Specification of Genetic Search Directions in Cellular Multi-objective Genetic Algorithms

When we try to implement a multi-objective genetic algorithm (MOGA) with variable weights for finding a set of Pareto optimal solutions, one difficulty lies in determining appropriate search directions for genetic search. In our MOGA, a weight value for each objective in a scalar fitness function was randomly specified. Based on the fitness function with the randomly specified weight values, a pair of parent solutions are selected for generating a new solution by genetic operations. In order to find a variety of Pareto optimal solutions of a multi-objective optimization problem, weight vectors should be distributed uniformly on the Pareto optimal surface. In this paper, we propose a proportional weight specification method for our MOGA and its variants. We apply the proposed weight specification method to our MOGA and a cellular MOGA for examining its effect on their search ability.