A hybrid multi-objective extremal optimisation approach for multi-objective combinatorial optimisation problems

Extremal optimisation (EO) is a relatively recent nature-inspired heuristic whose search method is especially suitable to solve combinatorial optimisation problems. To date, most of the research in EO has been applied for solving single-objective problems and only a relatively small number of attempts to extend EO toward multi-objective problems. This paper presents a hybrid multi-objective version of EO (HMEO) to solve multi-objective combinatorial problems. This new approach consists of a multi-objective EO framework, for the coarse-grain search, which contains a novel multi-objective combinatorial local search framework for the fine-grain search. The chosen problems to test the proposed method are the multi-objective knapsack problem and the multi-objective quadratic assignment problem. The results show that the new algorithm is able to obtain competitive results to SPEA2 and NSGA-II. The non-dominated points found are well-distributed and similar or very close to the Pareto-front found by previous works.