Abstract: The rank and density of the population are first defined and then the density distribution variance and uniform distribution index function of solutions in objective space are clearly given. The rank is a measure of the quality of solutions, and the density distribution variance is a measure of the uniformity of the distribution of solutions. Using these two measures as two objective functions, the multi-objective optimization problem is finally converted into a two objective optimization problem. For the transformed problem, a novel genetic algorithm is proposed. In designing the algorithm, the uniform distribution index function is integrated into the mutation operator to adaptively adjust the search. As a result, the solutions will gradually move to the entire Pareto front and their distribution will gradually become uniform.

Key words: new model, multi-objective genetic algorithm, rank and density, uniform distribution