A zero-wait job shop scheduling method based on forward-reverse hybrid schedule strategy

Abstract

The present application relates to zero waiting job shop problem technical field, especially to a kind of zero waiting job shop scheduling method based on positive and negative mixed timetable strategy, comprising: S1, the workpiece process data of zero waiting job shop scheduling problem is obtained, set population size, maximum genetic generation;Multiple crossover rate and mutation rate parameter combinations are generated;S2, initial population is generated using extended three-section coding structure;S3, the fitness value of each individual chromosome is calculated;S4, select the optimal individual chromosome of front X, update current population;S5, select next generation population;S6, based on the optimization performance value of each parameter combination, select a parameter combination, in turn execute cross operation and variation operation to next generation population, obtain new generation population;S7, whether reach maximum genetic generation is judged, if reach, then output optimal scheduling scheme, otherwise return S3.The present application can realize the effective balance of overall exploration of solution space, search efficiency and solution quality.

Description

Technical Field

[0001] This invention relates to the field of zero-wait job shop problem technology, and in particular to a zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy. Background Technology

[0002] The No-wait Job-shop Scheduling Problem (NWJSP), an important extension of the classic job-shop scheduling problem, is characterized by the introduction of a zero-wait constraint. This constraint requires that all processes within the same job must be processed consecutively, with no idle or waiting time allowed between processes. This constraint makes the scheduling model more suitable for real-world industrial production scenarios with continuous or time-sensitive requirements, such as steel smelting, pharmaceutical production, and food processing. The introduction of the zero-wait constraint significantly increases the combinatorial complexity and solution difficulty of the problem, proving it to be a strongly NP-hard problem. On the other hand, this constraint helps to achieve lean production processes, effectively reducing work-in-process inventory, shortening manufacturing cycles, and minimizing resource idleness. Therefore, in-depth research on the NWJSP has significant theoretical value and engineering application implications for improving production efficiency and resource allocation in related industries.

[0003] In recent years, with technological advancements, the zero-wait job shop scheduling problem has garnered widespread attention from academia and industry. Current mainstream algorithms generally employ a "problem decomposition-cooperative optimization" framework, which decomposes the original problem into a process sequencing subproblem and a timetable generation subproblem, and optimizes both through a cooperative mechanism. The main differences between algorithms lie in the design of the search paradigm and the handling mechanism of the timetable generation subproblem. The timetable generation mechanism directly determines the algorithm's search capability and optimization efficiency in the solution space, and is crucial to the overall performance of the algorithm.

[0004] However, in-depth analysis reveals that existing metaheuristic algorithms for solving the NWJSP problem still have the following technical limitations:

[0005] First, the single timetable generation strategy limits the scope of solution space exploration. Existing algorithms typically employ only a single forward or reverse timetable generation strategy. This single strategy struggles to fully cover the potential optimal solution region when faced with complex zero-wait constraints. Since zero-wait constraints require strict continuity between processes, a single strategy is prone to getting trapped in local optima, failing to effectively explore potential high-quality solutions in different directions within the solution space. This limitation is particularly pronounced in large-scale, multi-workpiece production scenarios, making it difficult for the algorithm to discover globally optimal or near-optimal scheduling schemes.

[0006] Secondly, it is difficult to achieve an effective balance between search efficiency and solution quality. Existing algorithms often face a contradiction between breadth and depth during the search process: overemphasizing global search leads to slow convergence and wasted computational resources; while focusing too much on local search easily leads to getting trapped in local optima and failing to obtain high-quality solutions. The root cause of this balance problem lies in the lack of an effective adaptive mechanism to dynamically adjust the search strategy, making it impossible for the algorithm to intelligently adjust the search intensity and direction according to problem characteristics and search progress at different solution stages.

[0007] Third, the parameter settings lack intelligent dynamic adjustment capabilities. Most existing algorithms typically use fixed values ​​or simple linear update strategies for key parameters such as crossover rate and mutation rate. This static parameter setting makes it difficult for the algorithm to maintain stable solution performance when facing NWJSP instances of different sizes and complexities. In particular, during the solution process, when the algorithm encounters search bottlenecks or performance degradation, the lack of an effective parameter adaptive mechanism to adjust the search strategy in a timely manner affects the overall performance and robustness of the algorithm.

[0008] The aforementioned technical limitations often result in low solution efficiency, unstable solution quality, and poor adaptability when solving large-scale, complex real-world NWJSP problems, severely restricting their further application and promotion in actual industrial production. These limitations are particularly pronounced when facing dynamically changing production environments and diverse scheduling requirements.

[0009] Therefore, how to achieve a comprehensive exploration of the solution space and an effective balance between search efficiency and solution quality in zero-wait job shop scheduling has become an urgent problem to be solved. Summary of the Invention

[0010] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy, which can achieve a comprehensive exploration of the solution space and an effective balance between search efficiency and solution quality in zero-wait job shop scheduling.

