Solving many-objective problems using targeted search directions

Multi-objective evolutionary algorithms are efficient in solving problems with two or three objectives. However, recent studies have shown that they face many difficulties when tackling problems involving a larger number of objectives and their behaviors become similar to a random walk in the search space since most individuals become non-dominated with each others. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation called TSD-dominance (Targeted Search Directions based dominance) to deal with many-objective optimization problems. Our dominance relation has the ability to create a strict partial order on the set of Pareto-equivalent solutions using a set of well-distributed reference points, thereby producing a finer grained ranking of solutions. The TSD-dominance is subsequently used to substitute the Pareto dominance in NSGA-II. The new obtained MOEA, called TSD-NSGA-II has been statistically demonstrated to provide competitive and better results when compared with three recently proposed decomposition-based algorithms on commonly used benchmark problems involving up to twenty objectives.