A Set-Based Genetic Algorithm for Interval Many-Objective Optimization Problems

Interval many-objective optimization problems (IMaOPs), involving more than three objectives and at least one subjected to interval uncertainty, are ubiquitous in real-world applications. However, there have been very few effective methods for solving these problems. In this paper, we proposed a set-based genetic algorithm to effectively solve them. The original optimization problem was first transformed into a deterministic bi-objective problem, where new objectives are hyper-volume and imprecision. A set-based Pareto dominance relation was then defined to modify the fast nondominated sorting approach in NSGA-II. Additionally, set-based evolutionary schemes were suggested. Finally, our method was empirically evaluated on 39 benchmark IMaOPs as well as a car cab design problem and compared with two typical methods. The numerical results demonstrated the superiority of our method and indicated that a tradeoff approximate front between convergence and uncertainty can be produced.