Mating Scheme for Controlling the Diversity-Convergence Balance for Multiobjective Optimization

The aim of this paper is to clearly demonstrate the potential ability of a similarity-based mating scheme to dynamically control the balance between the diversity of solutions and the convergence to the Pareto front in evolutionary multiobjective optimization. The similarity-based mating scheme chooses two parents in the following manner. For choosing one parent (say Parent A), first a pre-specified number of candidates (say α candidates) are selected by iterating the standard fitness-based binary tournament selection. Then the average solution of those candidates is calculated in the objective space. The most similar or dissimilar candidate to the average solution is chosen as Parent A. When we want to increase the diversity of solutions, the selection probability of Parent A is biased toward extreme solutions by choosing the most dissimilar candidate. The strength of this diversity-preserving effort is adjusted by the parameter α . We can also bias the selection probability toward center solutions by choosing the most similar candidate when we want to decrease the diversity. The selection probability of the other parent (i.e., the mate of Parent A) is biased toward similar solutions to Parent A for increasing the convergence speed to the Pareto front. This is implemented by choosing the most similar one to Parent A among a pre-specified number of candidates (say β candidates). The strength of this convergence speed-up effort is adjusted by the parameter β . When we want to increase the diversity of solutions, the most dissimilar candidate to Parent A is chosen as its mate. Our idea is to dynamically control the diversity-convergence balance by changing the values of two control parameters α and β during the execution of evolutionary multiobjective optimization algorithms. We examine the effectiveness of our idea through computational experiments on multiobjective knapsack problems.