Order batching method fusing local search fox optimization algorithm

Abstract

The invention discloses an order batching method fused with a local search fox optimization algorithm, and relates to the field of logistics. The invention relates to an order batching method fused with a local search fox optimization algorithm. The method comprises the following steps: generating data according to order and cargo information; determining a mathematical model of an order batching strategy; and optimizing the generated mathematical model by adopting a fusion local search fox optimization algorithm, and determining an optimal order batching scheme. According to the method, chaotic mapping and local search strategies are introduced, the local optimization capacity of the algorithm is enhanced, the convergence capacity of the algorithm is improved, and the solving quality and the solving rate of the algorithm are improved.

Description

Technical Field

[0001] The invention belongs to the field of logistics and relates to an order batching method integrating a local search fox optimization algorithm. Technical Background

[0002] Nowadays, intelligent manufacturing is an important direction for my country to move towards high-end, internationalized and intelligent manufacturing. Intelligent manufacturing mainly improves production efficiency and quality by integrating new technologies to achieve the purpose of reducing resource and energy consumption. In the context of intelligent manufacturing, more and more factories' picking systems have changed from the original "people to goods" picking mode to the "goods to people" picking mode. Compared with the "people to goods" picking mode, the "goods to people" mode chooses to introduce automated equipment and intelligent algorithms to replace manual handling of goods and deliver the goods to the pickers.

[0003] More than 60% of the warehouse's operating costs are attributed to order picking. Improving picking efficiency is one of the most important factors in achieving higher efficiency at the operational level. In the "goods-to-person" picking system based on bin robots, due to the dynamic nature of the robot, choosing a reasonable order batching strategy can reduce the total distance the robot walks and improve picking efficiency while meeting the robot's maximum load capacity. Therefore, considering the need for rapid response to manufacturing orders, how to divide N orders into B batches and consider the shortest path that minimizes the robot's maximum load capacity is a key issue in improving customer service satisfaction, improving the overall warehouse operating efficiency, and reducing logistics costs.

[0004] The existing order batching solution algorithms can be mainly divided into precise algorithms, heuristic algorithms, meta-heuristic algorithms, etc. The swarm intelligence algorithm does not need to construct a set of equations, but only needs to set a suitable fitness function, and the optimal estimation solution can be obtained through the algorithm search strategy. When the order batch size is more than two orders, the order batching problem is regarded as an NP-hard problem. Compared with other algorithms, the swarm intelligence algorithm can get a better solution to the NP-hard problem faster. But at the same time, according to the NFL (No-Free-Lunch) theory, different intelligent algorithms are suitable for different optimization problems, and there is no optimization method that is completely applicable to all problems. Moreover, in the application of the order batching solution algorithm, the intelligent optimization algorithm has problems such as slow convergence speed in the later stage and easy to fall into the local optimal value. Therefore, it is very important to find a suitable intelligent algorithm model for the order batching problem and improve its shortcomings. Summary of the invention

[0005] In view of this, the object of the present invention is to provide an order batching method integrating a local search fox optimization algorithm.

[0006] The present invention is achieved through the following technical solutions:

[0007] An order batching method integrating a local search fox optimization algorithm comprises the following steps:

[0008] STEP1: Generate data based on order and goods information;

[0009] STEP 2: Determine the mathematical model of order batching strategy;

[0010] STEP3: Determine the initial parameters such as solution dimension D, maximum number of iterations MAXGEN, population size NIND, upper limit Ub and lower limit Lb;

[0011] STEP4: The mathematical model generated by STEP2 is optimized by using the fusion local search fox optimization algorithm to determine the optimal order batching plan. STEP1 generates data based on warehouse shelves and order information. Specifically, the information of each product on the shelf is converted into a four-dimensional array, and the shelf number, row and column number, and weight of the product are recorded respectively; the products contained in each order are converted into numbers, and a cell array is constructed to store the product numbers.

