Adaptive diversity maintenance and convergence guarantee in multiobjective evolutionary algorithms

The issue of obtaining a well-converged and well-distributed set of Pareto optimal solutions efficiently and automatically is crucial in multiobjective evolutionary algorithms (MOEAs). Many studies have proposed different evolutionary algorithms that can progress towards Pareto optimal sets with a wide-spread distribution of solutions. However, most mathematically convergent MOEAs desire certain prior knowledge about the objective space in order to efficiently maintain widespread solutions. We propose, based on our novel E-dominance concept, an adaptive rectangle archiving (ARA) strategy that overcomes this important problem. The MOEA with this archiving technique provably converges to well-distributed Pareto optimal solutions without prior knowledge. ARA complements the existing archiving techniques, and is useful to both researchers and practitioners.