Notes on: Hansen, N. (2016): The cma evolution strategy: a tutorial

Table of Contents

Overview

Notation

  • hansen16_cma_evolut_strat_bed561b338628a088ae69301d4bba9fd83a70bd2.png indexes the generation / g-th evolution step
  • hansen16_cma_evolut_strat_3e4b9dd18a1412fd208ba8e16159fae49c420797.png denotes the covariance matrix of at generation hansen16_cma_evolut_strat_bed561b338628a088ae69301d4bba9fd83a70bd2.png / the g-th evolution step
  • hansen16_cma_evolut_strat_b78659f3ce21bfa989db0fb3cad46b69651a5665.png is the "overall" std. dev., or step-size, at generation hansen16_cma_evolut_strat_bed561b338628a088ae69301d4bba9fd83a70bd2.png
  • hansen16_cma_evolut_strat_31ee38fe4195efaca108808ca9c59b6a0ac7d392.png is the k-th offstring (individual, search-point) from generation hansen16_cma_evolut_strat_2454daa72e7008acb124944b3f9aaf0ecdf81ee7.png
  • hansen16_cma_evolut_strat_57d871bfa920199a2193423779eb1baeb86dfcc9.png is the mean value of the search distribution at generation hansen16_cma_evolut_strat_bed561b338628a088ae69301d4bba9fd83a70bd2.png
  • hansen16_cma_evolut_strat_67f0ca7fbf931bc171d59ac9ecb3a54dba84c053.png is the population size, sample size, or number of offsprings
  • hansen16_cma_evolut_strat_6cb7bbe1e67d5ea25c699bb27960ab046beb6d7a.png is a sub-selection size of the population

Basics

A population of new search points (individuals, offspring) is generated by sampling form a multivariate normal distribution.

The goal is to define a "evoluation", i.e. hansen16_cma_evolut_strat_c5e07ec553f5f329b2dfdc0c7a994ed2701c84d0.png, hansen16_cma_evolut_strat_1f5227165bae98e1edf11c2ab3024ab0e1112ac3.png and hansen16_cma_evolut_strat_92d9ef8c65c3c5294e4046475f6f8295686624c4.png for the next generation given the previous one.

Basic equation for sampling search points, for generation number hansen16_cma_evolut_strat_2a1b0746b5084350e83bb6f18a29cfdccf3d043d.png is

hansen16_cma_evolut_strat_25ea378b35ddb68d0322a2fe1ed17d67370fead2.png

Selection and recombination

  • Want to combine previous generation of the population to obtain the mean of the next generation
  • New mean hansen16_cma_evolut_strat_1e7c4a12228e67f8e51fac2d0cc71b86f66e82f2.png of the search dist. is a /weighted average of hansen16_cma_evolut_strat_8700f80c4895c66c1fb785c5b0cf5c4b6f532c75.png selected points from previous generation

    hansen16_cma_evolut_strat_c69ec320bd00a51f19bc3c27a838f96f4ec2951e.png