Flexible workshop scheduling optimization method and system based on improved ant lion optimization algorithm

Abstract

The invention discloses a flexible workshop scheduling optimization method and system based on an improved ant lion optimization algorithm, and the method comprises the steps: obtaining selectable processing equipment data of each process of each workpiece and processing data corresponding to the selectable processing equipment data, constructing a flexible workshop scheduling optimization model according to the optional processing equipment data and the processing data; and solving the flexible workshop scheduling optimization model according to a preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling scheme. The improved ant lion optimization algorithm is applied to solution of a flexible workshop scheduling model, an optimal scheduling scheme can be rapidly obtained, and it is guaranteed that the maximum completion time is minimized.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible job shop scheduling, and particularly relates to a flexible job shop scheduling optimization method and system based on an improved ant lion optimization algorithm. Background Technique

[0002] The flexible job shop scheduling problem (FJSP) plays an important role in the field of production manufacturing. Its main goal is to improve production efficiency and reduce costs by optimizing the scheduling of workshop resources. Compared with the classical job shop scheduling problem (JSP), the core feature of FJSP is that the operations of each workpiece can be processed on any machine in a predetermined set of machines, which provides greater flexibility for scheduling and can more realistically reflect the complexity and variability in the actual production process. However, this flexibility also brings a significant increase in computational complexity. Therefore, how to determine the operation arrangement of workpieces to be processed quickly and accurately through an effective optimization method while ensuring scheduling flexibility, and then generate a reasonable Gantt chart, has become the core problem in the design of flexible job shop scheduling.

[0003] With the continuous development of computer science and technology, researchers use computer technology to model and identify parameters for the flexible job shop scheduling problem, and conduct global searches through optimization algorithms to effectively arrange workshop resources and finally achieve the optimal production scheduling plan. Existing algorithms for flexible job shop scheduling optimization mainly include symbiotic organism search algorithm, memetic algorithm, and vulture optimization algorithm. These swarm intelligence algorithms have been widely used in the field of industrial production optimization. However, the flexible job shop scheduling problem is a complex non-linear optimization problem, and traditional optimization algorithms often have difficulty quickly and accurately solving various constraints and objectives in scheduling. Therefore, how to find an efficient optimization method that can balance global and local searches has become the key problem in flexible job shop scheduling optimization. Summary of the Invention

[0004] The present invention provides a flexible job shop scheduling optimization method and system based on an improved ant lion optimization algorithm to solve the technical problem that traditional optimization algorithms often have difficulty quickly and accurately solving various constraints and objectives in scheduling.

[0005] In a first aspect, the present invention provides a flexible job shop scheduling optimization method based on an improved ant lion optimization algorithm, including: Obtain the optional processing equipment data of each operation of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; Solve the flexible job shop scheduling optimization model according to a preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling plan, wherein the process of solving the flexible job shop scheduling optimization model specifically includes: Encode the operation set and machine set, and initialize the tabu list; Use the good point set initialization method to assign a machine to each operation; Generate the initial solution set by decoding the initial population ; For the initial solution set Iterate the population using the IALO algorithm. In each iteration, use the roulette wheel strategy to select an antlion for each ant. The ant performs a random walk based on curve displacement around the selected antlion to explore a new solution space region and obtain a new population ; Update the population using the critical path MCP strategy And perform tabu search. If it is better than the current solution, update the tabu list to obtain a new ; If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, continue the iteration; Output the global optimal scheduling scheme and the minimum makespan of each generation.

[0006] In a second aspect, the present invention provides a flexible job shop scheduling optimization system based on an improved antlion optimization algorithm, including: A construction module configured to obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; A solving module configured to solve the flexible job shop scheduling optimization model according to a preset multi-strategy collaborative antlion optimization algorithm to obtain an optimal scheduling scheme, wherein the process of solving the flexible job shop scheduling optimization model specifically includes: Encode the operation set and machine set, and initialize the tabu list; Use the good point set initialization method to assign a machine to each operation; Generate the initial solution set by decoding the initial population ; For the initial solution set Iterate the population using the IALO algorithm. In each iteration, use the roulette wheel strategy to select an antlion for each ant. The ant performs a random walk based on curve displacement around the selected antlion to explore a new solution space region and obtain a new population ; Update the population using the critical path MCP strategy And perform tabu search. If it is better than the current solution, update the tabu list to obtain a new ; If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, continue the iteration; Output the globally optimal scheduling scheme and the minimum makespan of each generation.

