On Geometrically Fast Convergence to Optimal Dominated Hypervolume of Set-based Multiobjective Evolutionary Algorithms

The Pareto front of a multiobjective optimization problem can be approximated neatly by some versions of evolutionary algorithms. The quality of the approximation can be measured by the hypervolume that is dominated by the approximation. Open questions concern the existence of population-based evolutionary algorithms whose population converge to an approximation of the Pareto front with maximal dominated hypervolume for a given reference point and, if applicable, the convergence velocity. Here, the existence of such an algorithm is proven by providing a concrete example that converges to the maximal dominated hypervolume geometrically fast.