Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms

Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the epsilon-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the epsilon-dominance concept, there are still difficulties in computing an appropriate value of epsilon that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone epsilon-dominance, which is a variant of the epsilon-dominance, to overcome these limitations. Cone epsilon-dominance maintains the good convergence properties of epsilon-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone epsilon-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the epsilon-dominance.