A Multi-Objective Particle Swarm Optimization Algorithm for a Possibilistic Open Shop Problem to Minimize Weighted Mean Tardiness and Weighted Mean Completion Times

We consider an open shop scheduling problem. At first, a bi-objective possibilistic mixed-integer programming formulation is developed. The inherent uncertainty in processing times and due dates as fuzzy parameters, machine-dependent setup times and removal times are the special features of this model. The considered bi-objectives are to minimize the weighted mean tardiness and weighted mean completion times. After converting the original formulation into a single-objective crisp one by using an interactive approach and obtaining the Pareto-optimal solutions for small-sized instances, an efficient multi-objective particle swarm optimization (MOPSO) is proposed in order to achieve a good approximate Pareto-optimal set for medium and large-sized examples. This algorithm exploits new selection regimes of the literature for the global best and personal best. Furthermore, a modified decoding scheme is designed to reduce the search area in the solution space, and a local search algorithm is proposed to generate initial particle positions. Finally, the efficiency of the proposed MOPSO (PMOPSO) is shown by comparing with the common MOPSO (CMOPSO) by the use of the design of experiments (DOE) based on three comparison metrics.