Multi-objective hybrid genetic algorithm for solving integrated process planning and scheduling problems
By proposing a multi-objective hybrid genetic algorithm (LG_HGA) in the integrated process planning and scheduling problems, using three-layer encoding and global search operator NSGA_II, combined with the decision tree regression model and multi-neighborhood search, the existing algorithm has poor convergence in large-scale and complex problems, and more efficient process planning and scheduling optimization is achieved.
Patent Information
- Application Number
- CN202411820200.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-04-18
AI Technical Summary
When facing large-scale and complex integrated process planning and scheduling problems, existing multi-objective evolution algorithms have problems such as poor convergence and difficulty in finding high-precision solutions.
A multi-objective hybrid genetic algorithm (LG_HGA) is proposed, using a three-layer coding scheme and the global search operator NSGA_II, combined with a decision tree regression model and multi-neighborhood search, to achieve synchronous solution of process planning and scheduling.
Through LG_HGA, global and local better solutions that integrate process planning and scheduling problems can be effectively found, which improves optimization performance and accuracy, and balances exploration and development.
Smart Images
Figure CN119849604A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of production scheduling, and in particular to a multi-objective hybrid genetic algorithm for solving integrated process planning and scheduling problems. Background Art
[0002] The integrated process planning and scheduling problem is to transform the process planning and scheduling problem from the traditional step-by-step solution to a joint solution method, which is one of the research hotspots in the field of workshop scheduling. Manufacturing units with reconfigurable capabilities can enable production workshops to adapt to rapidly changing production environments. Therefore, the integrated process planning and scheduling problem with reconfigurable units has gained increasing attention in academia and industry. Multi-objective evolutionary algorithms are classic algorithms for solving workshop scheduling problems, but they have the disadvantages of poor convergence and difficulty in finding high-precision solutions when facing large-scale and complex optimization problems. Summary of the invention
[0003] In view of the above problems, an embodiment of the present invention provides a multi-objective hybrid genetic algorithm for solving the problem of integrating process planning and scheduling.
[0004] The embodiment of the present invention provides a multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling, including:
[0005] S1, the population is randomly initialized to obtain the initial population;
[0006] S2. Calculate the target value of each individual in the population, where one individual represents a feasible solution for completing all workpieces, and the target value is a value that represents the maximum completion time and the total weighted delay;
[0007] S3, select evolutionary individuals according to the calculated target value, use the global search operator NSGA_II to perform crossover and mutation operations on the chromosomes of the evolutionary individuals, so as to find the global optimal solution;
[0008] S4, determine the neighborhood structure of the global optimal solution, and use the decision tree regression model to predict the probability of the neighborhood structure improving the global optimal solution to obtain a better solution during the evolution process;
[0009] S5. When the probability is greater than the local search threshold, the neighborhood structure corresponding to the maximum probability is used for local search to generate a local better solution; the global better solution and the local better solution are added to the initial population, and a new initial population is obtained using the non-dominated sorting and elite selection strategies;
[0010] S6. When there is no probability greater than the local search threshold, add the global optimal solution to the initial population, and use the non-dominated sorting and elite selection strategies to obtain a new initial population;
[0011] S7, determine whether the set maximum number of evolution generations is met, if so, use the new initial population as the result of the multi-objective hybrid genetic algorithm, if not, return to S2.
[0012] Optionally, to facilitate chromosome manipulation, individuals use a three-level encoding scheme:
[0013] The first layer, denoted as L p , represents the process planning scheme for each workpiece;
[0014] The second layer, denoted as L m , represents the manufacturing unit assigned in sequence to each operation used to complete the workpiece;
[0015] The third layer, denoted as L j , indicating the assembly order of all operations.
[0016] Optionally, the process of using the global search operator NSGA_II in S3 to perform crossover and mutation operations on the chromosomes of the evolving individuals to find a globally optimal solution includes:
[0017] For each individual, a first probability is randomly generated and the first probability is less than the crossover probability P. c In the case of L, the chromosome crossover operation is performed on the individual, and the crossover operation includes: m Use uniform crossover UX; for L j Adopt order-based crossover POX with priority preservation;
[0018] For each individual after the crossover operation, a second probability is randomly generated, and when the second probability is less than the mutation probability P m In the case of L, the individual chromosome is mutated. The mutation operation includes: p Randomly select multiple workpieces and rearrange the process planning scheme for L m After randomly selecting some operations, switch to another optional manufacturing unit, for L j Randomly select some positions to exchange.
