Adaptive directional local search strategy for hybrid evolutionary multiobjective optimization

A novel adaptive local search method is developed for hybrid evolutionary multiobjective algorithms (EMOA) to improve convergence to the Pareto front in multiobjective optimization. The concepts of local and global effectiveness of a local search operator are suggested for dynamic adjustment of adaptation parameters. Local effectiveness is measured by quantitative comparison of improvements in convergence made by local and genetic operators based on a composite objective. Global effectiveness is determined by the ratio of number of local search solutions to genetic search solutions in the nondominated solution set. To be consistent with the adaptation strategy, a new directional local search operator, eLS (efficient Local Search), minimizing the composite objective function is designed. The search direction is determined using a centroid solution of existing neighbor solutions without making explicit calculations of gradient information. The search distance of eLS decreases adaptively as the optimization process converges. Performances of hybrid methods NSGA-II + eLS are compared with the baseline NSGA-II and NSGA-II + HCS1 for multiobjective test problems, such as ZDT and DTLZ functions. The neighborhood radius and local search probability are selected as adaptation parameters. Results show that the present adaptive local search strategy can provide significant convergence enhancement from the baseline EMOA by dynamic adjustment of adaptation parameters monitoring the properties of multiobjective problems on the fly.