On gradient based local search methods in unconstrained evolutionary multi-objective optimization

Evolutionary algorithms have been adequately applied in solving single and multi-objective optimization problems. In the singleobjective case various studies have shown the usefulness of combining gradient based classical methods with evolutionary algorithms. However there seems to be limited number of such studies for the multi-objective case. In this paper, we take two classical methods for unconstrained multi-optimization problems and discuss their use as a local search operator in a state-of-the-art multi-objective evolutionary algorithm. These operators require gradient information which is obtained using finite difference method and using a stochastic perturbation technique requiring only two function evaluations. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of resulting hybrid algorithms in solving a large class of complex multi-objective optimization problems. We also discuss a new convergence metric which is useful as a stopping criteria for problems having an unknown Paretooptimal front.