Research On Flexible Flow Shop Scheduling Of Non-equivalent Parallel Machines Based On Improved NSGA-Ⅱ

The flexible flow shop scheduling problem of non-equivalent parallel machines is widely used in the production line shop where a variety of new and old machines are mixed.The difference in processing technology of different kinds of parallel machines leads to different matching degree between product orders and different kinds of machines.Under normal circumstances,most enterprises through manual,semi-automatic and automatic three types of machine coexisting nonequivalent parallel machine workshop to improve the order and machine matching degree to obtain high stability of the machine,but the improvement of order and machine matching degree is often accompanied by the reduction of processing efficiency or increase in energy consumption.This situation causes enterprises to face the order and machine matching degree,the maximum completion time and energy consumption three difficult balance problems.Traditional scheduling methods are difficult to solve the above problems,so this paper constructs a three-objective FFSP-NPM mathematical model with the objectives of minimizing the maximum completion time,minimizing the energy consumption,and high matching degree between orders and machines.An improved NSGA-Ⅱ algorithm which combines the non-dominant sorting genetic algorithm with the entropy weight approaching the ideal solution is proposed to obtain the three-objective optimal combination solution and determine the job assignment scheme.The matching degree between order and machine is difficult to be quantified based on system dynamics and decision tree.Through system dynamics,the main factors affecting the difference of different parallel machines are screened,and the positive and negative feedback relationship between each factor and different parallel machines is established,which provides the main constraint conditions and classification criteria for the decision tree classification of order and machine priority level.The priority factor was used to quantify the different priority levels of the decision tree,which was used as the standard to measure the matching degree between the order and the machine.The mathematical model of the three-objective FFSP-NPM was constructed by combining the maximum completion time and energy consumption.In order to improve the applicability of NSGA-Ⅱ algorithm in solving the three-objective FFSPNPM,a double-layer segmented encoding and decoding method was designed and the crossover mutation operator was improved according to the large difference in the application range of the products processed by different parallel machines.In addition,considering that the algorithm is difficult to identify the three-objective optimal combination solution,NSGA-Ⅱ algorithm is designed and improved with entropy weight TOPSIS method.The improved NSGA-Ⅱ algorithm takes the production line balance time as the basic requirement to segment the data of Pareto frontier surface,and evaluates the relative optimal solution set after segmentation by entropy weight TOPSIS method,so as to clarify the three-objective optimal combination solution and its job assignment scheme.Taking the solving of the job assignment problem of die cutting indentation shop scheduling in a corrugated carton enterprise as an example,the improved NSGA-Ⅱ algorithm was used to solve the model,and the results were compared with the traditional scheduling method and the classical NSGA-Ⅱ algorithm to verify that the improved algorithm has better solving performance.