hellwigm/pccmsa-es

Matlab code of the pcCMSA-ES for noisy optimization

The pcCMSA-ES using linear regression analysis

1. REFERENCE:

   Hellwig, Michael; Beyer, Hans-Georg, "Evolution under Strong Noise: A Self-Adaptive Evolution Strategy Can Reach the Lower Performance Bound - the pcCMSA-ES", J. Handl et al. (Ed.): Parallel Problems Solving from Nature - PPSN XIV, pp. 26-37, Edinburgh Napier University, Edinburgh, Scotland, UK, Springer, 2016.

2. NOTICE:

   The pcCMSA-ES code is made available for reproduction of reported results and testing. The use of the code is permitted subject to the condition of properly acknowledging this source (https://github.com/hellwigm/pcCMSA-ES/) as well as citing the relevant papers.

3. The pcCMSA-ES:

   The pcCMSA-ES is based on the well-known Covariance Matrix Self-Adaptation Evolution Strategy (CMSA-ES). Incorporating a rather simple population control mechanism togehter with an appropriate noise detection method, the population control Covariance Matrix Self-Adaptation Evolution Strategy (pcCMSA-ES) is able to successfully deal with noisy optimization problems. The noise detection mechanism is based on applying linear regression analysis to a sequence of observed noisy objective function values. The slope of the estimated regression line governs the population control.Constructing a test statistic allows for the design of a hypothesis test that provides the decline requirement.

   negative slope w.r.t significance level \alpha --> reduce population size
   non-negative slope w.r.t significance level \alpha --> increase population size

   Notice, that representing a parametric approach, the use of linear regression analysis is only appropriate for additive normally distributed fitness noise disturbances. In order to tackle different forms of noise, the pcCMSA-ES may be equipped with a non-parametric noise detection method (e.g. maiking use of the Mann-Kendall test). In such cases the noise detection procedure LinearRegNegativetrend.m may simply be repalced with MannKendall.m.

4. File description:

• EllipsoidModel.m - Test function defining the fitness environment referred to as the (noisy) Ellipsoid model
• pcCMSAES.m - Main component of the pcCMSA-ES algorithm relying on either Linear Regression Analysis or the Mann Kendall Test for noise detection
• LinearRegNegativeTrend.m - Trend estimation making use of the linear regression line's slope and a corresponding hypothesis test
• MannKendallNegativeTrend.m - Alternative non-parametric trend estimation: The Mann-Kendall test for identification of significant downward montonic trend.
• RankPop.m - Ranking Procedure
• sample_Experiment.m - Executable for sample pcCMSA-ES runs