On operators and search space topology in multi-objective flow shop scheduling

Abstract

Multi-objective optimization using evolutionary algorithms identifies Pareto-optimal alternatives or their close approximation by means of a sequence of successive local improvement moves. While several successful applications to combinatorial optimization problems are known, studies of underlying problem structures are still scarce. The paper presents a study of the problem structure of multi-objective permutation flow shop scheduling problems and investigates the effectiveness of local search neighborhoods within an evolutionary search framework. First, small problem instances with up to six objective functions for which the optimal alternatives are known are studied. Second, benchmark instances taken from literature are investigated. It turns out for the investigated data sets that the Pareto-optimal alternatives are found relatively concentrated in alternative space. Also, it can be shown that no single neighborhood operator is able to equally identify all Pareto-optimal alternatives. Taking this into consideration, significant improvements have been obtained by combining different neighborhood structures into a multi-operator search framework.