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

## Table of Contents

## Overview

- "Deduces" the
**Covariance-Matrix Adaptation Evolution Strategy (CMA-ES)** - Great blog-post about the topic: http://blog.otoro.net/2017/10/29/visual-evolution-strategies/

## Notation

- indexes the generation / g-th evolution step
- denotes the covariance matrix of at generation / the g-th evolution step
- is the "overall" std. dev., or step-size, at generation
- is the k-th offstring (individual, search-point) from generation
- is the
**mean value**of the search distribution at generation - is the
**population size**,**sample size**, or**number of offsprings** - 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. , and for the next generation given the previous one.

Basic equation for sampling search points, for generation number is

## Selection and recombination

- Want to combine previous generation of the population to obtain the
*mean*of the*next*generation New mean of the search dist. is a /weighted average of selected points from previous generation