[0007] In a third aspect, there is provided an electronic device, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute the steps of the flexible job shop scheduling optimization method based on the improved ant lion optimization algorithm according to any embodiment of the present invention.

[0008] In a fourth aspect, the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program instructions are executed by a processor, the processor is enabled to execute the steps of the flexible job shop scheduling optimization method based on the improved ant lion optimization algorithm according to any embodiment of the present invention.

[0009] The flexible job shop scheduling optimization method and system based on the improved ant lion optimization algorithm of the present application introduce a new good point set initialization strategy for generating a more uniform and higher-quality initial solution set, and introduce a curve displacement strategy in the random walk of ants to enhance their ability to escape from traps, making it have higher self-adaptability and robustness. The local search strategy introduces the idea of tabu search to improve the efficiency of the algorithm in global search and local exploitation. In addition, for the problem of multiple critical paths, three methods for solving critical paths are proposed, tested respectively, and the optimal critical path method is selected to solve the problem in combination with tabu search. The organic combination of these strategies significantly enhances the global exploration ability and the ability to escape from local optimal solutions of the algorithm, and effectively accelerates the convergence process of the algorithm. Applying the improved ant lion optimization algorithm to the solution of the flexible job shop scheduling model can quickly obtain the optimal scheduling scheme and ensure the minimization of the makespan. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0011] Figure 1 A Gantt chart of flexible job shop scheduling for a specific embodiment provided by an embodiment of the present invention; Figure 2 A flowchart of a flexible job shop scheduling optimization method based on the improved ant lion optimization algorithm provided by an embodiment of the present invention; Figure 3 A multiple critical path diagram for a specific embodiment provided by an embodiment of the present invention; Figure 4 A box plot of three MCP methods for a specific embodiment provided by an embodiment of the present invention; Figure 5 A schematic diagram of a special critical path situation for a specific embodiment provided by an embodiment of the present invention; Figure 6 A schematic diagram of an algorithm convergence curve for a specific embodiment provided by an embodiment of the present invention; Figure 7 A schematic diagram of the convergence curves of the EP algorithm and the IALO algorithm for a specific embodiment provided by an embodiment of the present invention; Figure 8 A structural block diagram of a flexible job shop scheduling optimization system based on an improved ant lion optimization algorithm provided by an embodiment of the present invention; Figure 9 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0013] A flexible job shop scheduling with a problem size of M N. M is the number of machines, and N is the number of workpieces to be processed. As Figure 1 shown, represents the processing process of the y-th process of the x-th workpiece, and the ordinate where it is located represents the specific machine for executing the process. For example represents the processing process of the 1st process of the 2nd workpiece, and the ordinate position indicates that the processing process is completed on M2. M1, M2, M3 represent machine numbers, representing the first, second, and third processing machines respectively, and so on. When arranging the processing of workpieces, it is strictly in accordance with the sequence of processes. The core of the scheduling task is to determine the processing sequence of the processes. Once the processing sequence is determined, since each process corresponds to only one available machine, the determination of the processing machine follows.

[0014] With the objective of minimizing the makespan, the processes are optimized on the premise of satisfying the processing sequence constraints of each workpiece. According to the definition of flexible job shop scheduling, the fitness function can be expressed as: , (1) In the formula, is the completion time of the j-th workpiece.

[0015] Please refer to Figure 2 , which shows a flowchart of a flexible job shop scheduling optimization method based on an improved ant lion optimization algorithm of the present application.

[0016] As Figure 2 shown, the flexible job shop scheduling optimization method based on the improved ant lion optimization algorithm specifically includes the following steps: Step S101, obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data.

[0017] Step S102, solve the flexible job shop scheduling optimization model according to a preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling plan.

[0018] The ant lion optimization algorithm updates and optimizes the position by simulating the foraging process of ant lions and the escape behavior of ants. And it is divided into three stages: digging traps, catching prey, and repairing traps. The diverse position update strategy of the ant lion optimization algorithm can explore the solution space more comprehensively and shows excellent performance in solving continuous and discrete optimization problems.

[0019] 1) Ants move randomly during the process of looking for food.

[0020] , (2) where is the cumulative sum calculation; T is the maximum number of iterations; t is the current number of iterations; is a random function.

[0021] , (3) where rand is a random number in the interval [0, 1].

[0022] During the optimization process, the positions of ants are saved and utilized: , (4) where is the matrix for saving the positions of each ant; represents the value of the j-th variable of the i-th ant; is the number of ants; is the number of variables.

[0023] During the optimization process, a fitness function is used and the fitness values of all ants are stored in a matrix.

