A partial enumeration heuristic for multi-objective flowshop scheduling problems

Abstract

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.

Keywords:

• flowshop scheduling
• multi-objective optimization
• combinatorial optimization
• heuristic

Acknowledgements

This research was partially funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). Part of this work was developed while Vinícius A Armentano was on a sabbatical year at the College of Business and Administration of the University of Colorado at Boulder with a fellowship from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP). We are also grateful to the referees for their valuable comments.