[0019] Optionally, the process of determining the neighborhood structure in S4 includes:
[0020] Find the critical path, which is the sequence of activities that takes the longest time from start to finish to complete all artifacts;
[0021] Neighborhood structure 1: According to the earliest deadline priority rule EDD, determine the workpiece with the earliest deadline on the critical path, and then j A gene position is randomly selected and inserted into a position in front of the selected gene;
[0022] Neighborhood structure 2: According to the earliest release time priority rule EST, determine the workpiece with the earliest release time on the critical path, and then j A gene position is randomly selected and inserted into a position in front of the selected gene;
[0023] Neighborhood structure 3: Randomly select artifacts on the critical path and rearrange the selected artifacts in the middle L p Process planning scheme;
[0024] Neighborhood structure 4: According to the minimum machine idle time rule MMIT, the operations on the critical path are randomly selected and assigned to the manufacturing unit with the least number of assembly operations.
[0025] Optionally, the training process of the decision tree regression model in S4 includes:
[0026] Constructing the knowledge base: In the evolutionary process, four neighborhood structures are used to evaluate the improvement of the current global optimal solution, and the evaluation standard is U = 0.6T + 0.4C max , T is the total weighted tardiness, C max is the maximum completion time; determine the number of newly generated individuals after evolution |P| and the number of individuals whose U value is better than the original individuals |BS|, so as to calculate the probability of obtaining a better solution by improving the global optimal solution with the neighborhood structure
[0027] Train a decision tree regression model to fit the data in the knowledge base.
[0028] Compared with the prior art, the invention has the beneficial effect of using chromosome encoding to solve process planning and scheduling problems simultaneously. The multi-objective hybrid genetic algorithm LG_HGA of the invention uses NSGA-II as a global search and adopts learning-guided multi-neighborhood search LG_MNS to achieve a better balance between exploration and exploitation. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute a limitation of the present invention. In the drawings:
[0030] Figure 1 A principle block diagram of a multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling provided by an embodiment of the present invention;
[0031] Figure 2 An example diagram of chromosome coding of an individual provided by an embodiment of the present invention;
[0032] Figure 3 An example diagram of the Pareto frontier PF for each algorithm of Example I1 provided in an embodiment of the present invention;
[0033] Figure 4 An example diagram of the Pareto frontier PF for each algorithm of Example I2 provided in an embodiment of the present invention;
[0034] Figure 5 An example diagram of the Pareto frontier PF for each algorithm of Example I3 provided in an embodiment of the present invention;
[0035] Figure 6 An example diagram of the Pareto frontier PF for each algorithm of Example I4 provided in an embodiment of the present invention;
[0036] Figure 7 An example diagram of the Pareto frontier PF for each algorithm of Example I5 provided in an embodiment of the present invention;
[0037] Figure 8 IGD trend diagram for each algorithm of Example I1 provided by the embodiment of the present invention;
[0038] Fig. 9 IGD trend diagram for each algorithm of Example I2 provided by the embodiment of the present invention;
[0039] Fig.10 IGD trend diagram for each algorithm of Example 13 provided by the embodiment of the present invention;
[0040] Fig.11 IGD trend diagram for each algorithm of Example 14 provided by the embodiment of the present invention;
[0041] Fig.12 IGD trend diagram for each algorithm of Example I5 provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0042] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.
[0043] The embodiment of the present invention provides a multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling, and the implementation principle is as follows: Figure 1 As shown, the method specifically includes:
[0044] S1. The population is randomly initialized to obtain the initial population.
[0045] S2. Calculate the target value of each individual in the population, where an individual represents a feasible solution for completing all workpieces, and the target value is a value that represents the maximum completion time and the total weighted delay.
