A New Decomposition-Based NSGA-II for Many-Objective Optimization

Multiobjective evolutionary algorithms (MOEAs) have proven their effectiveness and efficiency in solving problems with two or three objectives. However, recent studies show that MOEAs face many difficulties when tackling problems involving a larger number of objectives as their behavior becomes similar to a random walk in the search space since most individuals are nondominated with respect to each other. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation to deal with many-objective optimization problems and a new diversity factor based on the penalty-based boundary intersection method. Our reference point-based dominance (RP-dominance), has the ability to create a strict partial order on the set of nondominated solutions using a set of well-distributed reference points. The RP-dominance is subsequently used to substitute the Pareto dominance in nondominated sorting genetic algorithm-II (NSGA-II). The augmented MOEA, labeled as RP-dominance-based NSGA-II, has been statistically demonstrated to provide competitive and oftentimes better results when compared against four recently proposed decomposition-based MOEAs on commonly-used benchmark problems involving up to 20 objectives. In addition, the efficacy of the algorithm on a realistic water management problem is showcased.