Can evolutionary programs efficiently adapt to solve optimization problems? This paper analyzes the convergence properties of evolutionary programs with a specific focus on self-adaptation of strategy parameters. Formal proofs of the long-term behavior produced by our self-adaptation method are included. Both elitist and non-elitist ES variants are analyzed. Evolutionary programs are capable of finding good solutions to difficult optimization problems. Previous analysis of their convergence properties has normally assumed the strategy parameters are kept constant, although in practice these parameters are dynamically altered. In this paper, we propose a modified version of the 1/5-success rule for self-adaptation in evolution strategies (ES). The work offers a modified version of the 1/5-success rule for self-adaptation in evolution strategies. This includes formal proofs of the long-term behavior produced by the self-adaptation method for both elitist and non-elitist ES variants. Preliminary tests indicate an ES with our modified self-adaptation method compares favorably to both a non-adapted ES and a 1/5-success rule adapted ES. This suggests that the proposed self-adaptation method enhances the performance of evolutionary programs, offering a more robust approach to optimization. Thus formal proofs of the long-term behavior produced by our self-adaptation method are included.
Published in Evolutionary Computation, this paper aligns with the journal's focus on computational methods inspired by natural evolution. It analyzes the convergence properties of evolutionary programs with self-adaptation, fitting within the journal's scope of advancing knowledge in evolutionary computation and optimization techniques.