Ranking-based multi/many-objective evolutionary optimization with hierarchical evaluation rules and its application in water distribution network

Abstract

To solve multi/many-objective optimization problems characterized by complex Pareto fronts, we propose a two-phase ranking-based multi-objective evolutionary algorithm with hybrid convergence rules. Firstly, we introduce a novel hybrid convergence criterion by integrating Pareto dominance, localized pruning power (LPP), and distance-based measure. Secondly, we design a two-phase ranking-based selection strategy. Specifically, we employ the acute angle between objective vector and reference vector to divide the current population into multiple sub-populations. In the first-phase ranking, the solutions within each subpopulation are sorted according to the hybrid convergence rule. The best solutions are chosen based on the angle-based diversity criterion into separate fronts. In the second-phase selection, a specific number of solutions with best diversity are further selected to the next generation based upon their front-level assignments. To obtain better diversity of selected solutions, we employ the maximum angle between solutions and the sum of normalized objectives of solutions to assist the selecting process. The experimental results, which encompass benchmark problems involving up to 10 objectives as well as two real-world application instances, validating our proposed algorithm’s competitiveness and effectiveness.