An incremental learning evolutionary algorithm for many-objective optimization with irregular Pareto fronts

Abstract

Multi objective optimization problems (MOPs) with irregular Pareto Fronts (PFs) appear frequently in a large of practical cases. Proximity and diversity are the key indicators for decomposition-based multi-objective evolutionary algorithms (MOEA/D) to solve MOPs, which are decided by the neighborhood structure and a set of predefined direction vectors. In certain MOPs with irregular PFs, the effectiveness of MOEA/D is restricted by the shape of the PF. This limitation arises because MOEA/D generates direction vectors in a uniform manner, which can result in invalid direction vectors due to the irregularity of the PF. When dealing with many-objective optimization problems (MaOP) that have irregular PFs, such as degenerate or disconnected PFs, this decline in effectiveness becomes particularly problematic. To address this limitation, a copula incremental learning (CIL) scheme has been developed to progressively extract implicit knowledge on the appropriate distribution of direction vectors for generating non-uniform direction vectors. Additionally, a niche hierarchical selection (NHS) methodology is employed to construct the neighborhood structure and prevent the generation of duplicate solutions. These enhancements are designed to improve the overall effectiveness of MOEA/D. Efficiency is further ensured through the use of convergence-guided direction (CGD) to approximate irregular PFs. Statistical analysis indicates that the proposed method outperforms other competitive algorithms across most test benchmarks, particularly in its ability to effectively address MaOPs with irregular PFs.