[0011] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0012] A zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy includes the following steps:

[0013] S1. Obtain workpiece process data for the zero-wait job shop scheduling problem, and set the population size and maximum number of generations; use the uniform design method to generate multiple combinations of crossover rate and mutation rate parameters, and initialize and optimize the performance value for each parameter combination;

[0014] S2. An initial population is generated using an extended three-segment coding structure, which includes a workpiece sequence string for determining the workpiece processing order, a time schedule strategy selection string for selecting a time schedule strategy, and a scheduling direction selection string for determining the scheduling direction.

[0015] S3. For each individual chromosome in the current population, based on the values ​​of its timetable strategy selection string and scheduling direction selection string, decode it using the corresponding forward and reverse mixed timetable strategy to generate a feasible scheduling solution under zero waiting constraints, and calculate the fitness value of each individual chromosome.

[0016] S4. Select the best individual chromosome with the highest fitness value (X) in the current population after fitness value is calculated in S3. Optimize it using a fast local search based on exchange mutation. Replace the original individual chromosome with the optimized new individual chromosome to update the current population.

[0017] S5. A strategy combining elite retention and binary tournament selection is adopted to select the next generation of the population from the current population after the S4 update.

[0018] S6. Based on the current optimization performance value of each parameter combination, select a parameter combination from the multiple parameter combinations in S1 using a roulette wheel approach. Perform crossover and mutation operations sequentially on the next generation population selected in S5 to obtain a new generation population. If the average fitness value of the new generation population or the fitness value of the best individual chromosome is improved compared to the current population at the beginning of this iteration, then increase the optimization performance value of the parameter combination selected in this iteration.

[0019] S7. Determine whether the maximum number of generations set in S1 has been reached. If it has, output the optimal scheduling scheme in the current population. Otherwise, take the new generation population obtained in S6 as the current population and return to S3.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] 1. Achieving comprehensive exploration of the solution space. This method organically combines forward and reverse time scheduling strategies through the time schedule strategy selection string and scheduling direction selection string in the extended three-segment coding structure, forming a hybrid forward and reverse time scheduling strategy. Compared with the single time schedule generation strategy commonly used in existing technologies, this hybrid strategy can explore the solution space from different directions and angles, effectively avoiding the defect of single strategies easily getting trapped in local optima, significantly expanding the search range of the algorithm, and increasing the probability of discovering the global optimum or high-quality solution.

[0022] 2. Improving the balance between search efficiency and solution quality. This method employs a strategy combining elite preservation and binary tournament selection for population selection, ensuring the genetic continuity of superior individuals while maintaining population diversity. Simultaneously, it refines the optimization of top-ranked individuals through fast local search based on crossover mutation, achieving an effective combination of global and local search. Compared to existing techniques that rely on a single search strategy and struggle to balance breadth and depth, this method continuously improves solution quality while maintaining search efficiency, achieving an organic unity between search efficiency and solution quality.

[0023] 3. Intelligent Dynamic Adjustment of Parameters. This method innovatively employs a uniform design approach to generate multiple combinations of crossover and mutation rates. Based on the optimization performance values ​​of each parameter combination, the optimal parameter combination is dynamically selected using a roulette wheel approach. When a parameter combination improves population performance, its optimization performance value increases accordingly, resulting in a higher selection probability in subsequent iterations. Compared to existing techniques that use fixed or simple linear parameter updates, this adaptive mechanism intelligently adjusts parameters based on the algorithm's real-time performance, significantly improving the algorithm's adaptability and robustness, enabling it to better handle zero-wait job shop scheduling problems of varying scales and complexities.

[0024] Through the synergistic effect of the aforementioned technological innovations, the efficiency of solving the zero-wait-time job shop scheduling problem has been significantly improved. When facing large-scale, complex real-world production scenarios, this method can stably output high-quality scheduling solutions, effectively shortening manufacturing cycles, reducing work-in-process inventory, and minimizing resource idleness. It provides a more reliable and efficient scheduling solution for continuous or time-sensitive industrial production scenarios such as steel smelting, pharmaceutical production, and food processing.

[0025] In summary, this method can achieve a comprehensive exploration of the solution space and an effective balance between search efficiency and solution quality in zero-wait job shop scheduling.

[0026] Preferably, when the gene value of the timetable strategy selection string is 1, it indicates the use of a non-delayed timetable strategy, and when it is 0, it indicates the use of an active timetable strategy; when the gene value of the scheduling direction selection string is 1, it indicates the use of forward scheduling, and when it is 0, it indicates the use of reverse scheduling.

[0027] This setup, through gene-level policy semantic mapping, makes the selection of scheduling strategies part of the evolutionary process, effectively enhancing the algorithm's exploration flexibility and optimization depth in the solution space.