[0046] In practice, in order to facilitate chromosome manipulation, individuals use a three-layer encoding scheme:
[0047] The first layer, denoted as L p , represents the process planning scheme for each workpiece;
[0048] The second layer, denoted as L m , represents the manufacturing unit assigned in sequence to each operation used to complete the workpiece;
[0049] The third layer, denoted as L j , indicating the assembly order of all operations.
[0050] The length of each chromosome is equal to the sum of all workpiece operations. The chromosome encoding example is Figure 2 As shown; when decoding, first read L p The chromosome fragment corresponding to each workpiece in L is used to determine the process planning scheme. The number on the chromosome represents the serial number of each operation of the workpiece. Then, L is read sequentially. m The chromosome fragment of each workpiece in the L is read in turn to identify the manufacturing unit selected for each operation. Each number in the chromosome represents the serial number of the available manufacturing unit for each operation. j of each gene to determine the order of operations on the same manufacturing unit.
[0051] S3. Select the evolutionary individuals according to the calculated target value, and use the global search operator NSGA_II to perform crossover and mutation operations on the chromosomes of the evolutionary individuals to find the global optimal solution.
[0052] In the implementation, the widely used NSGA-II is used for global search, wherein the crossover and mutation methods of NSGA-II are improved as follows:
[0053] Due to the numerous and complex constraints between the process stages, only L p Perform mutation operation. p The mutation operation consists of randomly selecting several artifacts and rearranging their process plans.
[0054] For L m The uniform crossover method (UX) is adopted, and mutation is performed by randomly selecting some operations and then switching to another optional manufacturing unit.
[0055] For L j The priority-preserving order-based crossover (POX) is used, and the mutation operation randomly selects some positions for exchange.
[0056] Specifically, the process of using the global search operator NSGA_II in S3 to perform crossover and mutation operations on the chromosomes of evolving individuals to find the global optimal solution includes:
[0057] For each individual, a first probability is randomly generated and the first probability is less than the crossover probability P. c In the case of L, the chromosome crossover operation is performed on the individual, and the crossover operation includes: m Use uniform crossover UX; for L j Adopt order-based crossover POX with priority preservation;
[0058] For each individual after the crossover operation, a second probability is randomly generated, and when the second probability is less than the mutation probability P m In the case of L, the individual chromosome is mutated. The mutation operation includes: p Randomly select multiple workpieces and rearrange the process planning scheme for L m After randomly selecting some operations, switch to another optional manufacturing unit, for L j Randomly select some positions to exchange.
[0059] In order to make the genetic algorithm effectively search the solution space and improve the global optimization performance while maintaining the diversity of the population, it is necessary to reasonably set the crossover probability and mutation probability. c and mutation probability P m The value of is determined by orthogonal experiments.
[0060] S4. Determine the neighborhood structure of the global optimal solution, and use the decision tree regression model to predict the probability of the neighborhood structure improving the global optimal solution to obtain a better solution during the evolution process.
[0061] In practice, the present invention proposes four neighborhood structures based on critical paths and heuristic rules, and the specific operations are as follows:
[0062] Find the critical path. The critical path is the sequence of activities that takes the longest time from the start time to the end time to complete all workpieces. When there are multiple critical paths, a critical path is randomly selected.
[0063] Neighborhood structure 1: According to the earliest deadline priority rule EDD, determine the workpiece with the earliest deadline on the critical path, and then j A gene position is randomly selected and inserted into a position in front of the selected gene;
[0064] Neighborhood structure 2: According to the earliest release time priority rule EST, determine the workpiece with the earliest release time on the critical path, and then jA gene position is randomly selected and inserted into a position in front of the selected gene;
[0065] Neighborhood structure 3: Randomly select artifacts on the critical path and rearrange the selected artifacts in the middle L p Process planning scheme;
[0066] Neighborhood structure 4: According to the minimum machine idle time rule MMIT, the operations on the critical path are randomly selected and assigned to the manufacturing unit with the least number of assembly operations.
