# Lyapunov design of a simple step-size adaptation strategy based on success

Claudia R. Correa, Elizabeth F. Wanner*, Carlos M. Fonseca

*Corresponding author for this work

Research output: Chapter in Book/Published conference outputConference publication

## Abstract

A simple success-based step-size adaptation rule for singleparent Evolution Strategies is formulated, and the setting of the corresponding parameters is considered. Theoretical convergence on the class of strictly unimodal functions of one variable that are symmetric around the optimum is investigated using a stochastic Lyapunov function method developed by Semenov and Terkel [5] in the context of martingale theory. General expressions for the conditional expectations of the next values of step size and distance to the optimum under (1 +, λ)-selection are analytically derived, and an appropriate Lyapunov function is constructed. Convergence rate upper bounds, as well as adaptation parameter values, are obtained through numerical optimization for increasing values of λ. By selecting the number of offspring that minimizes the bound on the convergence rate with respect to the number of function evaluations, all strategy parameter values result from the analysis.

Original language English Parallel Problem Solving from Nature – PPSN XIV 14th International Conference, Edinburgh, UK, September 17-21, 2016, Proceedings Julia Handl, Emma Hart, Peter R. Lewis, et al Cham (CH) Springer 101-110 10 978-3-319-45823-6 978-3-319-45822-9 https://doi.org/10.1007/978-3-319-45823-6_10 E-pub ahead of print - 31 Aug 2016 14th International Conference on Parallel Problem Solving from Nature - Edinburgh, United KingdomDuration: 17 Sept 2016 → 21 Sept 2016

### Publication series

Name Lecture Notes in Computer Science Springer 9921 0302-9743 1611-3349

### Conference

Conference 14th International Conference on Parallel Problem Solving from Nature PPSN 2016 United Kingdom Edinburgh 17/09/16 → 21/09/16

## Keywords

• convergence rate
• evolution strategy
• Lyapunov function theory

## Fingerprint

Dive into the research topics of 'Lyapunov design of a simple step-size adaptation strategy based on success'. Together they form a unique fingerprint.
• ### Parallel Problem Solving from Nature – PPSN XIV: 14th International Conference, Edinburgh, UK, September 17-21, 2016, Proceedings

Handl, J. (ed.), Hart, E. (ed.), Lewis, P. R. (ed.), López-Ibáñez, M. (ed.), Ochoa, G. (ed.) & Paechter, B. (ed.), 31 Aug 2016, Cham (CH): Springer. 1026 p. (Theoretical Computer Science and General Issues; vol. 9921)

Research output: Book/ReportScholarly edition

• ### Preface

Handl, J., Hart, E., Lewis, P. R., López-Ibáñez, M., Ochoa, G. & Paechter, B., 31 Aug 2016, Parallel Problem Solving from Nature – PPSN XIV: 14th International Conference, Edinburgh, UK, September 17-21, 2016, Proceedings. Handl, J., Hart, E., Lewis, P. R. & et al (eds.). Cham (CH): Springer, p. V-VI 2 p. (Theoretical Computer Science and General Issues; vol. 9921).

Research output: Chapter in Book/Published conference outputForeword/postscript