[0028] Preferably, in step S3, when the scheduling direction selection string indicates forward scheduling and the timetable strategy selection string indicates a non-delayed timetable strategy, the start time of each workpiece is determined sequentially according to the workpiece sequence string, under the conditions of satisfying the start time sequence constraints of the scheduled workpieces, as well as equipment constraints and process constraints. The start time and completion time of the remaining processes of each workpiece are then calculated according to the following formula:

[0029] (1);

[0030] (2);

[0031] in, This represents the i-th workpiece in the workpiece sequence string; Indicates workpiece The number of processes; Indicates workpiece The processing time for the j-th process; Indicates workpiece Start time of the j-th process; Indicates workpiece The completion time of the j-th process; the subscript j+1 indicates the (j+1)-th process.

[0032] With this setup, the recursive decoding mechanism achieves efficient and deterministic generation of feasible scheduling solutions while ensuring that the zero-wait constraint is strictly satisfied. Compared with the heuristic insertion method or iterative correction method commonly used in existing methods, this scheme directly drives the start time of subsequent processes through the completion time of the preceding process, avoiding redundant verification and correction steps, and greatly improving the computational efficiency and reliability of decoding a single individual. This provides key support for genetic algorithms to maintain high population update speed and solution quality stability in large-scale problems.

[0033] Preferably, in step S3, when the scheduling direction selection string indicates forward scheduling and the time schedule strategy selection string indicates active time schedule strategy, the start time of each workpiece is determined sequentially according to the order of the workpiece sequence string, under the condition that only equipment constraints and process constraints are satisfied; and the start time and completion time of the remaining processes of each workpiece are calculated according to formulas (1) and (2).

[0034] This setup, by embedding a strategy-level flexible decision-making mechanism within a zero-wait rigid framework, achieves a balance between constraint compliance and scheduling optimization, enhancing the algorithm's adaptability to dynamic resource competition in actual production.

[0035] Preferably, in step S3, when the scheduling direction selection string indicates reverse scheduling, the workpiece sequence string is... Reverse to the reverse decoding sequence ,in where n is the total number of workpieces;

[0036] Decode the sequence in reverse order Based on the order of the timetable strategy selection string, the corresponding non-delayed timetable strategy or active timetable strategy is used for decoding. The start time of the remaining processes of each workpiece in the reverse-order decoding sequence is calculated according to the following formula. and completion time :

[0037] ;

[0038] ;

[0039] Among them, subscript Represents the reverse decoding sequence The i-th workpiece; Indicates workpiece The number of processes;

[0040] The maximum completion time of the reverse scheduling solution is calculated using the following formula. :

[0041] ;

[0042] Then calculate the start time of each workpiece in the original problem using the following formula:

[0043] ;

[0044] in, Indicates the workpiece in the original problem The start time of the first process. This represents the processing time of the j-th process for the i-th workpiece in the reverse-order decoding sequence; Reverse decoding sequence The number of workpieces in the process;

[0045] Calculate the start and finish times of the remaining processes for each workpiece in the original problem using equations (1) and (2).

[0046] This setup, by constructing the schedule from the endpoint in reverse order, naturally avoids the problem of repeated conflicts and delays in subsequent processes caused by improper early process arrangement in forward order scheduling. Especially when there are long processing time processes or bottlenecks in key equipment, it can more reasonably allocate idle time periods of equipment and reduce global waiting accumulation. Compared with the traditional method that only uses forward order scheduling, this scheme significantly enhances the algorithm's sensitivity and responsiveness to the constraints at the end of the schedule, making the search process more likely to converge to a high-quality solution and effectively making up for the structural bias of single-direction scheduling.

[0047] Preferably, in step S4, the fast local search based on interchange mutation includes:

[0048] Obtain the optimal set of individuals with the highest fitness values ​​(X) in the current population. Let the length of the workpiece sequence string be m, and let k = round(m / 2).

[0049] When the scheduling direction selection string indicates forward scheduling, an interchange mutation is performed within the range of the k-th to the (m-1)-th position of the workpiece sequence string; when the scheduling direction selection string indicates reverse scheduling, an interchange mutation is performed within the range of the 1-th to the (k-1)-th position of the workpiece sequence string.

[0050] The fitness of the new individual chromosome generated by the mutation is quickly evaluated. If the fitness value of the new individual chromosome is better than that of the original individual chromosome, the original individual chromosome is replaced with the new individual chromosome.

[0051] This setup, by adaptively limiting the scope of the swap mutation based on the scheduling direction, allows the local search to focus on the process intervals that significantly contribute to the maximum completion time, avoiding the destruction of feasible solutions or invalid perturbations caused by global random mutations. It significantly improves the accuracy and convergence efficiency of the local search while maintaining population diversity.

[0052] Preferably, in step S5, the strategy combining elite retention with binary tournament selection includes:

[0053] The chromosome of the individual with the best fitness value in the current population is directly copied to the next generation population;

[0054] Repeat the following steps until the number of individuals in the next generation population reaches the population size set in S1: randomly select two individual chromosomes from the current population, and select the individual chromosome with the higher fitness value as the individual in the next generation population.

[0055] Preferably, in step S1, generating multiple combinations of crossover rate and mutation rate parameters using a uniform design method includes:

[0056] Set the number of factor levels for crossover rate Pc and variation rate Pm;

[0057] Determine the required uniform design table based on the set number of factor levels. Where n is the number of parameter combinations, q is the number of levels, and m is the number of factors;

[0058] Based on the determined uniform design table It uses tables to determine multiple parameter combinations for crossover rate and variation rate.

