The convergence of a multi-objective evolutionary algorithm based on grids

Evolutionary algorithms are especially suited for multi-objective optimization problems. Many evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms are relatively scarce. This paper analyzes the convergence properties of a simple pragmatic (mu+1)-MOEA. The convergence of MOEAs is defined and the general convergence conditions are studied. Under these conditions, it is proven that the proposed (mu+1)-MOEA converges almost surely to the Pareto-optimal front.