On a Multi – Objective Evolutionary Algorithm and Its Conver gence to the Pareto Set

Although there are many versions of evolutionary algorithms that are tailored to multi–criteria optimization, theoret ical results are apparently not yet available. Here, it is shown that results known from the theory of evolutionary algorithms in case of single criteri on optimization do not carry over to the multi–criterion case. At first, three different step size rules are investigated numerically for a selected prob lem with two conflicting objectives. The empirical results obtained by thes e experiments lead to the observation that only one of these step size rules may h ave the property to ensure convergence to the Pareto set. A theoretical a n lysis finally shows that a special version of an evolutionary algorithm wi th this step size rule converges with probability one to the Pareto set for thetest problem under consideration. Keywords—multi–criteriaoptimization, evolutionary algorithms, stochastic convergence to Pareto set