[0059] This setup, through a uniform design table, provides systematic and low-redundancy multi-combination coverage of crossover and mutation rates. While significantly reducing the number of parameter trials, it ensures that the interaction effects of key parameters are not overlooked, enabling the algorithm to quickly locate the effective parameter range in different problem instances, and greatly improving the scientific nature and robustness of parameter configuration.

[0060] Preferably, in step S6, when performing a crossover operation on the next generation population, the workpiece sequence string adopts a single-point sequential crossover method, and the timetable strategy selection string and the scheduling direction selection string both adopt the crossover inheritance parent method; when performing a mutation operation on the population obtained after the crossover operation, the workpiece sequence string adopts a swap mutation method, and the timetable strategy selection string and the scheduling direction selection string both adopt a binary mutation method.

[0061] Preferably, X is 20%.

[0062] This setup achieves the best balance between local search intensity and global exploration capability, ensuring that highly fit individuals are fully explored while avoiding population homogenization caused by an excessively high proportion of elites. Attached Figure Description

[0063] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0064] Figure 1 This is a flowchart of the method;

[0065] Figure 2 This is a schematic diagram of the extended three-segment coding structure in Example 2;

[0066] Figure 3 This is a decoding diagram based on the forward and reverse hybrid timetable strategy in Example 2;

[0067] Figure 4 This is a schematic diagram of the fast local search method based on interchange mutation in Example 2;

[0068] Figure 5 This is a comparison of the convergence curves of the scheduling method in Example 2 with other variant methods;

[0069] Figure 6 The optimal scheduling solution Gantt chart is obtained for the scheduling method in Example 2. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0072] Example 1

[0073] like Figure 1 As shown, this invention provides a zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy, comprising the following steps:

[0074] S1. Obtain workpiece process data for the zero-wait job shop scheduling problem, and set the population size and maximum number of generations; use the uniform design method to generate multiple combinations of crossover rate and mutation rate parameters, and initialize and optimize the performance value for each parameter combination.

[0075] In specific implementation, the method of generating multiple combinations of crossover rate and mutation rate parameters using a uniform design method includes:

[0076] Set the number of factor levels for crossover rate Pc and variation rate Pm;

[0077] Determine the required uniform design table based on the set number of factor levels. Where n is the number of parameter combinations, q is the number of levels, and m is the number of factors;

[0078] Based on the determined uniform design table It uses tables to determine multiple parameter combinations for crossover rate and variation rate.

[0079] By using a uniform design table to systematically and with low redundancy cover multiple combinations of crossover and mutation rates, the number of parameter trials is significantly reduced while ensuring that the interaction effects of key parameters are not missed. This enables the algorithm to quickly locate the effective parameter range in different problem instances, greatly improving the scientific nature and robustness of parameter configuration.

[0080] S2. An initial population is generated using an extended three-segment coding structure, which includes a workpiece sequence string for determining the workpiece processing order, a timetable strategy selection string for selecting a timetable strategy, and a scheduling direction selection string for determining the scheduling direction.

[0081] Each gene in the job sequence string is the job number; the gene value of the timetable strategy selection string is 0 or 1, denoted by the symbol TSS; the gene value of the scheduling direction selection string is 0 or 1, denoted by the symbol SDS. The definitions are as follows:

[0082] ;

[0083] .

[0084] In practice, the workpiece sequence string in the initialization population is initialized using a random initialization method, the timetable allocation strategy selection string is initialized using a simple random binary number initialization method, and the scheduling direction selection string is also initialized using a simple random binary number initialization method.

[0085] S3. For each individual chromosome in the current population, based on the values ​​of its timetable strategy selection string and scheduling direction selection string, decode it using the corresponding forward and reverse hybrid timetable strategy to generate a feasible scheduling solution under zero waiting constraints, and calculate the fitness value of each individual chromosome.

[0086] In practice, the scheduling direction of decoding is determined based on the SDS value; and the timetable strategy adopted for decoding is determined based on the TSS value.

[0087] Assume the workpiece sequence string is Decoding is performed in four different ways, as detailed below:

[0088] If both SDS and TSS are 1, then a forward-order scheduling and non-delay schedule strategy is adopted. The start time of n jobs is calculated sequentially through the following steps, and then the entire scheduling solution is obtained.

[0089] a) Let ;

[0090] b) Given workpiece Need to satisfy the constraints before and after the workpiece sequence Given equipment and process constraints, begin machining as early as possible and determine the workpiece. Start processing time ;

[0091] c) Obtain the workpiece sequentially according to equations (1) and (2). Start time of each other process and completion time ,in This refers to the workpiece. The number of processes.

[0092] (1)

[0093] (2)

[0094] in, This represents the i-th workpiece in the workpiece sequence string; Indicates workpiece The number of processes; Indicates workpiece The processing time for the j-th process; Indicates workpiece Start time of the j-th process; Indicates workpiece The completion time of the j-th process; the subscript j+1 indicates the (j+1)-th process.

