Study On Scheduling Problem Of Flexible Flow Shop Considering Single-stage Preventive Maintenance

With the rapid development of the global manufacturing industry,the pressure of market competition has gradually increased.While enterprises are seeking technological breakthroughs,scientifically and rationally arranging production resources and ensuring the stable and efficient operation of equipment are the new directions for maximizing corporate profits.Production scheduling is one of the important elements.The production mode of the workshop has gradually changed from single machine and parallel machine to flow-shop scheduling and hybrid flow-shop scheduling.In the actual production process,as the operating time increases,the reliability of the equipment gradually decreases and the failure rate gradually increases.Preventive maintenance of the equipment must be carried out.The coupling between production goals and equipment management goals is serious,making it more difficult to make production scheduling plans.This topic takes the mixed flow shop as the research object,and takes the system makespan(completion time)and the preventive maintenance cost per unit time of the equipment as the optimization objective for joint optimization.The main research content includes the following points:Research the problems of mixed flow shop scheduling and single-phase preventive maintenance.First,it analyzes the production process constraints and time constraints of the mixed flow shop system;secondly,the preventive maintenance objects are determined according to the actual application scenarios,that is,in the special production stage of certain devices,only a single-stage parallel machine is taken preventive maintenance operations,such as aerospace,precision instruments,etc.,which require extremely high precision or expensive equipment production stage;finally,based on the reliability theory of the equipment,the preventive maintenance operation of the equipment is carried out.Based on the above research,quantify the coupling relationship between production scheduling and equipment maintenance,a multi-objective mathematical programming model with the system’s minimized completion time and single-phase preventive maintenance costs as the optimization goals is established.Aiming at the multi-objective optimization problem in this paper,a non-dominated Sorting Genetic Algorithms Ⅱ(NSGA-Ⅱ)with an elite strategy is selected.In combination with the particularity of this subject,an adaptive NSGA-Ⅱ algorithm is proposed,which improves the selection method and the probability of cross mutation.A two-part coding method is adopted,that is,matrix coding is used for the production part,and 0/1 coding is used for the maintenance part;the ideas of non-dominated layer extraction and tournament selection filling is introduced to increase diversity while ensuring the number of populations;considering the disadvantages of the fixed cross-mutation probability,an adaptive cross-mutation operator is designed,in the early stage of the algorithm,the search range of the algorithm is increased with a higher probability of cross mutation,and the probability is reduced in the later iteration to achieve the effect of retaining the optimal solution,which improves the population diversity and the convergence speed of the algorithm,and overcomes the premature phenomenon.Using C++ language to write programs,comparing the traditional NSGA-Ⅱ algorithm and the adaptive NSGA-Ⅱ algorithm for scheduling problems of different scales under different parameter conditions,and draw the Pareto frontier surface map.The number of frontier solutions,the spread range and the proportion of Pareto dominance are used as the evaluation indicators of the multi-objective optimization algorithm.The experimental results of multiple sets of data show that the adaptive NSGA-Ⅱ algorithm has better diversity,a wider spread range,and lower costs of makespan and single-stage preventive maintenance,and more cutting-edge solutions provide decision-makers with choices.