Clustering based online automatic objective reduction to aid many-objective optimization

Abstract

Starting from scalability to visualization, several challenges come into play when multi-objective optimization algorithms are applied to many-objective optimization problems. These challenges can be tackled using objective reduction algorithms. This work proposes a correlation based objective reduction algorithm. The set of points representing the Pareto-Front are clustered based on correlation distance. The constituent objectives belonging to the most compact cluster are pruned except the centroid. The reduction and search proceed while alternating between full set and reduced set. Number of clusters is gradually increased in order to zoom in the correlation structure of the objectives and the algorithm stops when the number of clusters equals to the number of objectives. This objective reduction leads to automatic detection of number of objectives, faster convergence as one or more number of objectives can be eliminated in reduction stages and improved performance as both global exploration and local exploitation of the search space are considered. The proposed approach of objective reduction is coupled with a differential evolution based multi-objective optimization technique to develop a solution framework for many-objective optimization problems. The efficacy of the proposed approach is tested on several benchmark functions viz. DTLZ1, DTLZ2, DTLZ3 and DTLZ4 for 10 and 20 objectives. Convergence metric and hypervolume indicator are used for comparing the performance of the proposed solution framework with other popular multi-objective optimization algorithms.