A Localized High-Fidelity-Dominance based Many-Objective Evolutionary Algorithm

—Over the last decade or more, the development of Many-objective Evolutionary Algorithms (MaOEAs) ca-pable of dealing with four or more objectives simultaneously has been of dominant interest for the researchers. The associated challenges relate to - the inability of the Pareto-dominance concept to induce selection pressure for convergence, representation of a large-dimensional Pareto front with a limited set of points, and difficulty in visualization and decision making. This has led researchers to recognize the utility of the use of reference vectors to ensure uniformity/diversity in a large-dimensional space even with a reasonably limited number of points. In effect, decomposition-based MaOEAs and even their hybrids which conjunctly rely on Pareto-dominance for convergence, have demonstrated a lot of promise. This paper proposes a novel hybrid MaOEA, namely, HFiDEA, where in diversity is ensured through the use of reference vectors, while convergence in pursued through the newly proposed localized high fidelity dominance definition. The latter, referred to as lhf-dominance , marks the first attempt to overcome the limitations of Pareto-dominance by factoring - the number of objectives in which a solution is better or worse, than the other; the degree by which a solution is better or worse in the objectives, than the other; and the scope for incorporating decision maker’s preferences between objectives. Besides these fundamental contributions, this paper also addresses on-the-fly timing for nadir point estimation and self-termination of HFiDEA. While the former positively impacts diversity maintenance, the latter is critically important when the Pareto-front is not known a priori. The efficacy of HFiDEA is demonstrated through its comparison with other MaOEAs, over a wide range of test problems.

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