Abstract
Low carbon manufacturing has received increasingly more attention in the context of global warming. The flexible job shop scheduling problem (FJSP) widely exists in various manufacturing processes. Researchers have always emphasized manufacturing efficiency and economic benefits while ignoring environmental impacts. In this paper, considering carbon emissions, a multi-objective flexible job shop scheduling problem (MO-FJSP) mathematical model with minimum completion time, carbon emission, and machine load is established. To solve this problem, we study six variants of the non-dominated sorting genetic algorithm-III (NSGA-III). We find that some variants have better search capability in the MO-FJSP decision space. When the solution set is close to the Pareto frontier, the development ability of the NSGA-III variant in the decision space shows a difference. According to the research, we combine Pareto dominance with indicator-based thought. By utilizing three existing crossover operators, a modified NSGA-III (co-evolutionary NSGA-III (NSGA-III-COE) incorporated with the multi-group co-evolution and the natural selection is proposed. By comparing with three NSGA-III variants and five multi-objective evolutionary algorithms (MOEAs) on 27 well-known FJSP benchmark instances, it is found that the NSGA-III-COE greatly improves the speed of convergence and the ability to jump out of local optimum while maintaining the diversity of the population. From the experimental results, it can be concluded that the NSGA-III-COE has significant advantages in solving the low carbon MO-FJSP.
Highlights
The flexible job scheduling problem (FJSP) is an extension of the classic job scheduling problem (JSP) and is closer to the actual production environment
By studying the differences in exploration and developmental capabilities of different NSGA-III variants in the MO-FJSP decision space, indicator-based thought is introduced into NSGA-III, a genetic model of multiple populations and multiple crossover operators is established, and a new evolutionary mechanism is proposed
In order to verify the advantages of the NSGA-III-COE in the MO-FJSP decision space exploration and development capabilities, a large number of computational experiments were carried out
Summary
The flexible job scheduling problem (FJSP) is an extension of the classic job scheduling problem (JSP) and is closer to the actual production environment. A large number of research results have appeared [8,9,10,11,12,13,14,15,16,17,18,19] In these studies, the objective function of the problem is rarely to minimize carbon emissions or total energy consumption. This paper establishes an MO-FJSP model targeting carbon emissions, the completion time, and the machine load and modifies NSGA-III [20]. By studying the differences in exploration and developmental capabilities of different NSGA-III variants in the MO-FJSP decision space, indicator-based thought is introduced into NSGA-III, a genetic model of multiple populations and multiple crossover operators is established, and a new evolutionary mechanism is proposed. Quantities of experiments in this paper prove that the NSGA-III-COE achieves good results in solving the low carbon MO-FJSP and verifies the advantages and the competitiveness of the NSGA-III-COE in solving the low carbon MO-FJSP
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