[0024] , (5) Wherein, is a matrix for storing the fitness of each ant; In addition to ants, it is assumed that antlions are also hidden somewhere in the search space, and their positions and fitness values are stored: , (6) Wherein, is a matrix for storing the position of each antlion, is the i th dimension value of the j th angle; , (7) Wherein, is a matrix for storing each fitness value; represents the value of the jth dimension of the ith antlion, is the objective function.

[0025] , (8) Wherein, is the position of the ith ant in the tth iteration, is the lower bound of the value of the ith variable when the ant moves randomly, is the upper bound of the value of the ith variable when the ant moves randomly; is the lower boundary value of the ith variable in the search space; is the upper boundary value of the ith variable in the search space at the tth iteration.

[0026] 2) The mathematical model corresponding to the antlion trap is as follows: The traps created by antlions will affect the random walking route of ants. To mathematically model this assumption.

[0027] , (9) Wherein, A is the position of selecting the jth antlion at the tth iteration; is the lower boundary value of the ith variable in the search space at the tth iteration; is the upper boundary value of the ith variable in the search space at the tth iteration.

[0028] , (10) Wherein, I is a ratio; is the minimum value of all variables in the tth iteration, represents the maximum value including all variables in the tth iteration. is a ratio, T is the maximum number of iterations, is a constant. When t > 0.1t = 2; when t > 0.5T, = 3; when t > 0.75T, = 4; when t > 0.9T, = 5; when t > 0.95T, = 6.

[0029] 3) Capture the prey and reconstruct the trap, specifically: When the fitness value of the ant is greater than that of the antlion, prey capture occurs. Then, the antlion will update to the latest position of the ant it has captured to improve its chance of capturing prey. This mechanism is as follows: , (11) In the formula, is the position of the j-th antlion at the t-th iteration; is the position of the i-th ant at the t-th iteration.

[0030] The antlion with the best fitness in the current iteration will be regarded as the elite antlion, which affects the random walk of all ants. Affected by the elite antlion and the roulette wheel selection antlion, the position update of the ant's random walk is as follows: , (12) In the formula, is the random walk generated by the ant around the antlion selected by the roulette wheel at the t-th iteration; is the random walk generated by the ant around the elite antlion at the t-th iteration; is the position of the k-th ant at the t-th iteration.

[0031] Multi-Strategy Cooperative Antlion Optimization Algorithm (MSALO): Initialize the population: The mathematical model description of the antlion optimization algorithm is as follows. Let the size of the antlion be P, and the initial ant population , the dimension of the feasible solution space is d, then the i-th ant in the solution space is represented as , and the initial antlion group of the antlion optimization algorithm is randomly generated in the solution space within a certain search range.

[0032] Randomly forming the initial population means that: in the process of flexible job shop scheduling optimization, the present invention aims at the makespan optimization. The problem to be optimized is to minimize the makespan, and each scheduling scheme is represented by an antlion , and each processed workpiece is represented by an antlion . Determine the working state of each processing machine and the workpiece processing sequence P, and combine them to form an antlion group, that is, the antlion is used to represent the solution of a scheduling scheme. Within a certain search parameter range, use the random rand function to determine each antlion in the antlion group to form the initial population.

[0033] For flexible job shop scheduling, the ant lion optimization algorithm better balances the global and local search performance of the algorithm, which is beneficial to the effective search for the global optimal solution and the improvement of the overall execution efficiency. However, the initial population distribution of the ant lion optimization algorithm is not uniform enough, which affects the convergence speed of the algorithm. Aiming at the above defects of the basic dandelion optimization algorithm, this paper proposes an improved ant lion optimization algorithm based on the good point set with an escape mechanism.

[0034] As is well known, the good point set sampling method can provide a better search starting point for the algorithm by selecting high-quality initial solutions or solution distributions, making the subsequent optimization process more effective and efficient, thereby improving the quality of the final solution. The good point set theory originated from the famous mathematician Hua Luogeng in China. Suppose Hs is the unit cube in the s-dimensional Euclidean space, and there is a point set: , (13) Its discrepancy satisfies: , (14) where, is a constant, only related to r, ε(ε>0). Then is called a good point set, and r is called the good point set. The value of the good point set r is: , (15) where p is the smallest prime number satisfying (p - 3) / 2 ≥ s.

[0035] Therefore, based on the good point set theory, the new initialization strategy is: , (16) In the formula, is the position of the i-th ant in the k-th iteration, is the upper bound, is the lower bound, is the good point set, is the number of iterations, s is the dimension of the good point set, is the parameter of the first dimension, is the parameter of the s-th dimension, is the number of the ant population.

