An Analytic Expression of Relative Approximation Error for a Class of Evolutionary Algorithms
This work addresses the need for theoretical analysis of solution quality in evolutionary computation, though it is incremental as it focuses on a specific class of algorithms.
The paper tackles the problem of quantifying solution quality in evolutionary algorithms by deriving an analytic expression for the relative approximation error as a function of generations, specifically for (1+1) strictly elitist evolutionary algorithms, and also provides expressions for fitness value and average convergence rate.
An important question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality in terms of the relative approximation error, which is defined by the error between 1 and the approximation ratio of the solution found by an evolutionary algorithm. Since evolutionary algorithms are iterative methods, the relative approximation error is a function of generations. With the help of matrix analysis, it is possible to obtain an exact expression of such a function. In this paper, an analytic expression for calculating the relative approximation error is presented for a class of evolutionary algorithms, that is, (1+1) strictly elitist evolution algorithms. Furthermore, analytic expressions of 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.