Hybridization of evolutionary algorithms with local search (LS) has already been investigated in many studies. Such a hybrid algorithm is often referred to as a memetic algorithm. Hart investigated the following four questions for designing efficient memetic algorithms for single-objective optimization: (1) How often should LS be applied? (2) On which solutions should LS be used? (3) How long should LS be run? (4) How efficient does LS need to be? When we apply LS to an evolutionary multiobjective optimization (EMO) algorithm, another question arises: (5) To which direction should LS drive? This paper mainly addresses the final issue together with the others. We apply LS to the set of non-dominated solutions that is stored separately from the population governed by genetic operations in a cellular multiobjective genetic algorithm (C-MOGA). The appropriate direction for the non-dominated solutions is attained in experiments on multiobjective classification problems.
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