[0036] To avoid too many ants wandering around some ant lions ineffectively, we adjusted their walking strategy to expand the search range. In natural hunting, when an ant falls into a trap, it will instinctively move away from the ant lion and try to escape. At the same time, when moving vertically, it will randomly wander horizontally, forming a curved trajectory. Therefore, we combined the random wandering and curved displacement of the ant, and used the sine and cosine functions to construct an escape strategy.

[0037] Since ants have two-dimensional visual perception, their escape direction is random, and the escape angle is represented by γ ∈ (0°, 360°). There are two ways for ants to escape: one is to gradually increase the escape force until the limit and then consume it, and the other is to gradually weaken after the initial maximum force. We use sin(γ) and cos(γ) to represent these two ways respectively, and simulate the ant's choice through a random variable To reflect the gradually weakening struggling force of the ant, a dynamic attenuation coefficient is added to the escape rule, represented by where a represents the initial intensity, t represents the current iteration number, and T represents the total number of iterations. At the same time, a random parameter D is used to represent that different ants may have different fighting intensities, is a random number, representing the state of ant i in the t-th iteration. Formulas (17) to (20) will be used to describe the ant's escape process. This method more realistically simulates the ant's escape behavior, expands its exploration range, and reduces the risk of falling into local optimal solutions.

[0038] , (17) , (18) , (19) , (20) In the formula, is a parameter that changes with the number of iterations, is a random number uniformly distributed between 0° and 360°, is a constant, with a value of 1 in the experiment, is the current iteration number, is the total number of iterations, is a random number uniformly distributed between 0 and 1, is the state of ant i in the t-th iteration, is the number of the ant population, is a random number uniformly distributed between 0 and 1, is the state of ant i in the (t + 1)-th iteration.

[0039] Tabu Search (TS) is one of the widely used and efficient search algorithms. In this paper, it is introduced into the search stage to avoid local optimal solutions and enhance the global search ability. The process is as follows: First, initialize the tabu list to the current solution and determine the global optimal solution; then conduct a neighborhood search. If a better solution is found and the better solution is not in the tabu list, update the tabu list and the global optimal solution; if the tabu list is full, delete the earliest solution and update the list. This process is repeated until the termination condition is met.

[0040] A multi-strategy collaborative ant lion optimization algorithm (MSALO) is proposed to solve the flexible job shop scheduling problem. The specific implementation steps are as follows: Step 1: Encode the operation set and machine set, and initialize the taboo list.

[0041] Step 2: Use the good point set initialization method to assign machines to each operation.

[0042] Step 3: Generate the initial solution set Ps by decoding the initial population.

[0043] Step 4: Use the IALO algorithm to iterate the population for the initial solution set Ps. In each round of iteration, use the roulette wheel strategy to select an ant lion for each ant, and the ant performs a random walk based on curve displacement around the selected ant lion to explore a new solution space region, obtaining a new population Pc.

[0044] Step 5: Update the population Pc using the critical path MCP method and perform taboo search. If it is better than the current solution, update the taboo list. Obtain a new Ps.

[0045] Step 6: If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, return to Step 2.

[0046] Step 7: Output the global optimal scheduling plan and the minimum makespan for each generation.

[0047] The maximum completion time of the flexible job shop scheduling is determined by the longest critical path, and the delay of tasks on the critical path will cause overall delays. Therefore, identifying and adjusting the activities on the critical path can effectively improve the scheduling efficiency.

[0048] There is usually only a single critical path in the flexible job shop scheduling plan, but in some cases, there may be multiple critical paths. As Figure 3 shown, moving the operations on a single critical path cannot reduce the completion time because the other critical paths remain unchanged. To solve this problem, three methods are tested in the present invention as described below: (1) MCP1: Move the common operations of multiple critical paths to break multiple critical paths.

[0049] (2) MCP2: Randomly select the critical operations of a single critical path, ignoring the influence of multiple critical paths to improve efficiency.

[0050] (3) MCP3: Move the critical operations of all critical paths, considering all possible situations to expand the solution space.

