considers capacity constraints during transportation in the joint replenishment and distribution stages.

[0060] like Figure 1 As shown in the figure, the central warehouse in the JRD model is i The product i will be replenished every k i T / f i The JRD model considering capacity constraints is constructed to determine the appropriate replenishment combination and distribution combination to obtain the minimum total supply chain cost. In this embodiment, the JRD model considering capacity constraints is as follows:

[0061]

[0062]

[0063]

[0064] In the formula, TC represents the total cost; C s,w represents the ordering cost; C h,w represents the inventory cost of the central warehouse; C o,w represents the delivery cost; C h,R represents the retailer's inventory cost; S w represents the main ordering cost; represents the delivery cost; T represents the unit time for replenishing goods; N represents the number of goods; i represents the product number, 1≤i≤N; represents the secondary ordering cost; k i represents the replenishment cycle multiplier of commodity i; f irepresents the delivery frequency of product i; D i represents the demand rate of commodity i; represents the unit inventory maintenance cost of item i in the central warehouse; b represents the unit inventory maintenance cost of commodity i at the retailer; i represents the unit mass of commodity i; B w It represents the maximum carrying capacity of the goods in the joint replenishment phase; It represents the maximum carrying capacity for commodity i during the distribution stage.

[0065] Among them, formula (2) indicates that the total amount of all commodities in the joint replenishment stage does not exceed the maximum carrying capacity; formula (3) indicates the distribution capacity limit of each commodity at each delivery in the distribution stage. i , f i and T, where T is represented as follows:

[0066]

[0067] S2. Optimize the JRD model considering capacity constraints to obtain the current optimal solution of the JRD model considering capacity constraints, and perform replenishment and delivery based on the current optimal solution. In this embodiment, the current optimal solution is the solution obtained under a limited number of iterations.

[0068] In this embodiment, an adaptive boosting optimization algorithm (ABOA) is used to optimize the JRD model considering capacity constraints. The adaptive boosting optimization algorithm draws on the boosting idea in machine learning, and seeks an approximate optimal solution by continuously reducing the distance (error) between the search individual and the optimal value (target); at the same time, by establishing a large number of targets and introducing randomness to help the search individual conduct extensive exploration in the early stage of iteration, reducing the number of targets in the later stage of iteration, and using greedy ideas to enhance the development ability of the search individual, thereby improving the accuracy of the optimal solution; finally, an adaptive greedy factor is designed to enable the algorithm to have the possibility of accepting a poor solution, ensuring its ability to jump out of the local optimal solution.

[0069] Specifically, Figure 2 As shown, the adaptive Boosting optimization algorithm includes:

[0070] Step 1: Set hyperparameters and generate initial individuals XA; the dimensions of the initial individuals correspond to the decision variables to be optimized in formula (4). The initial individual XA is as shown in formula (5), xa = round (rand × (UB-LB) + LB), round (·) represents the rounding function, UB and LB represent the decision variables k, i and f iThe maximum and minimum values ​​of . DM is the dimension and NP is the number of individuals. In ABOA, the decision variable k i and f i The maximum value UB is usually set to a larger value, and the decision variable k i and f i The minimum value of LB is usually set to 1.

[0071]

[0072] The meaning of individual dimension is as follows: Figure 3 As shown, when the number of items is 4, the individual dimension is 8. Item No. 2 is replenished every 2T time interval and delivered downstream 3 times.

[0073] Step 2: Calculate the target number of individuals.

[0074] The calculation methods include:

[0075]

[0076] In the formula, iter represents the current number of iterations; NP represents the number of individuals; floor represents the floor function; Miter represents the maximum number of iterations.

[0077] If iter=1, sort the individuals in the population according to the fitness value, and keep the first tar_num individuals as the target; if iter>1, merge the previous generation population and the current population, sort them according to the fitness value and keep the first tar_num individuals as the target. It can be concluded from the above formula that as the number of iterations increases, the number of targets gradually decreases, and the search individuals will also change from widely exploring multiple potential targets to exploring the optimal potential target.

[0078] Among them, the fitness value is an indicator used to evaluate the adaptability or quality of an individual in a group. The fitness value is usually obtained from an objective function (also called an evaluation function), which defines the optimization goal of the problem. The fitness value can be in any form, such as cost, distance, profit, error rate, etc., depending on the specific definition of the problem. In this embodiment, the fitness value is cost, that is, formula (1).

