A Many-Objective Evolutionary Algorithm With Pareto-Adaptive Reference Points

We propose a new many-objective evolutionary algorithm with Pareto-adaptive reference points. In this algorithm, the shape of the Pareto-optimal front (PF) is estimated based on a ratio of Euclidean distances. If the estimated shape is likely to be convex, the nadir point is used as the reference point to calculate the convergence and diversity indicators for individuals. Otherwise, the reference point is set to the ideal point. In addition, the estimation of the nadir point is different from what was widely used in the literature. The nadir point, together with the ideal point, provides a feasible way to deal with dominance resistant solutions, which are difficult to be detected and eliminated in Pareto-based algorithms. The proposed algorithm is compared with the state-of-the-art many-objective optimization algorithms on a number of unconstrained and constrained test problems with up to 15 objectives. The experimental results show that it performs better than other algorithms in most of the test instances. Moreover, the new algorithm shows good performance on problems whose PFs are irregular (being discontinuous, degenerated, bent, or mixed). The observed high performance and inherent good properties (such as being free of weight vectors and control parameters) make the new proposal a promising tool for other similar problems.