Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization

This paper studies the fuzzification of the Pareto dominance relation and its application to the design of Evolutionary Multi-Objective Optimization algorithms. A generic ranking scheme is presented that assigns dominance degrees to any set of vectors in a scale-independent, nonsymmetric and set-dependent manner. Based on such a ranking scheme, the vector fitness values of a population can be replaced by the computed ranking values (representing the ”dominating strength” of an individual against all other individuals in the population) and used to perform standard single-objective genetic operators. The corresponding extension of the Standard Genetic Algorithm, so-called Fuzzy-Dominance-Driven GA (FDD-GA), will be presented as well. To verify the usefulness of such an approach, an analytic study of the Pareto-Box problem is provided, showing the characteristical parameters of a random search for the Pareto front in a unit hypercube in arbitrary dimension. The basic problem here is the loss of dominated points with increasing problem dimension, which can be successfully resolved by basing the search procedure on the fuzzy dominance degrees.