Iterative greedy algorithm for man-machine cooperation

Abstract

The invention relates to an iterative greedy algorithm oriented to man-machine cooperation, which is characterized in that an NEH algorithm generates an operation seed sequence through a scheduling rule of longest processing time, destruction reconstruction is responsible for deleting some elements from a current solution, the elements are orderly inserted into the rest of partial solutions according to a greedy criterion, three different operators are designed, and the working efficiency is improved. The quality of the solution is improved, and a new solution is generated after damage reconstruction and a local search algorithm based on neighborhood disturbance are executed. The invention provides a production scheduling method based on an iterative greedy algorithm in order to solve the problems that an existing flow shop production scheduling method is single in application scene and low in solving speed. The traditional IG algorithm is improved, the production scene of man-machine cooperation and objective factors in the actual production process are considered, the application range of the algorithm is widened, and the solving precision and speed of the algorithm are improved. The method can be well applied to a man-machine cooperation assembly line workshop, and the universality is higher.

Description

Technical Field

[0001] The present invention relates to the technical field of flow shop scheduling optimization, and in particular to an iterative greedy algorithm oriented to human-machine collaboration. Background Art

[0002] Production scheduling is an important part of the manufacturing system, which directly affects the efficiency and competitiveness of the enterprise. Using safe and easy-to-use collaborative robots to participate in the production process together with operators, giving full play to their respective strengths, and realizing division of labor and collaborative work is an effective way to solve the low-cost, high-efficiency, flexible, and complex operation automation problems that traditional industrial robots are difficult to deal with. Efficient human-machine collaborative production scheduling methods can achieve efficiency improvement, energy saving, consumption reduction, emission reduction and cost reduction in the production and manufacturing process of enterprises, and give full play to the optimal performance of human-machine collaborative production systems. In view of the complexity and practical applicability of production scheduling problems in assembly lines, relevant fields have conducted extensive research and proposed a variety of heuristic algorithms.

[0003] IG (Iterative Greedy Algorithm) is an internationally recognized simple and effective algorithm for assembly line scheduling problems. See the journal "European Journal of Operational Research 177 (2007) 2033–2049", Yuan Shuaipeng et al. published a paper titled "Iterative Greedy Algorithm for Group Scheduling Problems in Two-stage Assembly Shops". This method established a mixed frame linear programming model with the goal of minimizing the maximum completion time, and proposed a co-evolutionary iterative greedy algorithm based on the characteristics of the problem. Although this method has improved the classic IG algorithm and improved the efficiency and robustness of the IG algorithm, this method does not take into account factors such as machine failures and order changes that may be encountered in production, nor does it take into account the application scenarios of human-machine collaboration in modern factory assembly line production, and cannot meet the guidance needs for actual production. Summary of the invention

[0004] The purpose of the present invention is to provide an iterative greedy algorithm for human-machine collaboration to solve the problems encountered in the above-mentioned background technology.

[0005] To achieve the above object, the technical solution of the present invention is as follows: An iterative greedy algorithm for human-machine collaboration, the method comprising the following steps: Step 1, Initialization method: The basic NEH initialization method generates a job seed sequence through the longest processing time (LPT) rule. Then, extract the jobs one by one from the seed sequence and insert them into the position where the best target value is obtained. For the flow shop scheduling problem with collaborative robots (FSPCR), we further extended NEH to the FSPCR scenario and named it NEH_C. For FSPCR, the LPT rule is as follows: calculate the total processing time of each job in two scenarios: only machines and workers, and machines and workers with collaborative robots, and then generate a seed sequence based on the non-descending total processing time of each job. Extract jobs from the seed sequence one by one and insert each job into the optimal position.

[0006] Step 2, destruction and reconstruction phase: Destruction and reconstruction is responsible for deleting some elements from the current solution and inserting these elements into the remaining partial solutions in order according to the greedy criterion. Destruction and reconstruction guides different search directions and improves the global search ability of the algorithm. In the destruction phase, d jobs are removed from the current solution π and put into the sequence τ. In the reconstruction phase, the jobs removed in the destruction phase need to be inserted into the optimal position of the current solution in sequence. Repeat the above process until each sub-region in the sequence τ is inserted and a new solution is formed.

