Adaptation of Reference Vectors for Evolutionary Many-objective Optimization of Problems with Irregular Pareto Fronts

For problems with irregular Pareto fronts, only part of the objective space is covered by optimal solutions. Most decomposition based evolutionary many-objective algorithms, however, predefine uniformly distributed weight or reference vectors, making them less suited for problems with irregular Pareto fronts, since many weight or reference vectors will be wasted. To address the above issue, this paper proposes a variant of the reference vector guided evolutionary algorithm by adjusting reference vectors according to the distribution of the solutions in the current population to make sure that most reference vectors are associated with solutions. A secondary selection criterion based on the dominance relationship is adopted in addition to the angle penalized distance based selection so that a sufficient number of solutions can survive and be passed to the next generation. Experiments on 12 irregular test problems with 60 instances show that the proposed algorithm is competitive compared to the state-of-the-art algorithms for solving problems with irregular Pareto fronts.