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KKT proximity measure for testing convergence in smooth multi-objective optimization

An earlier study defined a KKT-proximity measure to test the convergence property of an evolutionary algorithm for solving single-objective optimization problems. In this paper, we extend this measure for testing convergence of a set of non-dominated solutions to the Pareto-optimal front in the case of smooth multi-objective optimization problems. Simulation results of NSGA-II on different two and three objective test problems indicate the suitability of using the proximity measure as a convergence metric for terminating a simulation of an evolutionary multi-criterion optimization algorithm.