Objective reduction for many-objective optimization problems using objective subspace extraction

Multi-objective evolutionary algorithms (MOEAs) have shown their effectiveness in exploring a well converged and diversified approximation set for multi-objective optimization problems (MOPs) with 2 and 3 objectives. However, most of them perform poorly when tackling MOPs with more than 3 objectives [often called many-objective optimization problems (MaOPs)]. This is mainly due to the fact that the number of non-dominated individuals increases rapidly in MaOPs, leading to the loss of selection pressure in population update. Objective reduction can be used to lower the difficulties of some MaOPs, which helps to alleviate the above problem. This paper proposes a novel objective reduction framework for MaOPs using objective subspace extraction, named OSEOR. A new conflict information measurement among different objectives is defined to sort the relative importance of each objective, and then an effective approach is designed to extract several overlapped subspaces with reduced dimensionality during the execution of MOEAs. To validate the effectiveness of the proposed approach, it is embedded into a well-known and frequently used MOEA (NSGA-II). Several test MaOPs, including four irreducible problems (i.e. DTLZ1-DTLZ4) and a reducible problem (i.e. DTLZ5), are used to assess the optimization performance. The experimental results indicate that the performance of NSGA-II can be significantly enhanced using OSEOR on both irreducible and reducible MaOPs.