[0007] Step 3, local search algorithm: In the local search stage, common shift operators and swap operators are selected according to the characteristics of the problem. The shift operator ShiftOperator moves a randomly selected task on all production lines to a random position, while the swap operator SwapOperator randomly swaps two tasks on all production lines. The shift operator ShiftOperator and the swap operator SwapOperator may lead to different neighborhood structures. In order to maintain the diversity of the search process, this scheme also proposes a hybrid operator. In each iteration, the roulette wheel selection method is used to assign probabilities to the two operators. This ensures that both the effects of the translation operation and the effects of the swap operation are present during the search process. If a better solution is obtained, the solution π is updated.

[0008] Step 4, acceptance criteria of the solution: After executing the destruction and reconstruction and the local search algorithm based on neighborhood perturbation, a new solution will be generated. The acceptance criteria are used to decide whether to replace the current solution with the new solution to enter the next iteration. Inspired by the simulated annealing criterion in the IG algorithm, a corresponding acceptance criterion is proposed based on the characteristics of the problem. That is, if the new solution is better than the current solution, it replaces the current solution. Otherwise, the new solution is accepted with a certain probability. In addition, the optimal solution is also updated by comparing with the new solution. Before determining the acceptance probability, the temperature Temperature is calculated according to the formula, which takes into account the sum of the processing time in the two scenarios.

[0009] Step 5, calibration of the final solution: simulate different input levels of machines and the number of collaborative robots, as well as factors that may affect production during the search process. Set up small-scale, medium-scale, and large-scale instances, design experiments, and calibrate the proposed production scheduling method through variance analysis methods.

[0010] The variance analysis method is used to determine whether the new solution meets the iteration termination condition. If not, step 4 is repeated. If it is reached, the optimal solution is output. The optimal solution is the optimal scheduling sequence with the minimized maximum completion time.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: the production scheduling method takes the completion time as the objective function, and proposes an effective iterative greedy algorithm for the assembly line workshop with the participation of assisting robots in production; in terms of initialization method, the traditional NEH algorithm is extended to the assembly line workshop scheduling problem with the participation of collaborative robots, thereby increasing its application scenarios; in the local search stage, three different operators are designed according to the characteristics of the problem, thereby effectively improving the quality of the solution; in the design of the acceptance criterion of the solution, the influence of the processing time in different scenarios on the quality of the solution is taken into account, thereby effectively improving the stability of the production scheduling in the application scenario.

[0012] In order to solve the problem that the existing assembly line production scheduling method has a single application scenario and a slow solution speed, the present invention proposes a production scheduling method based on an iterative greedy algorithm. By improving the traditional IG algorithm, considering the production scenario of human-machine collaboration and the objective factors in the actual production process, the application scope of the algorithm is increased, and the accuracy and speed of the algorithm solution are improved. It can be well applied to assembly line workshops with human-machine collaboration and has stronger versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The disclosure of the present invention is described with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. In the accompanying drawings, the same reference numerals are used to refer to the same components. Among them: Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 A schematic diagram of a flow chart for constructing a heuristic algorithm for the present invention; Figure 3 It is a flowchart of the destruction and reconstruction algorithm of the present invention; Figure 4 It is a schematic diagram of the flow of the mixed operator operator of the present invention. DETAILED DESCRIPTION

[0014] In order to make the technical means, creative features, objectives and effects of the present invention easy to understand, the present invention is now further described in detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the relevant components of the present invention.

[0015] According to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art can propose a variety of interchangeable structural modes and implementation modes. Therefore, the following specific implementation modes and drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or restriction to the technical solution of the present invention.

