A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Many-objective optimization refers to the optimization problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence to the Pareto front for such problems, as almost all solutions in the population become non-dominated, resulting in loss of convergence pressure. However, for some problems, it may be possible to generate the Pareto front using only a few of the objectives, rendering the rest of the objectives redundant. Such problems may be reducible to a manageable number of relevant objectives, which can be optimized using conventional multiobjective evolutionary algorithms (MOEAs). For dimensionality reduction, most proposals in the paper rely on analysis of a representative set of solutions obtained by running a conventional MOEA for a large number of generations, which is computationally overbearing. A novel algorithm, Pareto corner search evolutionary algorithm (PCSEA), is introduced in this paper, which searches for the corners of the Pareto front instead of searching for the complete Pareto front. The solutions obtained using PCSEA are then used for dimensionality reduction to identify the relevant objectives. The potential of the proposed approach is demonstrated by studying its performance on a set of benchmark test problems and two engineering examples. While the preliminary results obtained using PCSEA are promising, there are a number of areas that need further investigation. This paper provides a number of useful insights into dimensionality reduction and, in particular, highlights some of the roadblocks that need to be cleared for future development of algorithms attempting to use few selected solutions for identifying relevant objectives.