[0051] To verify the performance of the three multi-critical path methods on the Ladata benchmark, 20 independent experiments were conducted to reduce random interference. Among them, Best represents the minimum makespan in 20 runs, Avg is the average makespan of 20 runs, and STD is the standard deviation. As shown in Table 1, MCP3 shows comprehensive advantages in all cases: its optimal solution Best is on average 5.8% and 9.1% higher than MCP1 and MCP2 respectively. In complex cases such as La01 and La03, MCP3 achieved results significantly better than the comparison schemes, such as 1390 and 1058 (MCP1: 1469 / 1156, MCP2: 1533 / 1187). For low-dimensional cases such as La04 and La05, MCP3 still maintains an average advantage of 1.5% - 2.7%, highlighting its global search ability. At the same time, the STD of MCP3 is on average 31.6% (MCP1) and 29.4% (MCP2) lower than that of the comparison methods. The standard deviation of the La03 instance is only 45.2, a decrease of 43.2% compared to 79.6 of MCP2. In addition, the box plot for evaluating the stability of RPD is as Figure 4 shown, and MCP3 has the best stability effect. As the problem complexity increases, the advantages of MCP3 become more significant, which stems from its unique critical path handling mechanism and enhanced neighborhood search strategy, effectively expanding the exploration depth of the solution space.

[0052] In simple instances, the three MCP methods exhibit similar performance characteristics. However, when the problem complexity increases and multiple critical paths are involved, their optimization effects show significant differences. As Figure 5 shown, when there are two independent and non-shared operation critical paths, it is difficult for a single operation to optimize both paths simultaneously. In this case, MCP1 may fail in local search due to its inability to identify common critical blocks. Although MCP2 and MCP3 perform similarly in terms of the quality of the optimal solution, MCP3 shows obvious advantages in dealing with multiple critical path problems due to its more stable search performance, and is therefore selected as the final optimization strategy.

[0053] Table 1 , The following experiment aims to demonstrate an application example of the improved ant lion optimization algorithm in flexible job shop scheduling optimization. To ensure the fairness and comparability of the experimental results, all algorithms participating in the comparison adopt unified experimental parameter settings, where the population size and the maximum number of iterations are set to 100 and 200 respectively. This setting ensures that different algorithms are evaluated under the same conditions, thus effectively verifying the superiority of the improved ant lion optimization algorithm in flexible job shop scheduling.

[0054] To comprehensively evaluate the performance of the IALO algorithm, a classic Fdate instance was selected and systematically compared with the Symbiotic Organisms Search algorithm (SOS), the Memetic algorithm (MA), and the Vulture Optimization algorithm (AO). The experimental results are shown in Table 3 and Figure 6 as follows, where "Time" represents the duration of a single iteration, "LB" represents the lower bound of the case, "Fitness" represents the fitness value, and "Iteration" represents the number of iterations.

[0055] As shown in Table 2, the IALO algorithm demonstrated significant advantages in 18 FJSP test instances. Specifically, in 13 cases, it successfully reached the lower bound (LB), and in 7 cases, the average solution was exactly the same as the optimal solution. Additionally, the IALO showed excellent convergence accuracy and stability. In low-dimensional cases such as SFJS01, SFJS02, and SFJS03, all algorithms were able to reach the lower bound, which verified the convergence behavior of the algorithms in low-complexity problems. In terms of global search ability, IALO obtained the optimal solution in 13 cases, and only 5 cases failed to reach the optimal solution. This performance was significantly better than the comparison algorithms: the WOA algorithm reached the optimal solution in 11 cases, while the GWO algorithm achieved the optimal solution in 9 cases. The excellent performance of IALO can be attributed to its dual innovation mechanisms: the initialization strategy based on the good point set, which enhanced the diversity of the population, and the improved random walk strategy, which effectively avoided ineffective searches. These innovations enabled IALO to maintain a balanced advantage in terms of convergence speed and solution quality in large-scale problems (such as SFJS05 and Mt03), thus providing an effective solution for complex scheduling problems.

[0056] To further improve the optimization performance of the IALO algorithm, a Multiple Critical Paths Optimization strategy (MCP3) was introduced. In 18 test cases, IALO reached the established lower bound in 17 cases and obtained an average solution exactly the same as the optimal solution in 15 cases, significantly outperforming the traditional algorithms. Taking the high-dimensional case MFJS05 as an example, IALO (MCP3) reduced the lower bound deviation by 63.4% compared to the version without MCP3, while compressing the standard deviation (STD) by 41.8%, verifying the dual improvement in solution quality and stability. This performance improvement was mainly due to the innovative design of the MCP3 strategy: by considering all critical operations on all critical paths simultaneously, it significantly expanded the neighborhood search space and effectively avoided the dilemma of traditional algorithms falling into local optimal solutions due to neglecting some critical paths. The experimental results fully verified the effectiveness of the MCP3 strategy in enhancing global search ability and improving the stability of solution quality.