[0016] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0017] like Figure 1 As shown, an iterative greedy algorithm for human-machine collaboration, the method specifically includes the following steps: Step 1: In the initialization phase, the classic NEH (Nawaz-Enscore-Ham) heuristic algorithm is used. The NEH algorithm first sorts the jobs according to the Longest Processing Time (LPT) rule to generate an initial seed sequence. The LPT rule determines the order of jobs based on the total processing time of each job on all machines, ensuring that longer jobs are scheduled first, thereby reducing the waiting time between jobs.

[0018] Next, the NEH algorithm was extended, and the NEH_C method was proposed specifically for the flowshop scheduling problem with collaborative robots (FSPCR). In NEH_C, the total processing time of each job is calculated in two scenarios: the machine and the worker alone, and the machine and the worker with collaborative robots. Then, according to the total processing time of each job, the seed sequence is generated by sorting in descending order.

[0019] Finally, jobs are extracted one by one from the seed sequence and inserted into the optimal position in the sequence using a heuristic algorithm to obtain the best overall objective value. This process is iterated until all jobs are scheduled into the sequence. The extension of the NEH_C method improves the quality of the initialization solution and lays a solid foundation for the subsequent optimization stage.

[0020] Step 2, destruction and reconstruction phase. In the destruction phase, d jobs are randomly selected from the current solution π and temporarily removed and placed in the sequence τ. This step is to break the fixed pattern of the existing job arrangement.

[0021] In the reconstruction phase, the jobs removed in the destruction phase are reinserted into the current solution according to a certain strategy. Each time a job is inserted, all possible positions are calculated by a heuristic algorithm, and the position that produces the best target value is selected for insertion. This process is carried out step by step until every sub-region in the sequence τ is rearranged.

[0022] This production scheduling method escapes from the local optimum through destruction and reconstruction and finds a possible better solution. The effect of this stage is that it can significantly improve the quality and diversity of the solution.

[0023] Step 3, local search, is used to find a better solution in the neighborhood of the current solution. Three types of operators are designed: the shift operator operator (ShiftOperator) moves a randomly selected task on all production lines to a random position, while the swap operator operator (SwapOperator) randomly swaps two tasks on all production lines. The shift operator operator and the swap operator operator may lead to different neighborhood structures. The hybrid operator operator (HybridOperator), in each iteration, uses roulette wheel selection to assign probabilities to the two operators, the shift operator operator or the swap operator operator. This ensures that both the effects of the translation operation and the effects of the swap operation are present during the search process. If a better solution is obtained, the solution π is updated.

[0024] Step 4, acceptance of the new solution, adopts a performance-based acceptance criterion, namely the acceptance strategy in the simulated annealing algorithm. In this stage, it is necessary to determine whether the solution generated in the local search phase can be used for the next iteration. If the new solution is better than the current solution in terms of the objective function, then the new solution will unconditionally replace the current solution and enter the next iteration.

[0025] If the new solution is not as good as the current solution, it is still accepted with a certain probability, which is based on the performance difference between the new and old solutions and the current temperature parameter. In this way, the algorithm can gradually move closer to the global optimal solution while maintaining a certain degree of randomness.

[0026] In addition, the optimal solution is also updated by comparing it with the new solution. Before determining the acceptance probability, the temperature is calculated according to the formula, which takes into account the sum of the processing time in the two scenarios. At the beginning of the algorithm, a higher initial test temperature is set so that all newly generated solutions are likely to be accepted. At each temperature, the algorithm performs multiple iterations to try to find a better solution in the neighborhood of the current solution. As the algorithm proceeds, the temperature is gradually lowered to reduce the probability of accepting a worse solution.

[0027] Step 5, during the calibration phase of the final solution, different input levels of machines and cobots were simulated, as well as various factors that could affect production. Small, medium, and large-scale instances were set up to evaluate the performance of the algorithm on problems of different sizes.

[0028] The variance analysis method is used to determine whether the new solution meets the iteration termination condition. If not, step 4 is repeated. If it is reached, the optimal solution is output. The optimal solution is the optimal scheduling sequence with the minimized maximum completion time.

