MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

This paper addresses the flexible job shop scheduling problem with controllable processing times (FJSP-CPT). The objective is to simultaneously minimize makespan and total energy consumption. To solve the problem, a mixed integer linear programming (MILP) model is developed, and then the epsilon method is used to obtain the optimal Pareto front for small-scale instances. In order to obtain approximate Pareto fronts for medium- and large-sized problems, we propose an efficient multi-objective hybrid shuffled frog-leaping algorithm (MOHSFLA). In the proposed MOHSFLA, the encoding method, the decoding method, the initiation method of the population and the evolution processes are designed. Specifically, an energy-efficient decoding with three energy-saving strategies, namely decelerating, Turning Off/On and postponing, is designed. In addition, a multi-objective variable local search (MO-VNS) algorithm is designed and embedded in the algorithm to enhance its local exploitation capability. Finally, numerical experiments are conducted to evaluate the performances of the proposed MILP model and MOHFSLA.