[0012] The aforementioned STEP 2 is to determine the mathematical model of the order batching strategy. Specifically, an integer programming model is constructed that takes into account the maximum loading capacity of the material box robot and the minimization of the shortest path as the optimization objectives, which can be described in mathematical language as follows:

[0013] Objective function:

[0014] Constraint 1:

[0015] Constraint 2:

[0016] Constraint 3:

[0017] Constraint 4:

[0018] Constraint 5:

[0019] Constraint 6:

[0020] Constraint 7:

[0021] Explanation of symbols:

[0022] O, order set, O = {1, 2, ..., n}

[0023] P, shelf set, P = {1, 2, ..., h}

[0024] W, batch set, W = {1, 2, ..., t}

[0025] D, the set of goods, D = {1, 2, ..., g}

[0026] B jm , the quantity of goods m required for batch j

[0027] Q im , the quantity of goods m required for order i

[0028] S j , the picking path of batch j, j∈W

[0029] t, constant, penalty factor for violating equipment load constraints

[0030] d, constant, picking table capacity

[0031] z, constant, number of shelves

[0032] X ij , the decision variable takes values ​​between 0 and 1, 1 means that order i is in batch j, and 0 means that it is not

[0033] C j , the decision variable takes values ​​of 0-1, 1 means that batch j violates the equipment loading constraint, and 0 means that it complies with the constraint

[0034] l ik , the decision variable takes values ​​between 0 and 1, 1 means that the goods of order i include shelf k, and 0 means that it does not include

[0035] The objective function is to minimize the total picking path. Constraint 1 means that each order will be assigned to a batch, constraint 2 means that each batch has an order, constraint 3 means that the order quantity of each batch does not exceed the capacity of the picking station, constraint 4 means that the number of goods required in the order is equal to the number of goods required in the batch, constraint 5 means that each shelf in each batch is visited at most once, and constraints 6 and 7 represent the value range of the decision variables.

[0036] The STEP3 determines initial parameters such as the dimension dim of the solution, the maximum number of iterations MAXGEN, the population size NIND, the upper limit Ub and the lower limit Lb; it is characterized in that the dimension dim of the solution is the dimension of the order batching plan, which can be set to the number of order batches M + the maximum order number N-1.

[0037] In the above-mentioned STEP4, the mathematical model generated in STEP2 is optimized by using the fusion local search fox optimization algorithm. The specific method is as follows:

[0038] (1) Initialize the population. Set the basic parameters of the algorithm, namely the maximum number of iterations MAXGEN, the population size NIND, the dimension of the solution dim, and the constants c1 and c2, representing the probability of successful hunting. Generate the initial population according to the dimension of the solution and the population size, and then optimize the initial population using the chaotic mapping.

[0039] (2) Calculate the objective function value of the individual and update the optimal individual and the search performance a. Decode the batch scheme of each individual in the population, calculate the objective function value of the individual, and traverse the population to select the optimal individual. Finally, introduce the Infinite Folding Iterative Chaotic Sequence (ICMIC) to optimize the search performance a, and its mapping expression is as follows:

[0040] z k+1 = sin(a / z k ), a ∈ (0, +∞)

[0041] where Z k is the current value of the k-th generation chaotic sequence, a is the control parameter, and its performance is the best when it is 4, so set a = 4.

[0042] (3) Update the position. Determine the position update formula of the individual by random numbers r and p (0 < r, p < 1). When r > 0.5, enter the exploitation mode. The individual needs to calculate the distance from the prey according to the time when the ultrasonic wave is transmitted back, calculate the height to jump through the parabola principle, and select the jump direction by the random number p. When p > 0.18, the next position update uses position formula 1, otherwise it uses position formula 2. When r <= 0.5, the individual will enter the exploration mode. The fox will perform random search according to the best position found so far in this stage, and the next position update uses position formula 3.

[0043] Position formula 1: X t+1 = 0.5 * st * 0.5 * 0.98 * t 2 * c1

[0044] Position formula 2: X t+1 = 0.5 * st * 0.5 * 0.98 * t 2 * c2

[0045] Position formula 3: X t+1 = bestX * rand(1, dim) * Mint * a

[0046] where t is a random number representing the time when the ultrasonic wave is transmitted back, bestX is the optimal individual, s is the wind speed, dim represents the dimension of the individual, MinT is the average hunting time of all individuals, and a is the search performance.

[0047] (4) Local search. After the FOX optimization algorithm obtains the approximate optimal solution, the top 10% of elite individuals are sorted and selected for local search. New solutions are formed by deleting operators and repairing operators. Then, the objective function values ​​of the two are compared and the better solution is retained.

[0048] (5) Record the global optimal individual and its objective function value, update the iteration counter GEN, and when the iteration counter exceeds the maximum number of iterations

[0049] When MAXGEN is reached, the iteration is terminated and the optimal solution is returned.

