Effects of diversity control in single-objective and multi-objective genetic algorithms

Abstract

This paper covers an investigation on the effects of diversity control in the search performances of single-objective and multi-objective genetic algorithms. The diversity control is achieved by means of eliminating duplicated individuals in the population and dictating the survival of non-elite individuals via either a deterministic or a stochastic selection scheme. In the case of single-objective genetic algorithm, onemax and royal road R 1 functions are used during benchmarking. In contrast, various multi-objective benchmark problems with specific characteristics are utilised in the case of multi-objective genetic algorithm. The results indicate that the use of diversity control with a correct parameter setting helps to prevent premature convergence in single-objective optimisation. Furthermore, the use of diversity control also promotes the emergence of multi-objective solutions that are close to the true Pareto optimal solutions while maintaining a uniform solution distribution along the Pareto front.

Theoretical analysis of diversity mechanisms for global exploration

“…The probability that during initialization either 0 n or 1 n is created is bounded by µ · 2 −n+1 , hence exponentially small. In the following, we assume that such an atypical initialization does not happen as this assumption only introduces an error probability of o (1).…”

“…Up to now, the use of diversity mechanisms has been assessed mostly by means of empirical investigations (e. g., [1,17]). Theoretical runtime analyses involving diversity mechanisms mostly use these mechanisms to enhance the performance of crossover.…”

Compressed-Objective Genetic Algorithm

“…Among these techniques, the genetic algorithm has been established as one of the most widely used methods [1,2,3,4,5,6,7,8]. Due to the parallel search nature of the algorithm, the approximation of multiple optimal solutions-the Pareto optimal solutions, comprising of non-dominated individuals-can be effectively executed.…”

“…A number of strategies have been successfully integrated into genetic algorithms to solve these problems, including a direct modification of selection pressure [1,2,3] and elitism [4,5,6,7,8]. Although they have been proven to significantly improve the search performance of genetic algorithms, virtually all reported results deal with only few objectives.…”

Rigorous analyses of simple diversity mechanisms

“…It has been observed in numerous experiments [1,15] that the right use of a diversity strategy can play a key role for the success of an EA. As it is important to understand in practice successful algorithms also from a theoretical point of view, it is desirable to strengthen the theoretical understanding of diversity mechanisms.…”