  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.
