Improved NSGA-II for energy-efficient distributed no-wait flow-shop with sequence-dependent setup time

Abstract

This paper addresses a multi-objective energy-efficient scheduling problem of the distributed permutation flowshop with sequence-dependent setup time and no-wait constraints (EEDNWFSP), which have important practical applications. Two objectives minimization of both makespan and total energy consumption (TEC) are considered simultaneously. To address this problem, a new mixed-integer linear programming (MILP) model is formulated. Considering the issues faced in solving large-scale instances, an improved non-dominated sorting genetic algorithm (INSGA-II) is further proposed that uses two variants of the Nawaz-Enscore-Ham heuristic (NEH) to generate high-quality initial population. Moreover, two problem-specific speed adjustment heuristics are presented, which can enhance the qualities of the obtained non-dominated solutions. In addition, four local and two global search operators are designed to improve the exploration and exploitation abilities of the proposed algorithm. The effectiveness of the proposed algorithm was verified using extensive computational tests and comparisons. The experimental results show that the proposed INSGA-II is more effective compared to other efficient multi-objective algorithms.