Adaptive density-based clustering for many objective similarity or redundancy evolutionary optimization

With the increase in the number of objectives, the curse of dimensionality will eventually occur in some practical multi-objective optimization problems. This situation will become even worse when the multi-objective changes into many-objective optimization problems (MaOPs) with more than 15 objectives, which makes it more difficult for evolutionary computing. The persistent focus within the field has been on how to reduce the scale of problem-solving and alleviate the complexity of problems by analyzing the linear or nonlinear relationships between various objectives. Traditionally, the objectives relationships are typically presumed to be in conflict with each other, and yet similarity or redundancy may exist in some MaOPS. In this study, an adaptive evolutionary many-objective optimization algorithm with similarity or redundancy reduction based on adaptive density clustering denoted as AENec is proposed for MaOPs. In the AENec, the similarity or redundancy between objectives is analyzed for MaOPs for the first time and the redundance analyses method for objectives(RAMO) is designed with the limited Pareto front structure information during classic MaOPs evolutionary optimization(CMEVO). An adaptive density-based clustering algorithm (AEDBSCAN) is designed to configure the number of adaptive density clusters and automatically determine the extent of objective reduction. In addition, to avoid inconsistencies between the Pareto solutions post-reduction and the original MaOPs, the efficient non-redundant objective aggregation function (NROAF) is also devised. The parameters and algorithmic components of AENec are successfully analyzed on random test cases. The statistical results demonstrate that the proposed method outperforms other competitive algorithms on most test benchmarks and also especially verifies its effectiveness on MaOPs with similar or redundant objective relationships.