Some Issues on the Implementation of Local Search in Evolutionary Multiobjective Optimization

This paper discusses the implementation of local search in evolutionary multiobjective optimization (EMO) algorithms for the design of a simple but powerful memetic EMO algorithm. First we propose a basic framework of our memetic EMO algorithm, which is a hybrid algorithm of the NSGA-II and local search. In the generation update procedure of our memetic EMO algorithm, the next population is constructed from three populations: the current population, its offspring population generated by genetic operations, and an improved population obtained from the offspring population by local search. We use Pareto ranking and the concept of crowding in the same manner as in the NSGA-II for choosing good solutions to construct the next population from these three populations. For implementing local search in our memetic EMO algorithm, we examine two approaches, which have been often used in the literature: One is based on Pareto ranking, and the other is based on a weighted scalar fitness function. The main difficulty of the Pareto ranking approach is that the movable area of the current solution by local search is very small. On the other hand, the main difficulty of the weighted scalar approach is that the offspring population can be degraded by local search. These difficulties are clearly demonstrated through computational experiments on multiobjective knapsack problems using our memetic EMO algorithm. Our experimental results show that better results are obtained from the weighted scalar approach than the Pareto ranking approach. For further improving the weighted scalar approach, we examine some tricks that can be used for overcoming its difficulty.