[0079] Step 3: Calculate the potential position of the next generation population; and determine whether the potential position is better than the current position; if it is better than the current position, update the current position to the potential position; otherwise, calculate the greedy factor and probability threshold, and determine whether to update the position based on the probability threshold.

[0080] when or If rand ≥ 0.6, the potential position of the population is calculated as follows:

[0081]

[0082] distance i，j = abs(sorted_target i，j -xA i，j (iter)), (8)

[0083] t=(δ-1)×rand+1, (9)

[0084]

[0085] In the formula, round(·) represents the rounding function; b is a constant that controls the shape of the logarithmic spiral; the fluctuation range of t changes from [-1, 1] to [-2, 1] as the number of iterations increases; sorted_target represents all targets left after sorting; tar_num represents the number of targets; abs(·) represents the absolute value; xa i,j represents the jth dimension of the ith individual; δ decreases linearly from -1 to -2 as the number of iterations increases. In the early stage of the iteration, the search individual can explore the search space extensively, and as the number of iterations increases, the search individual will gradually approach its target.

[0086] when And rand < 0.6, the potential position of the population is calculated according to the following formula:

[0087] xp i，j =round(Best_P j -(Best_P j -mean(sorted_target j ))×rand), (11)

[0088] In the formula, Best_P represents the best solution in history; mean(·) represents the mean function. In the later stage of iteration, exploration should be reduced and development should be increased, and the approximate best solution should be found near the best solution in history.

[0089] The calculation methods of greedy factor and update threshold include:

[0090] T(iter)=T0-α, (12)

[0091]

[0092]

[0093] In the formula, T0 represents the initial greedy factor; α represents the update amplitude of the greedy factor; fitness represents the fitness function; p iIndicates the update threshold; xp i Indicates the potential position of the i-th individual in the population. During the iteration process, the greed factor T decreases with the increase in the number of iterations, causing the update threshold to change from high to low, that is, a certain degree of exploration can be carried out in the early stage, and some solutions that are worse than the current ones can be accepted; in the later stage, the probability of ABOA accepting poor solutions becomes lower.

[0094] If fitness(xp i )<fitness(xa i (iter)), then update to the potential position; if fitness(xp i )≥fitness(xa i (iter)) and rand <p i , then update to the potential position, otherwise, the current population individuals still retain the existing position.

[0095] Step 4: Calculate the fitness value of each individual in the updated population to obtain the current optimal individual; the updated fitness value is the total cost value;

[0096] Step 5: Determine whether the maximum number of iterations has been reached. When the maximum number of iterations has been reached, obtain the total cost value and the current optimal k i 、f i and T value.

[0097] Embodiment 2:

[0098] This embodiment provides a set of comparative experiments, using the differential evolution algorithm (DE) and the arithmetic optimization algorithm (AOA) as comparisons to verify the effectiveness of the adaptive boosting optimization algorithm (ABOA) proposed in the present invention in optimizing the joint replenishment and distribution integrated optimization problem.

[0099] Table 1 gives the basic data settings of the JRD model considering capacity constraints. The number of items is set to 20, 40, and 60 respectively. w They are set to 0.4 and 0.8 times the secondary ordering cost, that is, V = 0.4 and V = 0.8 respectively. The unit mass b of commodity i i Set to 6.25, the maximum carrying capacity of the goods in the joint replenishment phase is B w Set to 25000, the maximum carrying capacity B for commodity i in the distribution stage i r is set to 2000. Other data are randomly generated according to the data range shown in Table 1. Table 2 shows the solution results of the four schemes for the JRD problem considering capacity constraints. It can be concluded from Table 2 that the ABOA algorithm obtains the average value of the total cost, and the minimum and maximum values ​​are better than those of the AOA and DE algorithms.

[0100] Table 1

[0101]

[0102] Embodiment three:

[0103] This embodiment provides an optimization system for joint replenishment and distribution considering capacity constraints, which is used to apply the above-mentioned optimization method, including: a construction module and an optimization module; the construction module is used to construct a JRD model considering capacity constraints during transportation in the joint replenishment stage and the distribution stage; the optimization module is used to optimize the JRD model considering capacity constraints to obtain the current optimal solution of the JRD model considering capacity constraints.