[0050] The beneficial effects of the present invention are as follows:

[0051] The order batching method disclosed in the present invention takes the maximum robot loading capacity and the minimum total picking path as the optimization goals, and uses the fusion local search fox optimization algorithm to solve the model and seek the optimal batching solution. The simulation experiment results show that compared with the results based on the firefly algorithm, there are better quality solutions and less computing time. It can provide certain theoretical support for improving the efficiency of factory material preparation and picking. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is an operation flow chart of the goods-to-person picking system for warehouse material preparation in the present invention;

[0053] Figure 2 It is a flow chart of an order batching method integrating a local search fox optimization algorithm in the present invention;

[0054] Figure 3 It is a flow chart of the fox optimization algorithm integrating local search in the present invention;

[0055] Figure 4 A schematic diagram of the individual coding in the present invention;

[0056] Figure 5 This is a schematic diagram of the present invention and warehouse shelf placement;

[0057] Figure 6 A comparison chart of the running results of the present invention and other algorithms in a medium-scale example;

[0058] Figure 7 It is the convergence diagram of the medium-scale example of the present invention; DETAILED DESCRIPTION

[0059] In order to better understand the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the drawings in the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0060] like Figure 2As shown, the present invention is an order batching method integrating a local search fox optimization algorithm, and the specific steps are as follows:

[0061] First, data is generated based on order and cargo information. Warehouse material preparation and picking operation process, such as Figure 1 As shown in the figure, it can be seen that the traditional order batching method is not completely applicable to the goods-to-person picking system. Since the goods-to-person picking system is carried by robots, it is necessary to consider whether the weight of the goods is within a reasonable range. At the same time, in order to improve the overall picking efficiency, the total picking distance of the robot needs to be the shortest. Therefore, reference Figure 5 The warehouse shelf placement, based on the location information and weight of each product, generates shelf data for standardization, and generates a code for the product in order to associate the relationship between the order and the product. The code must be unique and standardized. Specifically, the information of each product on the shelf is converted into a four-dimensional array, which records the shelf number, row and column number, and weight of the product; the products included in each order are converted into numbers and stored in a cell array.

[0062] Then, the mathematical model of the order batching strategy is determined. Specifically, an integer programming model is constructed that takes into account the maximum loading capacity of the bin robot and the minimization of the shortest path as the optimization goal, which can be described in mathematical language as follows:

[0063] Objective function:

[0064] Constraint 1:

[0065] Constraint 2:

[0066] Constraint 3:

[0067] Constraint 4:

[0068] Constraint 5:

[0069] Constraint 6:

[0070] Constraint 7:

[0071] Explanation of symbols:

[0072] O, order set, O = {1, 2, ..., n}

[0073] P, shelf set, P = {1, 2, ..., h}

[0074] W, batch set, W = {1, 2, ..., t}

[0075] D, the set of goods, D = {1, 2, ..., g}

[0076] B jm , the quantity of goods m required for batch j

[0077] Q im , the quantity of goods m required for order i

[0078] S j , the picking path of batch j, j∈W

[0079] t, constant, penalty factor for violating equipment load constraints

[0080] d, constant, picking table capacity

[0081] z, constant, number of shelves

[0082] X ij , the decision variable takes values ​​between 0 and 1, 1 means that order i is in batch j, and 0 means that it is not

[0083] C j , the decision variable takes values ​​of 0-1, 1 means that batch j violates the equipment loading constraint, and 0 means that it complies with the constraint

[0084] l ik , the decision variable takes values ​​between 0 and 1, 1 means that the goods of order i include shelf k, and 0 means that it does not include

[0085] The objective function is to minimize the total picking path. Constraint 1 means that each order will be assigned to a batch, constraint 2 means that each batch has an order, constraint 3 means that the order quantity of each batch does not exceed the capacity of the picking station, constraint 4 means that the number of goods required in the order is equal to the number of goods required in the batch, constraint 5 means that each shelf in each batch is visited at most once, and constraints 6 and 7 represent the value range of the decision variables.

[0086] Finally, the generated mathematical model is optimized using the fusion local search fox optimization algorithm to determine the optimal order batching plan. The algorithm flow chart is as follows: Figure 3 As shown, the specific steps are as follows:

[0087] Step 1: Initialize the population. Set the basic parameters of the algorithm, that is, the maximum number of iterations MAXGEN is set to 100, the population size NIND is set to 50, the dimension of the solution dim is set to 29, and the constants c1 and c2 are set to 0.18 and 0.82 respectively. Generate the initial population according to the dimension of the solution and the population size, and then use the chaotic map to optimize each individual. The individual encoding is as follows: Figure 4As shown in the figure. Where N is the individual length, m is the number of order batches, n is the number of orders, and n + 1 is the identification point of the first batch and the second batch. When decoding, the individual position can be converted into an order batching scheme through this identification.