[0095] d) Repeat steps b) and c) until the start and finish times of all operations for all n workpieces are calculated.

[0096] If the SDS value is 1 and the TSS value is 0, then a forward-order scheduling and proactive timetable strategy is adopted. The start times of the n jobs are calculated sequentially through the following steps to obtain the entire scheduling solution. The specific steps are as follows:

[0097] a) Let ;

[0098] b) Given workpiece Processing should begin as early as possible while meeting equipment and process constraints, and the workpiece should be determined. Start processing time ;

[0099] c) Calculate the workpiece according to equations (1) and (2) in sequence. Start time of each other process and completion time ,in This refers to the workpiece. The number of processes;

[0100] d) Repeat steps b) and c) until the start and finish times of all operations for all n workpieces are calculated.

[0101] If the SDS value is 0 and the TSS value is 1, then the reverse scheduling and non-delayed schedule strategy will result in the actual decoded artifact sequence becoming... ,in The start times of n workpieces are calculated sequentially through the following steps, thus obtaining the entire scheduling solution. The specific steps are as follows:

[0102] a) Let ;

[0103] b) Given workpiece Need to satisfy the constraints before and after the workpiece sequence Given equipment and process constraints, begin processing as early as possible and determine the workpiece. Start processing time ;

[0104] c) Calculate the workpiece sequentially according to equations (3) and (4). Start time of each other process and completion time ,in This refers to the workpiece. The number of processes.

[0105] (3);

[0106] (4);

[0107] Among them, subscript Represents the reverse decoding sequence The i-th workpiece; Indicates workpiece The number of processes;

[0108] d) Repeat steps b) and c) until the start time and completion time of all operations for n workpieces are calculated;

[0109] e) Based on equations (5) and (6), the workpiece in the original problem is calculated sequentially. Start time .

[0110] (5);

[0111] (6);

[0112] in, Indicates the workpiece in the original problem The start time of the first process. This represents the processing time of the j-th process for the i-th workpiece in the reverse-order decoding sequence; Reverse decoding sequence The number of workpieces in the process;

[0113] f) Calculate the workpiece sequentially according to equations 1) and (2). Start time of each other process and completion time ;

[0114] g) Repeat steps e) and f) until the start and finish times of all operations for all n workpieces are calculated.

[0115] If both SDS and TSS values ​​are 0, then a reverse scheduling and proactive timetable strategy is adopted, and the actual decoded workpiece sequence becomes... ,in The start times of n workpieces are calculated sequentially through the following steps, thus obtaining the entire scheduling solution. The specific steps are as follows:

[0116] a) Let ;

[0117] b) Given workpiece Processing should begin as early as possible while meeting equipment and process constraints, and the workpiece should be determined. Start processing time ;

[0118] c) Calculate the workpiece sequentially according to equations (3) and (4). Start time of each other process and completion time ,in This refers to the workpiece. The number of processes.

[0119] d) Repeat steps b) and c) until the start time and completion time of all operations for n workpieces are calculated;

[0120] e) Calculate the workpiece in the original problem according to equations (5) and (6) in sequence. Start time .

[0121] f) Calculate the workpiece sequentially according to equations (1) and (2). Start time of each other process and completion time ;

[0122] g) Repeat steps e) and f) until the start and finish times of all operations for all n workpieces are calculated.

[0123] S4. Select the best individual chromosomes with the highest fitness values ​​(X) in the current population after fitness values ​​are calculated in S3. Optimize them using a fast local search based on crossover mutation. Replace the original individual chromosomes with the optimized new individual chromosomes to update the current population. Here, X is set to 20% based on the Pareto 80 / 20 principle.

[0124] In specific implementation, the fast local search based on interchange mutation includes:

[0125] Obtain the set of the top 20% of individuals in the current population based on their fitness values. Let the length of the workpiece sequence string be m, and let k = round(m / 2).

[0126] When the scheduling direction selection string indicates forward scheduling, an interchange mutation is performed within the range of the k-th to the (m-1)-th position of the workpiece sequence string; when the scheduling direction selection string indicates reverse scheduling, an interchange mutation is performed within the range of the 1-th to the (k-1)-th position of the workpiece sequence string.

[0127] The fitness of the new individual chromosome generated by the mutation is quickly evaluated. If the fitness value of the new individual chromosome is better than that of the original individual chromosome, the original individual chromosome is replaced with the new individual chromosome.

[0128] To better understand the operation of S4, the following algorithm diagram is provided:

[0129]

[0130] S5 employs a strategy that combines elite retention with binary tournament selection to select the next generation of the population from the current population updated in S4.

[0131] In practice, the strategy combining elite retention with binary tournament selection includes:

[0132] The chromosome of the individual with the best fitness value in the current population is directly copied to the next generation population;

[0133] Repeat the following steps until the number of individuals in the next generation population reaches the population size set in S1: randomly select two individual chromosomes from the current population, and select the individual chromosome with the higher fitness value as the individual in the next generation population.