[0029] Through variance analysis, the key factors that affect the quality of the solution can be identified and the algorithm parameters can be adjusted accordingly. This calibration process helps to improve the practicality and reliability of the algorithm and ensure its effective application in actual production scheduling problems.

[0030] Embodiment 2, scheme based on embodiment 1: See also Figure 2 ,In step 1, the LPT rule used in the improved NEH_C is as follows: ,Calculate the total processing time of each job in all two cases, and generate a seed sequence in ,non-descending order according to the total processing time of each job.,Extract jobs from the seed sequence one by one and insert each ,job into the best position.

[0031] Specifically, ① use the LPT rule to generate a seed sequence, that is, generate a seed sequence φ in non-descending order of the total processing time. ② extract the i-th job from the seed sequence φ in turn. For each job φ(i), loop through each production line, find the optimal insertion position in each production line, and calculate the total processing time after insertion. ③ For each production line, record the minimum value and the corresponding position generated, and further obtain the global minimum value and the optimal position. It should be noted that the above operations are performed for each task. ④ Finally, return the final production sequence π and the total processing time for each production line.

[0032] In simple terms: First, find the best position for each job on each production line. For a given production line, test the job at every possible position, and the best position of the job (bp k) is the position where the optimal target value (lv) calculated by the formula is the lowest. For all production lines, the optimal position of the operation (bp k* ) is the position where the optimal objective value (lv) is the lowest. Then, insert the job into bp k* For the above operations, execute each job flow one by one.

[0033] See also Figure 3 ,In step 2, the sequence τ is initialized to store the jobs removed from the current solution π, and d is determined based on the average number of jobs on each production line.

[0034] In the destruction phase, d jobs are taken from the current solution π and put into a sequence τ. The preset d is variable depending on the experimental scale. For small-scale instances, d is randomly generated from the range [n,n + 1]. For medium-scale instances, d is randomly generated from the range [n,n + 2]. For large-scale instances, d is randomly generated from the range [n,n + 3]. Compared with the fixed preset d, the dynamic d that takes into account the problem scale and randomness can expand a more diverse search area to obtain better solutions.

[0035] In the reconstruction phase, the jobs that need to be removed in the destruction phase are inserted into the optimal position of the current solution in sequence. That is, in the reconstruction phase, each job j in τ is traversed, the total processing time of inserting τ(j) into each possible position in the current solution π is calculated, and the optimal insertion position corresponding to the minimum total processing time is found. This phase is iteratively run until each sub-region in the sequence τ is inserted and a new solution is formed.

[0036] See also Figure 4 In step 3, three operators are set. The shift operator operator (shiftOperator) moves a randomly selected job to a random position in all production lines. The swap operator operator (swapOperator) randomly selects two jobs from all production lines for swapping. The hybrid operator operator (hybridOperator) uses the roulette wheel selection method to assign probabilities to the two operators, dynamically adjusts the selection probability according to the fitness of each operator, and then updates the solution π if a better solution is obtained. The hybrid operator operator enhances the diversity of search during the local search process and helps the algorithm jump out of the local optimal solution. The performance of the algorithm can be further fine-tuned by adjusting the probability of using shift and swap operations.

[0037] The process of the mixed operator is as follows: initialize the fitness vector and calculate the roulette selection algorithm total_fitness, calculate the selection probability pro of the current operator, generate a random number rand_num, and determine whether rand_num is less than pro. If the random number is not less than pro, use the shift operator and update fitness. If the random number is less than pro, use the exchange operator and update fitness. Finally, return the optimized solution π and fitness value fit.

[0038] In step 4, it is determined whether the solution generated in the local search phase can be used for the next iteration. In the existing public technologies, most IG algorithms use the simulated annealing criterion at temperature T. According to the characteristics of the flow shop scheduling problem, the following new formula is set: Among them, t is the parameter to be calibrated; n is the total number of jobs that need to be scheduled in the assembly line; m is the total number of machines used on each production line in the assembly line; P1 is the sum of the processing time of each job in the scenario with only machines and workers; P2 is the processing time of machines and workers in the scenario with collaborative robots.

