Multi-objective Variable Neighborhood Search algorithms for a just-in-time single machine scheduling problem

In this paper, we analyze the performance of two multi-objective algorithms based on the Variable Neighborhood Search (VNS). The first algorithm was proposed by Geiger and the second algorithm is proposed in this work. The algorithms are applied to solve the single machine scheduling problem with sequence dependent setup times and distinct due windows. We consider minimizing the total weighted earliness/tardiness and the total flow time criteria. The proposed multi-objective VNS algorithm generates good non-dominated solutions (an approximation of the Pareto-optimal solutions) in reasonable computation time. The performance of the algorithms is tested on a set of medium and large size instances. The computational results show that our approach is promising heuristic for multi-objective optimization.