[0134] S6. Based on the current optimization performance value of each parameter combination, select a parameter combination from the multiple parameter combinations in S1 using a roulette wheel approach. Perform crossover and mutation operations sequentially on the next generation population selected in S5 to obtain a new generation population. If the average fitness value of the new generation population or the fitness value of the best individual chromosome is improved compared to the current population at the beginning of this iteration, then increase the optimization performance value of the parameter combination selected in this iteration.

[0135] In practice, when performing crossover operations on the next generation population, the workpiece sequence string adopts the single-point sequential crossover method, and the timetable strategy selection string and the scheduling direction selection string both adopt the crossover inheritance parent method; when performing mutation operations on the population obtained after the crossover operation, the workpiece sequence string adopts the swap mutation method, and the timetable strategy selection string and the scheduling direction selection string both adopt the binary mutation method.

[0136] S7. Determine whether the maximum number of generations set in S1 has been reached. If it has, output the optimal scheduling scheme in the current population. Otherwise, take the new generation population obtained in S6 as the current population and return to S3.

[0137] This method organically combines forward and reverse timetable strategies through the timetable strategy selection string and scheduling direction selection string in the extended three-segment coding structure, forming a hybrid forward-reverse timetable strategy. Compared with the single timetable generation strategy commonly used in existing technologies, this hybrid strategy can explore the solution space from different directions and angles, effectively avoiding the defect of single strategies easily getting trapped in local optima, significantly expanding the search range of the algorithm, and increasing the probability of finding the global optimum or high-quality solutions. In addition, this method uses a strategy combining elite preservation and binary tournament selection for population selection, which ensures the genetic continuation of excellent individuals and maintains population diversity. At the same time, it achieves a fine-grained optimization of the top-ranked optimal individuals through fast local search based on crossover mutation, realizing an effective combination of global search and local search. Compared with the problem of single search strategy and difficulty in balancing breadth and depth in existing technologies, this method can continuously improve the quality of solutions while ensuring search efficiency, achieving an organic unity of search efficiency and solution quality. Furthermore, this method innovatively employs a uniform design approach to generate multiple combinations of crossover and mutation rates. Based on the optimization performance values ​​of each parameter combination, it dynamically selects the optimal parameter combination using a roulette wheel approach. When a parameter combination improves population performance, its optimization performance value increases accordingly, thus obtaining a higher selection probability in subsequent iterations. Compared to existing techniques that use fixed parameters or simple linear updates, this adaptive mechanism intelligently adjusts parameters based on the algorithm's real-time performance, significantly improving the algorithm's adaptability and robustness, enabling it to better handle zero-wait job shop scheduling problems of varying scales and complexities.

[0138] Through the synergistic effect of the aforementioned technological innovations, the solution efficiency for the zero-wait-time job shop scheduling problem has been significantly improved. When facing large-scale, complex real-world production scenarios, this method can consistently output high-quality scheduling solutions, effectively shortening manufacturing cycles, reducing work-in-process inventory, and minimizing resource idleness. It provides a more reliable and efficient scheduling solution for continuous or time-sensitive industrial production scenarios such as steel smelting, pharmaceutical production, and food processing. This method can achieve a comprehensive exploration of the solution space and an effective balance between search efficiency and solution quality in zero-wait-time job shop scheduling.

[0139] Example 2

[0140] To better understand this method, the following example is provided.

[0141] 1. Determine the relevant parameters of the proposed zero-wait job shop scheduling method, including population size (POPsize) and maximum generation number (GEN). max The number of levels q for crossover rate and variation rate and their corresponding uniform design tables wait.

[0142] 2. Population initialization based on extended three-segment coding structure: To more clearly describe the designed extended three-segment coding structure, a simple example is given, which includes 3 types of workpieces (J1, J2, J3) and 3 machines (M1, M2, M3), with 3, 3, and 3 processes for each workpiece, respectively.

[0143] The extended three-segment encoding structure consists of three parts: the job sequence string, the timetable strategy selection string, and the scheduling direction selection string. The job sequence string (JSS) uses job-based encoding, where each digit represents the job number, and each digit appears only once, such as... Figure 2 The third digit in the workpiece sequence string is 3, representing workpiece number 3, i.e., workpiece J3; the time-table strategy string (TSS) has a numeric value of 1 or 0, representing a non-delayed time-table strategy and an active time-table strategy, respectively. Figure 2 The TSS value is 1, indicating that the chromosome decoding process uses a non-delayed schedule strategy; the Scheduling Direction String (SDS) has a value of 1 or 0, representing forward and reverse scheduling respectively. Figure 2 The value of TSS is 1, which indicates that the chromosome decoding process adopts the forward scheduling direction.

[0144] In the initialization of the population, the workpiece sequence string is initialized using a random initialization method; the timetable strategy selection string is initialized using a simple random binary number initialization method; and the scheduling direction selection string is also initialized using a simple random binary number initialization method, ultimately generating a population with a number of individuals of POPsize.