[0088] Step2: Calculate the objective function value of the individual and update the optimal individual and search performance a. Decode the batching scheme of each individual in the population, calculate the objective function value of the individual, and traverse the population to select the optimal individual. Finally, introduce the Infinite Folding Iterative Chaotic Sequence (ICMIC) to optimize the search performance a.

[0089] Step3: Update the position. Determine the individual's position update formula by random numbers r and p (0 < r, p < 1). When r > 0.5, enter the development mode. The individual needs to calculate the distance from the prey according to the time when the ultrasonic wave is transmitted back, calculate the height to jump through the parabola principle, and select the jumping direction by the random number p. Different jumping directions have different position update formulas. In the wind speed formula, t is a random number representing the time when the ultrasonic wave is transmitted back, bestX is the best individual, and s is the calculated wind speed. When p > 0.18, the next position update uses position formula 1, otherwise it is position formula 2. Position formula 1 and 2 only differ in the constants c1 and c2, representing the probability of successful hunting. When r <= 0.5, the individual enters the search mode. The fox conducts a random search based on the best position of the fox found so far at this stage. The fox has no jumping skills at this stage because it must walk randomly in the search area to explore the prey. The walking formula is shown as position formula 3.

[0090] Wind speed formula:

[0091] Position formula 1: X t+1 = 0.5 * st * 0.5 * 0.98 * t 2 * c1

[0092] Position formula 2: X t+1 = 0.5 * st * 0.5 * 0.98 * t 2 * c2

[0093] Position formula 3: X t+1 = bestX * rand(1, dim) * Mint * a

[0094] Where t is a random number representing the time when the ultrasonic wave is transmitted back, bestX is the best individual, s is the wind speed, dim represents the individual dimension, MinT is the average hunting time of all individuals, and a is the search performance.

[0095] Step 4: Local search. After the FOX optimization algorithm obtains the approximate optimal solution, the top 10% of elite individuals are sorted and selected for local search. New solutions are formed by deleting operators and repairing operators, and then the objective function values ​​of the two are compared to retain the better solution.

[0096] Step 5: Record the global optimal individual and its objective function value, update the iteration counter GEN, and when the iteration counter exceeds the maximum number of iterations MAXGEN, terminate the iteration and return the optimal solution.

[0097] Finally, the simulation experiment is carried out to verify:

[0098] In order to verify the effectiveness of the present invention, simulation experiments were conducted from multiple aspects. The simulation experiment selected a total of 12 sets of data from a medium-scale example to compare the solution results of the firefly algorithm and the fusion local search fox optimization algorithm. The specific operation results are shown in Table 1. When the scale of operation gradually increases, the running time of the firefly algorithm is also 30.6 seconds longer than the fusion local search fox optimization algorithm on average due to the higher computational complexity. The running results of the algorithm of the present invention are 8.78% lower than those of the firefly algorithm on average. Analysis Figure 6 It can be seen that as the number of orders increases, the solution results also show an upward trend, but the algorithm proposed in the present invention is always better than the solution results of the firefly algorithm.

[0099] Table 1 Solution results of the scale example

[0100]

[0101] analyze Figure 7 From the convergence curve, we can see that when the number of iterations is 1-10, the running results of the FOX optimization algorithm converge quickly; when the number of iterations is in the range of 20-40, the FOX optimization algorithm can obtain the optimal solution.

[0102] In summary, the present invention has a fast convergence speed in order batch optimization, is not prone to falling into local optimality, and has a high solution accuracy.

[0103] Although the above describes an illustrative specific embodiment of the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiment. For ordinary technicians in this technical field, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. An order batching method integrating local search fox optimization algorithm, characterized in that: The following steps are involved: STEP1: Build shelf and order models based on historical order and cargo information; STEP2: Select picking paths and batching strategies and build order batching models; STEP3: Determine initial parameters such as solution dimension dim, maximum number of iterations MAXGEN, population size NIND, upper limit Ub and lower limit Lb; STEP4: When solving the mathematical model generated in STEP2 using the fusion local search fox optimization algorithm, use the Logistic-Sine-Cosine mapping to optimize the randomly generated order batching scheme, and introduce the ICMIC mapping to improve the search factor a so that it no longer changes linearly. After the fox algorithm is solved, use the local search algorithm to screen and optimize each individual to determine the optimal order batching scheme.

2. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: Build a shelf and order model based on historical order and goods information. Specifically, convert the goods information into an array of n rows and 4 columns, where each row records the shelf number, row and column number, and the weight of the goods; convert the goods contained in each order into standardized number records, and build a cell array to store the order information.

3. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: An integer programming model is constructed with the maximum loading capacity of the bin robot and the minimization of the total picking path as the optimization goal. Its objective function is: Where S j It represents the total distance of batch j of the order batching plan picked according to the S-type picking path. The specific calculation formula of the total distance S is as follows: S_len=La*((side-1)*cent+e*2) S_len=(La-1)*((side-1)*cent+e*2)+2*((Lb-1)*cent+e) S_cro=(max_No-1)*aisle*2+Aisle*2 S=S_len+S_cro La represents the number of shelves that need to be picked in the batch, side represents the number of shelf storage locations, cent represents the distance between adjacent storage locations in the shelf, e represents the distance from the picking channel to the transport channel, Lb represents the vertical number of the goods on the farthest shelf in the batch, max_No represents the number of the farthest shelf in the batch, aisle represents the distance between adjacent picking channels, Aisle represents the distance between the first shelf and the starting point, S_len is the horizontal distance calculation formula. First, the number of shelves needs to be determined, which is different when it is an even number or an odd number; S_cro is the vertical distance.

4. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: The dimension of the solution is the dimension of the order batching plan, which can be set to the number of order batches + the maximum order number - 1, so that special characters can be used to separate each batching plan.

5. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: In the population initialization stage, the Logistic-Sine-Cosine mapping is introduced to improve the initialization performance. The Logistic-Sine-Cosine mapping is a type of chaotic mapping with the characteristics of randomness, nonlinearity, and ergodicity. Its mapping expression is as follows: x(i+1)=cos(π(4rx(i)(1-x(i))+(1-r)sin(πx(i))-0.5)),r∈[0,1] Among them, x(i) is the current value of the i-th generation chaotic sequence, and a is the control parameter. When it is near 0.5, the mapping traversal performance is the best, so a = 0.5 is set; therefore, the initial position of the fox individual is: x i_initial (t)=BoundClamp(p t ,Ub,Lb) Where t is the number of iterations, x i_initial It represents the initial position of the i-th fox after iteration t times, Lb and Ub are the minimum and maximum values ​​of the boundary respectively, and BoundClamp is the boundary clamping function.

6. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: The fox optimization algorithm is a solution algorithm generated by imitating the hunting pattern of red foxes. During the hunting process of red foxes, the distance between the prey and itself is determined by perceiving the propagation of sound, and then different takeoff directions are selected for hunting behavior. Different takeoff directions are expressed by a mathematical formula as the position formula of the next position where the fox moves; at the same time, to accelerate the convergence speed of the overall algorithm, a random number r is introduced into the algorithm to introduce the global search position formula.

7. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: The specific position update formula is as follows: The position update formula of the individual is determined by the random numbers r and p (0 < r, p < 1); when r > 0.5, it enters the exploitation mode. The individual needs to calculate the distance from the prey according to the time when the ultrasonic wave is transmitted back, calculate the height to jump through the parabola principle, and select the jump direction by the random number p. When p > 0.18, the next position update uses position formula 1, otherwise it is position formula 2; when r <= 0.5, the individual enters the exploration mode; the fox will perform a random search according to the best position found so far at this stage, and the next position update uses position formula 3: Position formula 1: X t+1 =0.5*st*0.5*0.98*t 2 *c1 Position formula 2: X t+1 =0.5*st*0.5*0.98*t 2 *c2 Position formula 3: X t+1 =bestX*rand(1,dim)*Mint*a Among them, t is a random number representing the time when the ultrasonic wave is transmitted back, bestX is the best individual, s is the wind speed, dim represents the individual dimension, MinT is the average time used for hunting by all individuals, and a is changed from using a linear decrease in the original search performance algorithm to introducing the ICMIC mapping formula to change the change curve of a. The ICMIC mapping formula is as follows: Among them, a1 is the control parameter, and its value range is from 0 to positive infinity. When it is set to 4, the overall effect of the algorithm is the best, so a1 is set to 4. The order batching method integrating the local search fox optimization algorithm according to claim 1 is characterized in that: Local search is incorporated into the fox optimization algorithm, and the specific method is as follows: After the FOX optimization algorithm obtains an approximate optimal solution, the top 10% of the elite individuals are selected and sorted for local search. New solutions are formed through the deletion operator and the repair operator, and then the objective function values of the two are compared, and the better solution is retained.

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