Genetic algorithm convergence analysis using a unified representation of genes and the hamming distance

Abstract

This paper first introduces a unified representation of both real-coded genes and binary-coded genes, in order to efficiently analyse the convergence of a genetic algorithm. In the literature, the syntagm "the entire population premature convergence" is used with the meaning of closing the evolution before reaching the optimal point. It can be emphasised only on a test function with known landscape. If the function landscape is unknown, one can only notice the population convergence. This paper aims to answer to the question: "how can we influence the control parameters of the genetic algorithm so that the exploration period of the parameter space be longer and the risk of the premature convergence be reduced?" The answer to the above question implies the selection of a crossover operator with good performance in the landscape exploration and the use of two indicators for the detection of the population convergence. In order to choose the appropriate control parameters of the genetic algorithm, the fitness function landscape must be taken into consideration.