[0145] 3. Decoding based on a hybrid forward and reverse scheduling strategy: First, determine the scheduling direction of decoding based on the SDS value in the decoding chromosome; second, determine the scheduling strategy to be used for decoding based on the TSS value; then, according to the order of the workpieces on the workpiece sequence string, arrange the processes of all workpieces in the appropriate positions of the equipment using the determined decoding strategy; finally, obtain the feasible active scheduling solution of the original problem. Figure 3 The scheduling Gantt chart results are obtained by decoding the same process string 1-2-3 under four different combinations of SDS and TSS using the corresponding hybrid strategy.

[0146] 4. Adjustment strategy based on parameter combination performance: In the initialization phase, a uniform design method is used to generate multiple different combinations of Pc and Pm parameters, and the optimization performance of each parameter combination is initialized to 1. Before each iteration, a roulette wheel selection method (based on the optimization performance of parameter combinations) is used to randomly select a parameter combination from the multiple combinations as the parameters for this iteration; if the population average target value or the optimal individual target value is improved in this iteration, the optimization performance value of the parameter combination used in this iteration is increased.

[0147] A simple example is shown in Table 2. There are 6 combinations of Pc and Pm parameters. In the initial stage, the optimization performance value of each parameter combination is 1, and the selection probability of each combination is 1 / 6. Assuming that parameter combination 2 is selected as the parameter for the first iteration using the roulette wheel method, and the optimal individual objective value is improved in this iteration, the optimization performance of parameter combination 2 increases to 2. Before the second iteration, the selection probabilities of each parameter combination are 1 / 7, 2 / 7, 1 / 7, 1 / 7, 1 / 7, 1 / 7, and 1 / 7, respectively, as shown in the table below.

[0148]

[0149] 5. Fast Local Search Based on Interchange and Mutation: This method overcomes the poor local search capability of a single genetic algorithm. It utilizes a fast evaluation method during decoding to assess the new solution, effectively shortening the evaluation time. Its core idea is that the unchanged parts of the workpiece sequence do not need to be recalculated; only the changed parts need to be calculated. For example... Figure 4 In (a), when decoding in the forward order scheduling direction, only the latter half of the sequence altered by the interchange mutation is calculated, while in... Figure 4 In (b), when decoding in the reverse scheduling direction, only the first half of the sequence that has changed due to the interchange mutation is calculated.

[0150] To verify the effectiveness of the zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy proposed in this invention, the FT10 instance from the international standard test data Benchmark for the job shop scheduling problem was selected for testing.

[0151] The main parameter settings for the zero-wait job shop scheduling method proposed in this invention are as follows: POPsize=200, GENmax=50, and the parameter combinations of Pc and Pm are still shown in Table 2. Four variant methods are compared with it: Variant Method 1 (without the hybrid schedule strategy only), Variant Method 2 (without the forward and reverse scheduling strategy only), Variant Method 3 (without the fast local search only), and Variant Method 4 (without the parameter adjustment strategy only). The values ​​of Pc and Pm in Variant Method 4 were determined through extensive experiments before testing, and are set to 0.8 and 0.05 respectively.

[0152] The five comparison methods described above all maintain the same parameter settings, and the convergence curves of the solution process are shown in the figure below. Figure 5 As shown, it is easy to see that variant method 1 has a significant drawback in terms of slow convergence speed throughout the solution process; variant methods 2, 3, and 4, although they all have several consecutive uninterrupted convergences in the early stages, have slower convergence speeds or even stagnate in the later stages; the method of this invention improves the maximum completion time most frequently and has the best effect. In summary, the overall solution performance of the method of this invention is stronger than the other four variant methods. Figure 6 The optimal scheduling Gantt chart obtained by the method of this invention is 1609.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy, characterized in that, Includes the following steps: S1. Obtain workpiece process data for the zero-wait job shop scheduling problem, and set the population size and maximum number of generations; use the uniform design method to generate multiple combinations of crossover rate and mutation rate parameters, and initialize and optimize the performance value for each parameter combination; S2. An initial population is generated using an extended three-segment coding structure, which includes a workpiece sequence string for determining the workpiece processing order, a time schedule strategy selection string for selecting a time schedule strategy, and a scheduling direction selection string for determining the scheduling direction. S3. For each individual chromosome in the current population, based on the values ​​of its timetable strategy selection string and scheduling direction selection string, decode it using the corresponding forward and reverse mixed timetable strategy to generate a feasible scheduling solution under zero waiting constraints, and calculate the fitness value of each individual chromosome. S4. Select the best individual chromosome with the highest fitness value (X) in the current population after fitness value is calculated in S3. Optimize it using a fast local search based on exchange mutation. Replace the original individual chromosome with the optimized new individual chromosome to update the current population. S5. A strategy combining elite retention and binary tournament selection is adopted to select the next generation of the population from the current population after the S4 update. S6. Based on the current optimization performance value of each parameter combination, select a parameter combination from the multiple parameter combinations in S1 using a roulette wheel approach. Perform crossover and mutation operations sequentially on the next generation population selected in S5 to obtain a new generation population. If the average fitness value of the new generation population or the fitness value of the best individual chromosome is improved compared to the current population at the beginning of this iteration, then increase the optimization performance value of the parameter combination selected in this iteration. S7. Determine whether the maximum number of generations set in S1 has been reached. If it has, output the optimal scheduling scheme in the current population. Otherwise, take the new generation population obtained in S6 as the current population and return to S3.

2. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, When the gene value of the timetable strategy selection string is 1, it indicates the use of a non-delayed timetable strategy; when it is 0, it indicates the use of an active timetable strategy. When the gene value of the scheduling direction selection string is 1, it indicates the use of forward scheduling; when it is 0, it indicates the use of reverse scheduling.

3. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 2, characterized in that, In step S3, when the scheduling direction selection string indicates forward scheduling and the timetable strategy selection string indicates a non-delayed timetable strategy, the start time of each workpiece is determined sequentially according to the workpiece sequence string, under the conditions of satisfying the start time sequence constraints of the scheduled workpieces, as well as equipment constraints and process constraints. The start time and completion time of the remaining processes of each workpiece are then calculated according to the following formula: （1）； （2）； in, This represents the i-th workpiece in the workpiece sequence string; Indicates workpiece The number of processes; Indicates workpiece The processing time for the j-th process; Indicates workpiece Start time of the j-th process; Indicates workpiece The completion time of the j-th process; the subscript j+1 indicates the (j+1)-th process.

4. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 3, characterized in that, In step S3, when the scheduling direction selection string indicates forward scheduling and the time schedule strategy selection string indicates active time schedule strategy, the start time of each workpiece is determined sequentially according to the order of the workpiece sequence string, under the condition that only equipment constraints and process constraints are satisfied; and the start time and completion time of the remaining processes of each workpiece are calculated according to formulas (1) and (2).

5. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 3, characterized in that, In step S3, when the scheduling direction selection string indicates reverse scheduling, the workpiece sequence string is... Reverse to the reverse decoding sequence ,in where n is the total number of workpieces; Decode the sequence in reverse order Based on the order of the timetable strategy selection string, the corresponding non-delayed timetable strategy or active timetable strategy is used for decoding. The start time of the remaining processes of each workpiece in the reverse-order decoding sequence is calculated according to the following formula. and completion time : ； ； Among them, subscript Represents the reverse decoding sequence The i-th workpiece; Indicates workpiece The number of processes; The maximum completion time of the reverse scheduling solution is calculated using the following formula. : ； Then calculate the start time of each workpiece in the original problem using the following formula: ； in, Indicates the workpiece in the original problem The start time of the first process. This represents the processing time of the j-th process for the i-th workpiece in the reverse-order decoding sequence; For reverse decoding sequence The number of workpieces in the process; Calculate the start and finish times of the remaining processes for each workpiece in the original problem using equations (1) and (2).

6. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, In step S4, the fast local search based on interchange mutation includes: Obtain the optimal set of individuals with the highest fitness values ​​(X) in the current population. Let the length of the workpiece sequence string be m, and let k = round(m / 2). When the scheduling direction selection string indicates forward scheduling, an interchange mutation is performed within the range of the k-th to the (m-1)-th position of the workpiece sequence string; when the scheduling direction selection string indicates reverse scheduling, an interchange mutation is performed within the range of the 1-th to the (k-1)-th position of the workpiece sequence string. The fitness of the new individual chromosome generated by the mutation is quickly evaluated. If the fitness value of the new individual chromosome is better than that of the original individual chromosome, the original individual chromosome is replaced with the new individual chromosome.

7. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, In step S5, the strategy combining elite retention with binary tournament selection includes: The chromosome of the individual with the best fitness value in the current population is directly copied to the next generation population; Repeat the following steps until the number of individuals in the next generation population reaches the population size set in S1: randomly select two individual chromosomes from the current population, and select the individual chromosome with the higher fitness value as the individual in the next generation population.

8. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, In step S1, the generation of multiple combinations of crossover rate and mutation rate parameters using the uniform design method includes: Set the number of factor levels for crossover rate Pc and variation rate Pm; Determine the required uniform design table based on the set number of factor levels. Where n is the number of parameter combinations, q is the number of levels, and m is the number of factors; Based on the determined uniform design table It uses tables to determine multiple parameter combinations for crossover rate and variation rate.

9. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, In step S6, when performing crossover on the next generation population, the workpiece sequence string adopts the single-point sequential crossover method, and the timetable strategy selection string and the scheduling direction selection string both adopt the crossover inheritance parent method; when performing mutation on the population obtained after the crossover operation, the workpiece sequence string adopts the swap mutation method, and the timetable strategy selection string and the scheduling direction selection string both adopt the binary mutation method.

10. The zero-wait job shop scheduling method based on a hybrid forward and reverse timetable strategy as described in claim 1, characterized in that, X is 20%.

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