[0057] Figure 6Shows the comparison results of the iterative curve graph algorithm based on six different cases. It is worth noting that IALO exhibits the optimal convergence characteristics in all scenarios. In the SFJS10 and Mt01 cases, the final fitness values of IALO are 23.6% and 17.9% lower than those of ALO, respectively. It should be specifically pointed out that in the MFJS05 scenario, the fitness fluctuation range of IALO (less than 5%) is significantly lower than that of WOA (about 12%) and GWO (about 18%). Although there are significant differences in the fitness ranges in each subfigure, IALO always maintains the smoothest convergence trajectory. Especially in the MFJS01 case, compared with ALO, the change rate of the curve slope is reduced by 38%, further supporting the effectiveness of the MCP3 strategy in balancing global exploration and local exploitation.

[0058] Table 2 , To further verify the effectiveness of the proposed IALO algorithm, a practical case study was conducted. Six different-sized workshop cases, labeled Case01 to Case06, were tested.

[0059] The IALO algorithm was compared with the traditional evolutionary programming (EP) algorithm and the scheduling rule methods (Dispatch1 and Dispatch2). The specific scheduling rules are as follows: (1) Maximum remaining operations rule (MOR): Prioritize scheduling the job with the most remaining operations.

[0060] (2) Global shortest processing time rule (GSPTR): Assign the operation to the available machine with the shortest processing time.

[0061] (3) Workload consideration rule (WCR): Prioritize assigning the operation to the available machine with the lowest workload.

[0062] It can be observed that the MOR rule mainly solves the operation sequencing sub-problem in the flexible job shop scheduling, while GSPTR and WCR aim to solve the machine assignment problem. Therefore, Dispatch1 consists of MOR and GSPTR, while Dispatch2 is formed by combining MOR with WCR. Both scheduling rules contain a random component, which may lead to different decisions under the same conditions, resulting in differences in the results. Therefore, the results presented in this paper are based on the average values of multiple experiments. Each case was independently tested 20 times, and the optimal solution and the average solution were recorded. The detailed calculation results are shown in Table 3.

[0063] As shown in Table 3, the optimal solutions obtained by IALO are always better than or comparable to those of other algorithms in all test cases. For example, in Case01, the optimal solution obtained by IALO is 2035, which is significantly better than Dispatch1 (2697), Dispatch2 (2892), and EP (2137). Similarly, in Case03 and Case04, IALO obtained optimal solutions of 2335 and 2442 respectively, further verifying its strong global search ability. In addition, IALO performs excellently in terms of mean and standard deviation (STD). From Case01 to Case06, the average solutions of IALO are always better than or comparable to those of other algorithms, and its standard deviation is usually low. Taking Case01 as an example, the average solution obtained by IALO is 2042.2, and the standard deviation is 5.9, which is significantly lower than Dispatch1 (2872.0, 92.1) and Dispatch2 (3030.4, 83.5), indicating that IALO has higher robustness. As Figure 7 shown, the convergence speed of IALO is significantly faster than that of the traditional EP algorithm. Even for large-scale problems, it can find high-quality solutions within 100 seconds. In conclusion, IALO shows strong global search ability and stability when solving scheduling problems. Whether in terms of optimal solutions or average solutions, it has significant advantages. This further highlights its effectiveness in solving complex optimization problems.

[0064] Table 3 , The beneficial effects of the present invention are as follows: An improved ant lion optimization algorithm combined with tabu search is proposed to solve the flexible job shop scheduling problem. Based on the existing ant lion optimization algorithm, a new good point set initialization strategy is introduced to generate a more uniform and higher-quality initial solution set. A curve displacement strategy is introduced into the random walk of ants to enhance their ability to escape from traps, making it more adaptable and robust. The local search strategy introduces the idea of tabu search to improve the efficiency of the algorithm in global search and local development. In addition, for the problem of multiple critical paths, three methods for solving critical paths are proposed, tested respectively, and the optimal critical path method is selected to be solved in combination with tabu search. The organic combination of these strategies significantly enhances the global exploration ability and local optimal solution escape ability of the algorithm, and effectively accelerates the convergence process of the algorithm. Applying the improved ant lion optimization algorithm to solve the flexible job shop scheduling model can quickly obtain the optimal scheduling plan and ensure the minimization of the makespan.