[0067] In implementation, in order to strengthen the selection of evolutionary direction and maintain the balance between exploration and development, the learning-guided multi-neighborhood search LG_MNS uses the decision tree regression model DTR. The training process of the decision tree regression model DTR is as follows:
[0068] Constructing the knowledge base: In the evolutionary process, four neighborhood structures are used to evaluate the improvement of the current global optimal solution, and the evaluation standard is U = 0.6T + 0.4C max , T is the total weighted tardiness, C max is the maximum completion time; determine the number of newly generated individuals after evolution |P| and the number of individuals whose U value is better than the original individuals |BS|, so as to calculate the probability of obtaining a better solution by improving the global optimal solution with the neighborhood structure
[0069] Train a decision tree regression model to fit the data in the knowledge base.
[0070] S5. When the probability is greater than the local search threshold, the neighborhood structure corresponding to the maximum probability is used for local search to generate a local better solution; the global better solution and the local better solution are added to the initial population, and a new initial population is obtained using the non-dominated sorting and elite selection strategies.
[0071] In the implementation, it is determined whether the current iteration needs to perform a local search, and which neighborhood is used for the local search when executing the multi-objective hybrid genetic algorithm of the present invention. In each iteration, the DTR prediction value R is used. i , which means the probability of finding a better solution if the neighborhood i (i = 1, 2, 3, 4) is used for local search; according to R i , find the best neighborhood n (n=1,2,3,4). If R n >T ls , then a local search is performed in the neighborhood n; otherwise, no local search is performed. ls It is the threshold number of local searches to be performed, determined by orthogonal experiments.
[0072] S6. When there is no probability greater than the local search threshold, the global optimal solution is added to the initial population, and a new initial population is obtained using the non-dominated sorting and elite selection strategies.
[0073] S7, determine whether the set maximum number of evolution generations is met, if so, use the new initial population as the result of the multi-objective hybrid genetic algorithm, if not, return to S2.
[0074] Experimental Design
[0075] Five examples of different scales are used to evaluate the performance of the multi-objective hybrid genetic algorithm LG_HGA of the present invention, as shown in Table 1:
[0076]
[0077] Table 1 Instance scale
[0078] Parameter setting: All parameters related to the algorithm LG_HGA are shown in Table 2. MAXGEN is set to 100 according to experience. Other parameters are determined by orthogonal experiments. The optimal parameter combination is NIND = 40, P c =0.9, P m =0.4, T ls =50, lsize=5, MaxIterNum=5, nsize=20.
[0079]
[0080]
[0081] Table 2 Parameters and their descriptions
[0082] Comparison Design: LG_HGA is compared with NSGA-II, RVEA, MOEA / D, and NSGA-III. Each algorithm is programmed in Python and executed on a computer with an Intel(R) Core i5-10400F CPU 2.90GHz and 16.0GB memory. The running time of the algorithm is controlled by adjusting the population size NIND to ensure that the running time of LG_HGA and other algorithms is similar. Other parameters of all algorithms remain unchanged. Each algorithm is run independently 30 times and evaluated using the error ratio (ER) and inversion generation distance (IGD) index.
[0083] Results and Discussion: The Pareto frontier PF of each algorithm is as follows Figure 3-Figure 7 It is clear that LG_HGA identifies a superior solution in every instance.
[0084] ER is used to measure the proportion of solutions in the solution set that do not belong to the Pareto approximation frontier. The smaller the ER, the higher the quality of the solution set. The ER values of each algorithm are shown in Table 3. It can be observed that the solution set obtained by LG_HGA is the frontier closest to the Pareto approximation.
[0085]
[0086] Table 3 ER value of each algorithm
[0087] IGD is a comprehensive indicator widely used to evaluate multi-objective optimization algorithms. It simultaneously evaluates the convergence and diversity of the solution set. The smaller the IGD value, the better the overall performance of the algorithm. Figure 4 The trend graph in is the average IGD value of each generation. It can be seen from the figure that LG_HGA converges faster and has a lower IGD value.
[0088] Table 4 lists the IGD values of the last generation of each algorithm. The trend is as follows Figure 8-Figure 12 In almost all cases, LG_HGA always has the best IGD mean, median, and standard deviation values.
[0089]
[0090]
[0091] Table 4 Statistics of the last generation of IGD
[0092] In summary, the feasibility and efficiency of the LG_HGA proposed in the present invention have been verified.
