Adaptive Normal-Boundary Intersection Directions for Evolutionary Many-Objective Optimization with Complex Pareto Fronts

Decomposition-based Many-Objective Evolutionary Algorithms (MaOEAs) usually adopt a set of pre-defined distributed weight vectors to guide the solutions towards the Pareto optimal Front (PF). However, when solving Many-objective Optimization Problems (MaOPs) with complex PFs, the effectiveness of MaOEAs with a fixed set of weight vectors may deteriorate which will lead to an imbalance between convergence and diversity of the solution set. To address this issue, we propose here an Adaptive Normal-Boundary Intersection Directions Decomposition-based Evolutionary Algorithm (ANBID-DEA), which adaptively updates the Normal-Boundary Intersection (NBI) directions used in MP-DEA. In our work, we assist the selection mechanism by progressively adjusting the NBI directions according to the distribution of the population to uniformly cover all the parts of the complex PFs (i.e., those that are disconnected, strongly convex, degenerate, etc.). Our proposed ANBID-DEA is compared with respect to five state-of-the-art MaOEAs on a variety of unconstrained benchmark problems with up to 15 objectives. Our results indicate that ANBID-DEA has a competitive performance on most of the considered MaOPs.