Multi-Objective Parallel Variable Neighborhood Search for Energy Consumption Scheduling in Blocking Flow Shops

Blocking flow shop scheduling problem has been extensively studied because of its widespread industrial applications. However, the existing research mostly aims at makespan or total flow time minimization and ignores the criterion for energy saving. This paper investigates the blocking flow shop scheduling problem with both makespan and energy consumption criteria. First, the multi-objective model of blocking flow shop scheduling is formulated in consideration of machine energy consumed in blocking and idle time. Then, a multi-objective parallel variable neighborhood search (MPVNS) algorithm is proposed to solve this problem. An improved Nawaz–Enscore–Ham-based heuristic is developed to generate initial solutions, and a variable neighborhood search is designed to explore these solutions in parallel. Furthermore, an insertion-based pareto local search method is embedded to enhance the exploitation of the algorithm. Finally, in order to validate its effectiveness, the MPVNS is compare with other two effective multi-objective metaheuristics by computational experiments based on well-known benchmark instances. The experimental results illustrate that the proposed algorithm is superior to non-dominated sorting genetic algorithm (II) and bi-objective multi-start simulated annealing algorithm in terms of set coverage and hypervolume measures.