Metaheuristics for multiobjective optimization in energy-efficient job shops

Energy awareness is one of the most relevant research directions in scheduling problems. In this paper we consider the minimization of both the makespan and the energy consumption in the classical job shop scheduling problem. The energy model considered allows several possible states for the machines: off, stand-by, idle, setup and processing. To solve this multi-objective problem we propose an NSGA-II based evolutionary algorithm combined with local search and a heuristic procedure to improve the energy consumption of a given schedule. We also propose an advanced constraint programming (CP) approach as well as a Mixed-Integer Linear Programming (MILP) model, to the aim of comparing their performances against those obtained with the NSGA-II. The experimental study is performed against a benchmark set that extends by 41 instances of increasing size, the set tackled in the previous literature against the same problem. The experiments demonstrate the superiority of the NSGA-II algorithm over all other methods, despite the utilization of CP and MILP allows to draw interesting conclusions on the overall solution optimality, revealing that there is still room for further optimization.