Adaptive Diversity Maintenance and Convergence Guarantee in Multiobjective Evolutionary Algorithms

The trade-off between obtaining a wellconverged and well-distributed set of Pareto optimal solutions, and obtaining them efficiently and automatically is an important issue in multi-objective evolutionary algorithms (MOEAs). Many studies have depicted different approaches that evolutionary algorithms can progress towards the Pareto optimal set with a wide-spread distribution of solutions. However, most mathematically convergent MOEAs desire certain prior knowledge of the solution space in order to efficiently maintain widespread solutions. In this paper, we propose, based on the E-dominance concept, an Adaptive Rectangle Archiving (ARA) strategy that overcomes this practically crucial problem. The MOEAs with this archiving technique provably converge to welldistributed Pareto sets without a priori. ARA complements the existing archiving techniques, and is useful to both researchers and practitioners.