Non-dominated sorting on performance indicators for evolutionary many-objective optimization

Abstract

Much attention has been paid to evolutionary multi-objective optimization approaches to efficiently solve real-world engineering problems with multiple conflicting objectives. However, the loss of selection pressure and the non-uniformity in the distribution of the Pareto optimal solutions in the objective space can impede both dominance-based and decomposition-based multi-objective optimizers when solving many-objective problems. In this work, we circumvent this issue by exploiting two performance indicators, and use these in an optimizer’s environmental selection via non-dominated sorting. This effectively converts the original many-objective problem into a bi-objective one. Our convergence performance criterion tries to balance the performance of individuals in different parts of the objective space. The angle between solutions on objective space is adopted to measure the diversity of each individual. Using these solutions can be separated into different layers easily, which is often not possible for the original many-objective optimization representation. The performance of the proposed method is evaluated on the DTLZ benchmark problems with up to 30 objectives, and MaF test suite with 10, 15, 20 and 30 objectives. The experimental results show that our proposed method is competitive compared to six recently proposed algorithms, especially for solving problems with a large number of objectives.