Abstract. 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 -dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the -dominance concept, there are still difficulties in computing an appropriate value of 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 -dominance, which is a variant of thedominance, to overcome these limitations. Cone -dominance maintains the good convergence properties of -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 -dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the -dominance.
Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) represent a widely used class of population-based metaheuristics for the solution of multicriteria optimization problems. We introduce the MOEADr package, which offers many of these variants as instantiations of a componentoriented framework. This approach contributes for easier reproducibility of existing MOEA/D variants from the literature, as well as for faster development and testing of new composite algorithms. The package offers an standardized, modular implementation of MOEA/D based on this framework, which was designed aiming at providing researchers and practitioners with a standard way to discuss and express MOEA/D variants. In this paper we introduce the design principles behind the MOEADr package, as well as its current components. Three case studies are provided to illustrate the main aspects of the package.
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