[0104] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. An optimization method for joint replenishment and distribution with capacity constraints, characterized in that: The following steps are involved: S1. Constructing a JRD model that considers capacity constraints during transportation in the joint replenishment stage and the distribution stage; wherein the JRD model that considers capacity constraints includes: ， ， ， In the formula, TC represents the total cost; C s,w represents the ordering cost; C h,w represents the inventory cost of the central warehouse; C o,w represents the delivery cost; C h,R represents the retailer's inventory cost; S w represents the main ordering cost; s i R represents the delivery cost; T represents the unit time for product replenishment; N represents the number of products; i represents the product number; s i w represents the secondary ordering cost; k i represents the replenishment cycle multiplier of commodity i; f i represents the delivery frequency of product i; D i represents the demand rate of commodity i; h i w represents the unit inventory maintenance cost of item i in the central warehouse; h i R b represents the unit inventory maintenance cost of commodity i at the retailer; i represents the unit mass of commodity i; B w It represents the maximum carrying capacity of the goods in the joint replenishment phase; represents the maximum carrying capacity for commodity i during the distribution stage; S2. Optimizing the JRD model considering capacity constraints to obtain a current optimal solution of the JRD model considering capacity constraints; and performing replenishment and delivery based on the current optimal solution; Based on the JRD model considering capacity constraints, the optimal k is obtained i 、f i and the optimal T, where the optimal T is expressed as T * , T * It is expressed as follows: ； Adopting an adaptive Boosting optimization algorithm to optimize the JRD model considering capacity constraints; The adaptive Boosting optimization algorithm includes: Step 1: Set hyperparameters and generate initial individuals; the dimensions of the initial individuals correspond to the decision variables k to be optimized. i and f i ; Step 2, calculate the target number of individuals; when the current iteration number is 1, sort the individuals in the population according to the fitness value, and keep the first tar_num individuals as the target; when the iteration number is greater than 1, merge the previous generation population and the current population, sort the individuals in the population according to the fitness value, and keep the first tar_num individuals as the target; Step 3, calculate the potential position of the next generation population; and determine whether the potential position is better than the current position; if it is better than the current position, update the current position to the potential position; otherwise, calculate the greedy factor and the probability threshold, and determine whether to update the position based on the probability threshold; Step 4: Calculate the fitness value of each individual in the updated population to obtain the current optimal individual; the updated fitness value is the total cost value; Step 5: Determine whether the maximum number of iterations has been reached. When the maximum number of iterations has been reached, obtain the total cost value and the current optimal k i 、f i and T value; The method for calculating the target quantity includes: ， In the formula, iter represents the current number of iterations; NP represents the number of individuals; floor represents the rounding function; Miter represents the maximum number of iterations; when or And rand ≥ 0.6, the calculation method of the potential position of the population includes: ， ， ， ， In the formula, round(·) represents the rounding function; b is a constant that controls the shape of the logarithmic spiral; the fluctuation range of t changes from [-1, 1] to [-2, 1] as the number of iterations increases; sorted_target represents all targets left after sorting; tar_num represents the number of targets; abs(·) represents the absolute value; xa i,j represents the jth dimension of the i-th individual; δ decreases linearly from -1 to -2 as the number of iterations increases; when And rand < 0.6, the calculation method of the potential position of the population includes: ， Where Best_P represents the historical optimal solution; mean(·) represents the mean function; The calculation method of the greedy factor and the probability threshold includes: ， ， ， In the formula, T0 represents the initial greedy factor; α represents the update amplitude of the greedy factor; fitness represents the fitness function; p i represents the probability threshold; xp i represents the potential position of the i-th individual in the population.

2. An optimization system for combined replenishment and distribution taking into account capacity constraints, the system being used to apply the method of claim 1, characterized in that: include: Building modules and optimizing modules; The building module is used to build a JRD model that considers capacity constraints during transportation in the joint replenishment phase and the distribution phase; The optimization module is used to optimize the JRD model considering the capacity limitation to obtain the current optimal solution of the JRD model considering the capacity limitation.

Images