[0065] In the present invention, the good point set strategy generates an initial population, enabling the algorithm to obtain a larger search range with a uniform distribution and a better initial solution set in the early stage, which is conducive to maintaining the diversity of the population in the early stage and obtaining better global search ability. In addition, a curve displacement strategy is introduced into the random walk of ants, balancing global search and local exploitation, ensuring the convergence speed and stability in the later stage of the algorithm, and improving the optimization effect of the makespan. The method of moving all critical operations on the critical path increases the neighborhood solutions of the scheduling scheme, providing more possible solutions when the algorithm solves the optimal solution. In summary, the simulation experiment results prove that the method has good optimization results, can improve the optimization efficiency of the flexible job shop scheduling, and thus provides a new method and technology for the actual job shop scheduling optimization.

[0066] Please refer to Figure 8 , which shows the structural block diagram of the flexible job shop scheduling optimization system based on the improved ant lion optimization algorithm of the present application.

[0067] As Figure 8 shown, the flexible job shop scheduling optimization system 200 includes a construction module 210 and a solution module 220.

[0068] Among them, the construction module 210 is configured to obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; The solution module 220 is configured to solve the flexible job shop scheduling optimization model according to a preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling scheme. Among them, the process of solving the flexible job shop scheduling optimization model specifically includes: Encoding the operation set and the machine set, and initializing the taboo list; Using the good point set initialization method to allocate machines for each operation; Generating an initial solution set by decoding the initial population ; For the initial solution set The IALO algorithm is used to iterate the population. In each round of iteration, the roulette wheel strategy is used to select an ant lion for each ant, and the ants perform a random walk based on curve displacement around the selected ant lion to explore a new solution space region and obtain a new population ; Updating the population using the critical path MCP strategy And performing taboo search. If it is better than the current solution, update the taboo list to obtain a new ; If the termination condition is met, output the result and terminate the algorithm. Otherwise, continue the iteration; Output the global optimal scheduling scheme and the minimum makespan of each generation.

[0069] It should be understood that Figure 8 the various modules described in Figure 1 correspond to the respective steps in the method described in the reference Figure 8 . Thus, the operations, features, and corresponding technical effects described above for the method also apply to

[0070] the various modules in and will not be elaborated herein. In some other embodiments, the embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored. When the program instructions are executed by a processor, the processor is caused to execute the flexible job-shop scheduling optimization method based on the improved ant lion optimization algorithm in any of the above method embodiments; As an implementation manner, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are set as: Obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job-shop scheduling optimization model according to the optional processing equipment data and the processing data; Solve the flexible job-shop scheduling optimization model according to a preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling scheme, wherein the process of solving the flexible job-shop scheduling optimization model specifically includes: Encode the operation set and the machine set, and initialize the taboo list; ; For the initial solution set perform population iteration using the IALO algorithm. In each round of iteration, use the roulette wheel strategy to select an ant lion for each ant, and the ant performs a random walk based on curve displacement around the selected ant lion to explore a new solution space region to obtain a new population ; Update the population using the critical path MCP strategy and perform taboo search. If it is better than the current solution, update the taboo list to obtain a new ; If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, continue the iteration; Output the global optimal scheduling scheme and the minimum makespan of each generation.

[0071] A computer-readable storage medium may include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the flexible job shop scheduling optimization system based on the improved ant lion optimization algorithm, etc. In addition, the computer-readable storage medium may include a high-speed random access memory, and may also include a memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the computer-readable storage medium may optionally include a memory remotely provided with respect to the processor, and these remote memories may be connected to the flexible job shop scheduling optimization system based on the improved ant lion optimization algorithm through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0072] Figure 9 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention, as Figure 9 shown, the device includes: a processor 310 and a memory 320. The electronic device may further include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330, and the output device 340 may be connected through a bus or other means, Figure 9 and taking connection through the bus as an example. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running non-volatile software programs, instructions, and modules stored in the memory 320, that is, implements the flexible job shop scheduling optimization method based on the improved ant lion optimization algorithm in the above method embodiment. The input device 330 may receive input digital or character information, and generate key signal inputs related to user settings and function controls of the flexible job shop scheduling optimization system based on the improved ant lion optimization algorithm. The output device 340 may include a display device such as a display screen.

[0073] The above electronic device may execute the method provided by the embodiment of the present invention, and has corresponding functional modules and beneficial effects for executing the method. For technical details not described in detail in this embodiment, reference may be made to the method provided by the embodiment of the present invention.

