An Indicator-Based Many-Objective Evolutionary Algorithm With Adaptive Reference Points Assisted by Growing Neural Gas Network

Many-objective optimization problems (MaOPs) pose significant challenges to the traditional multi-objective evolutionary algorithms (MOEAs) due to the loss of selection pressure. Recently, specific many-objective evolutionary algorithms (MaOEAs) have been proposed to solve MaOPs, among which the indicator-based MaOEAs are easy-to-use with good versatility. Inverted generational distance (IGD) is a reliable performance indicator to quantify the performance of MOEAs and MaOEAs. However, the bottleneck of applying IGD as the selection indicator in MaOEAs is the high dependence on the reference points specification over the Pareto front (PF). Most existing studies use the non-dominated solutions or the uniformly sampled points on the hyperplane as the reference points, which show poor adaptation in solving problems with various PF shapes. To address this issue, we propose to adaptively learn the distribution of the reference points using growing neural gas (GNG) network. To this end, a modified online GNG is designed to learn the topological structure of the PF using both the solutions stored in an external archive and the current population as the training data. The neurons in the GNG network and the normalized solutions in the archive are seen as the approximated reference points, based on which the IGD indicator contribution of each solution can be calculated to guide the evolutionary search. The experimental studies compare the proposed algorithm with eight state-of-the-art MaOEAs on solving 21 benchmark MaOPs. The results demonstrate that the proposed algorithm can achieve highly competitive performance when solving problems with both regular and irregular PFs.