An Analytic Expression of Performance Rate, Fitness Value and Average Convergence Rate for a Class of Evolutionary Algorithms

An important theoretical question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality of evolutionary algorithms in terms of the performance rate, which is defined by the difference between 1 and the approximation ratio of the best solution found in each generation. The performance rate can be represented by a function of time. With the help of matrix analysis, it is possible to obtain an exact expression of such a function. For the first time, an analytic expression for calculating the performance rate is presented in this paper for a class of evolutionary algorithms, that is, (1+1) strictly elitist evolution algorithms. Furthermore, analytic expressions for calculate the fitness value and the average convergence rate in each generation are also derived for this class of evolutionary algorithms. The approach is promising, and it can be extended to non-elitist or population-based algorithms too.