Evolutionary algorithm with a directional local search for multiobjective optimization in combinatorial problems

Evolutionary algorithms (EAs) are often employed to multiobjective optimization, because they process an entire population of solutions which can be used as an approximation of the Pareto front of the tackled problem. It is a common practice to couple local search with evolutionary algorithms, especially in the context of combinatorial optimization. In this paper a new local search method is proposed that utilizes the knowledge concerning promising search directions. The proposed method can be used as a general framework and combined with many methods of iterating over a neighbourhood of an initial solution as well as various decomposition approaches. In the experiments the proposed local search method was used with an EA and tested on 2-, 3- and 4-objective versions of two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the quadratic assignment problem (QAP). For comparison two well-known local search methods, one based on Pareto dominance and the other based on decomposition, were used with the same EA. The results show that the EA coupled with the directional local search yields better results than the same EA coupled with any of the two reference methods on both the TSP and QAP problems.