A mutation operator based on a Pareto ranking for multi-objective evolutionary algorithms

Evolutionary Algorithms, EA's, try to imitate, in some way, the principles of natural evolution and genetics. They evolve a population of potential solutions to the problem using operators such as mutation, crossover and selection. In general, the mutation operator is responsible for the diversity of the population and helps to avoid the problem of premature convergence to local optima (a premature stagnation of the search caused by the lack of population diversity). In this paper we present a new mutation operator in the context of Multi-Objective Evolutionary Algorithms, MOEA's, which makes use of the definition of Pareto optimality and manages the maximal amplitude or maximal step size of the mutation according to the Pareto layer of the individual and also of the iteration number. The behaviour of our mutation operator reveals that the use of variation operators which take into consideration the quality of the solutions, in terms of Pareto dominance or Pareto layers, can help to improve them. The Pareto based mutation operator proposed is compared with four well established and extensively used mutation operators: random mutation, non-uniform mutation, polynomial mutation and Gaussian mutation. The accomplished experiments reveal that our mutation operator performs, in most of the test problems considered, better than the others.