[0074] As an implementation manner, the above electronic device is applied to a flexible job shop scheduling optimization system based on the improved ant lion optimization algorithm and is used for a client, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein, the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to: Obtain the optional processing equipment data for each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; Solve the flexible job shop scheduling optimization model according to the preset multi-strategy collaborative ant lion optimization algorithm to obtain the optimal scheduling plan. Specifically, the process of solving the flexible job shop scheduling optimization model includes: Encode the operation set and the machine set, and initialize the taboo list; Use the good point set initialization method to allocate a machine for each operation; Generate an initial solution set by decoding the initial population ; For the initial solution set Adopt the IALO algorithm to perform population iteration. In each round of iteration, use the roulette wheel strategy to select an ant lion for each ant. The ant performs a random walk based on curve displacement around the selected ant lion to explore a new solution space region and obtain a new population ; Adopt the critical path MCP strategy to update the population And perform taboo search. If it is better than the current solution, update the taboo list to obtain a new ; If the termination condition is met, output the result and terminate the algorithm. Otherwise, continue the iteration; Output the global optimal scheduling plan and the minimum makespan of each generation.

[0075] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiments.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A flexible job shop scheduling optimization method based on an improved ant lion optimization algorithm, characterized in that Including: Obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; Solve the flexible job shop scheduling optimization model according to the preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling plan. Specifically, the process of solving the flexible job shop scheduling optimization model includes: Encode the operation set and the machine set, and initialize the tabu list; Use the good point set initialization method to allocate a machine for each operation; Generate an initial solution set by decoding the initial population ; For the initial solution set The IALO algorithm is used to iterate the population. In each round of iteration, the roulette wheel strategy is used to select an antlion for each ant. The ant performs a random walk based on curve displacement around the selected antlion to explore new solution space regions and obtain a new population ; Update the population using the critical path MCP strategy And perform tabu search. If it is better than the current solution, update the tabu list to obtain a new ; If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, continue to iterate; Output the global optimal scheduling plan and the minimum makespan of each generation.

2. An optimization method for flexible job-shop scheduling based on an improved ant lion optimization algorithm according to claim 1, characterized in that The initial solution set The expression of the initialization strategy is as follows: ， ， Wherein, is the position of the i-th ant in the k-th iteration, is the upper bound, is the lower bound, is the set of good points, is the number of iterations, s is the dimension of the set of good points, is the parameter of the first dimension, is the parameter of the s-th dimension, is the number of the ant population.

3. An optimization method for flexible job shop scheduling based on an improved ant lion optimization algorithm according to claim 1, characterized in that Wherein, The expression for the ant to perform a random walk based on curve displacement around the selected ant lion is: ， ， ， ， Wherein, is a parameter that varies with the number of iterations, is a random number uniformly distributed between 0° and 360°, is a constant, with a value of 1 in the experiment, is the current iteration number, is the total number of iterations, is a random number uniformly distributed between 0 and 1, is the state of ant i in the t-th iteration, is the number of the ant population, is a random number uniformly distributed between 0 and 1, is the state of ant i in the (t + 1)-th iteration.

4. A flexible job shop scheduling optimization method based on an improved ant lion optimization algorithm according to claim 1, characterized in that Updating the population using the critical path MCP strategy And performing tabu search. If it is better than the current solution, update the tabu list to obtain a new Including: Initialize the taboo list as the current solution and determine the global optimal solution; then perform a neighborhood search. If a better solution is found and the better solution is not in the taboo list, update the taboo list and the global optimal solution; if the taboo list is full, delete the earliest solution and update the taboo list to obtain a new .

5. A flexible job shop scheduling optimization system based on an improved ant lion optimization algorithm, characterized in that, Including: A construction module configured to obtain the optional processing equipment data of each process of each workpiece and the processing data corresponding to the optional processing equipment data, and construct a flexible job shop scheduling optimization model according to the optional processing equipment data and the processing data; A solving module configured to solve the flexible job shop scheduling optimization model according to the preset multi-strategy collaborative ant lion optimization algorithm to obtain an optimal scheduling plan. Specifically, the process of solving the flexible job shop scheduling optimization model includes: Encode the operation set and the machine set, and initialize the tabu list; Use the good point set initialization method to allocate a machine for each operation; Generate an initial solution set by decoding the initial population ; For the initial solution set The IALO algorithm is used to iterate the population. In each round of iteration, the roulette wheel strategy is used to select an antlion for each ant. The ant performs a random walk based on curve displacement around the selected antlion to explore new solution space regions and obtain a new population ; Update the population using the critical path MCP strategy And perform tabu search. If it is better than the current solution, update the tabu list to obtain a new ; If the termination condition is satisfied, output the result and terminate the algorithm; otherwise, continue to iterate; Output the global optimal scheduling plan and the minimum makespan of each generation.

6. An electronic device, characterized in that, Including: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, the method according to any one of claims 1 to 4 is implemented.

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