Research On Low-carbon Multi-Obiective Flexible Job-shop Scheduling Problem Based On Modified NSGA-Ⅲ

As the energy crisis and pollution become more and more apparent,low-carbon coal production has become an established and sustainable way of production.More and more attention has been paid to optimizing planning problems in modern production systems.Optimizing the production workshop planning issues not only improves a company’s resource utilization and production efficiency,but is also closely related to its contribution to society and the environment.Therefore,it is very important to optimize the planning issues of the production shop to protect the environment and save energy.This paper examines the multi-objective flexible job shop scheduling problem（MO-FJSP）and addresses the environmental pollution caused by the manufacturing process.The focus is on establishing low-carbon MO-FJSP models,researching and improving its solving algorithm.The paper first presents the research background and the current state of MO-FJSP,and presents the carbon emissions targets based on optimization targets for common planning problems,and presents a MO-FJSP mathematical model to minimize lead time,mechanical load,and carbon emissions.Explains how chromosomes are encoded and decoded,and reviews current literature.This paper summarizes instances of commonly used MO-FJSP tests and metrics for multi-objective optimization problems.Next,we will examine the MO-FJSP around the NSGA-Ⅲ and focus on the scientific problem of "how to better research and evolve in the area of decision making on flexible work warehouse planning problems".Initial experiments have shown that the crossover operator used to solve MO-FJSP is a performance bottleneck.In this paper,we introduce 5 crossover operators to NSGA-Ⅲ to generate 5 NSGA-Ⅲ variants by exploring and developing different variants in the field of decision making,flexible work warehouse planning.Test experimentally in some common reference cases of the problem.According to the research results,the article proposes an evolutionary mechanism that combines multi-group co-evolution and natural selection.This evolutionary mechanism takes advantage of the three existing crossover operators and uses the set coverage（SC）to guide the natural breadth of the population,creating Pareto-dominated index-based selection strategies.Combine with 3 optimal selection strategies.The effectiveness of the proposed evolutionary mechanism is verified by comparing it with NSGA-Ⅲ.Finally,the algorithm is compared and tested in three groups of known MO-FJSP test cases.NSGA-Ⅲ-COE is compared with many commonly used MOEAs to record the processing time of the CPU used in the algorithm and to analyze the sensitivity to parameter settings that can affect the performance of the algorithm.Experimental results show that NSGA-Ⅲ-COE achieves excellent solution efficiency,improves algorithm performance,and at the same time does not require higher computational costs.Compared to the widely used MOEA,NSGA-Ⅲ-COE showed excellent sensitivity to population size,population repeat time,and population mutation probability,and was excellent inclusive.NSGA-Ⅲ-COE is a very competitive algorithm for solving low-carbon MOFJSP with practical value.