Controlled Elitist Non-dominated Sorting Genetic Algorithms for Better Convergence

Preserving elitism is found to be an important issue in the study of evolutionary multi-objective optimization (EMO). Although there exists a number of new elitist algorithms, where elitism is introduced in different ways, the extent of elitism is likely to be an important matter. The desired extent of elitism is directly related to the so-called exploitation-exploration issue of an evolutionary algorithm (EA). For a particular recombination and mutation operators, there may exist a selection operator with a particular extent of elitism that will cause a smooth working of an EA. In this paper, we suggest an approach where the extent of elitism can be controlled by fixing a user-defined parameter. By applying an elitist multi-objective EA (NSGA-II) to a number of diffcult test problems, we show that the NSGA-II with controlled elitism has much better convergence property than the original NSGA-II. The need for a controlled elitism in evolutionary multi-objective optimiza- tion, demonstrated in this paper should encourage similar or other ways of implementing controlled elitism in other multi-objective evolutionary algorithms.