Summary: A multiobjective variable neighborhood descent (VND) based heuristic is developed to solve a bicriteria parallel machine scheduling problem. The problem considers two objectives, one related to the makespan and the other to the flow time, where the setup time depends on the sequence, and the machines are identical. The heuristic has a set of neighborhood structures based on swap, remove, and insertion moves. We propose changing the local search inside the VND to a sequential search through the neighborhoods to obtain nondominated points for the Pareto-front quickly. In the numerical tests, we consider a single-objective version of the heuristic, comparing the results on 510 benchmark instances to show that it is quite effective. Moreover, new instances are generated in accordance with the literature for the bicriteria problem, showing the ability of the proposed heuristic to return an efficient set of nondominate solutions compared with the well-known nondominated sorting genetic algorithm II.
{© 2019 The Authors. International Transactions in Operational Research © 2019 International Federation of Operational Research Societies}