[0039] This formula takes into account the sum of the processing time in two scenarios: when there are only machines and workers, and when there are machines and workers collaborating with collaborative robots. The parameter t is used to adjust the initial value and range of temperature. The summation part means that for each job and each production line, the sum of P1 and P2 is calculated respectively. Since there are n jobs and m production lines, each job and each production line will be traversed to accumulate all processing times. The processing time of each job includes not only the time P1 when there is no collaborative robot, but also the time P2 when there is a collaborative robot. Therefore, the time for each job is P1+P2. The constant factor plays the role of standardization and adjustment of magnitude. Since n and m represent the total number of jobs and the number of machines on each production line, respectively, their product Used to scale the summation result to ensure that the temperature calculation result is within the appropriate range.

[0040] In step 5, 10 test cases of three different sizes, large, medium and small, are set. The algorithm proposed in the present invention is compared with the genetic algorithm GA, the simulated annealing algorithm SA, and the taboo search algorithm TS. It is superior to several existing classic scheduling algorithms in terms of performance indicators such as total completion time, average completion time, maximum waiting time and resource utilization, and the t test is used to test the significance of the difference. It proves that the production scheduling method based on the iterative greedy algorithm proposed in the present invention is effective for the scheduling optimization problem of the human-machine collaborative flow shop.

[0041] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An iterative greedy algorithm for human-machine collaboration, characterized in that: The method comprises the following steps: Step 1, initialization method: the NEH algorithm generates a job seed sequence through the scheduling rule of the longest processing time; then, the jobs are extracted one by one from the seed sequence and inserted into the position where the best target value is obtained; Step 2, destruction and reconstruction phase: Destruction and reconstruction is responsible for deleting some elements from the current solution and inserting these elements into the remaining partial solutions in an orderly manner according to the greedy criterion; Step 3, local search algorithm: In the local search, a local search strategy of a shift operator, a swap operator, and a mixed operator is used according to the characteristics of the problem; a randomly selected task on all production lines is moved to a random position by the shift operator; two tasks on all production lines are randomly swapped by the swap operator; and a roulette wheel selection method is used to assign probabilities to the shift operator and the swap operator in each iteration by the mixed operator; Step 4, acceptance criteria of the solution: after executing the destruction and reconstruction and neighborhood perturbation-based local search algorithms, a new solution is generated; the acceptance criteria are used to decide whether to replace the current solution with the new solution to enter the next iteration; Step 5, calibration of the final solution: Simulating different input levels of machines and the number of collaborative robots, as well as the factors that may affect production during the search process, design experiments and calibrate the proposed production scheduling method through the variance analysis method.

2. The iterative greedy algorithm for human-machine collaboration according to claim 1, characterized in that: In step 1, the NEH algorithm is extended to the scenario of flow shop scheduling problem with the participation of collaborative robots and named NEH_C.

3. The iterative greedy algorithm for human-machine collaboration according to claim 2, characterized in that: The NEH algorithm calculates the total processing time of each job in the machine and human-machine collaboration scenarios respectively, then generates a seed sequence according to the non-descending total processing time of each job, takes out the jobs from the seed sequence in sequence, and inserts each job into the optimal position.

4. The iterative greedy algorithm for human-machine collaboration according to claim 1, characterized in that: In step 2, in the destruction phase, d jobs are removed from the current solution π and placed in the sequence τ; in the reconstruction phase, the jobs removed in the destruction phase need to be inserted into the optimal position of the current solution in sequence; the above process is repeated until each sub-region in the sequence τ is inserted to form a new solution.

5. The iterative greedy algorithm for human-machine collaboration according to claim 1, characterized in that: In step 3, if a better solution is obtained, the solution π is updated.

6. The iterative greedy algorithm for human-machine collaboration according to claim 1, characterized in that: In step 4, the corresponding acceptance criteria are proposed based on the problem characteristics: if the new solution is better than the current solution, it replaces the current solution; otherwise, the new solution is accepted with a certain probability; In addition, the optimal solution is also updated by comparing it with the new solution.

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