[0093] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims
1. A multi-objective hybrid genetic algorithm for solving integrated process planning and scheduling problems, characterized in that: include: S1, the population is randomly initialized to obtain the initial population; S2. Calculate the target value of each individual in the population, where one individual represents a feasible solution for completing all workpieces, and the target value is a value that represents the maximum completion time and the total weighted delay; S3, select evolutionary individuals according to the calculated target value, use the global search operator NSGA_II to perform crossover and mutation operations on the chromosomes of the evolutionary individuals, so as to find the global optimal solution; S4, determine the neighborhood structure of the global optimal solution, and use the decision tree regression model to predict the probability of the neighborhood structure improving the global optimal solution to obtain a better solution during the evolution process; S5. When the probability is greater than the local search threshold, the neighborhood structure corresponding to the maximum probability is used for local search to generate a local better solution; the global better solution and the local better solution are added to the initial population, and a new initial population is obtained using the non-dominated sorting and elite selection strategies; S6. When there is no probability greater than the local search threshold, add the global optimal solution to the initial population, and use the non-dominated sorting and elite selection strategies to obtain a new initial population; S7, determine whether the set maximum number of evolution generations is met, if so, use the new initial population as the result of the multi-objective hybrid genetic algorithm, if not, return to S2.
2. The multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling as claimed in claim 1, characterized in that: To facilitate chromosome manipulation, individuals use a three-level encoding scheme: The first layer, denoted as L p , represents the process planning scheme for each workpiece; The second layer, denoted as L m , represents the manufacturing unit assigned in sequence to each operation used to complete the workpiece; The third layer, denoted as L j , indicating the assembly order of all operations.
3. The multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling as claimed in claim 2, characterized in that: In S3, the global search operator NSGA_II is used to perform crossover and mutation operations on the chromosomes of evolving individuals to find the global optimal solution, including: For each individual, a first probability is randomly generated and the first probability is less than the crossover probability P. c In the case of L, the chromosome crossover operation is performed on the individual, and the crossover operation includes: m Use uniform crossover UX; for L j Adopt order-based crossover POX with priority preservation; For each individual after the crossover operation, a second probability is randomly generated, and when the second probability is less than the mutation probability P m In the case of L, the individual chromosome is mutated. The mutation operation includes: p Randomly select multiple workpieces and rearrange the process planning scheme for L m After randomly selecting some operations, switch to another optional manufacturing unit, for L j Randomly select some positions to exchange.
4. The multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling as claimed in claim 2, characterized in that: The process of determining the neighborhood structure in S4 includes: Find the critical path, which is the sequence of activities that takes the longest time from start to finish to complete all artifacts; Neighborhood structure 1: According to the earliest deadline priority rule EDD, determine the workpiece with the earliest deadline on the critical path, and then j A gene position is randomly selected and inserted into a position in front of the selected gene; Neighborhood structure 2: According to the earliest release time priority rule EST, determine the workpiece with the earliest release time on the critical path, and then j A gene position is randomly selected and inserted into a position in front of the selected gene; Neighborhood structure 3: Randomly select artifacts on the critical path and rearrange the selected artifacts in the middle L p Process planning scheme; Neighborhood structure 4: According to the minimum machine idle time rule MMIT, the operations on the critical path are randomly selected and assigned to the manufacturing unit with the least number of assembly operations.
5. The multi-objective hybrid genetic algorithm for solving the problem of integrated process planning and scheduling as claimed in claim 4, characterized in that: The training process of the decision tree regression model in S4 includes: Constructing the knowledge base: In the evolutionary process, four neighborhood structures are used to evaluate the improvement of the current global optimal solution, and the evaluation standard is U = 0.6T + 0.4C max , T is the total weighted tardiness, C max is the maximum completion time; determine the number of newly generated individuals after evolution |P| and the number of individuals whose U value is better than the original individuals |BS|, so as to calculate the probability of obtaining a better solution by improving the global optimal solution with the neighborhood structure Train a decision tree regression model to fit the data in the knowledge base.