XBBO/examples/CMAES

• CMA-ES
• • Introduction
  • Abstract
  • Usage
  • benchmark
  • Results
  • • Branin

CMA-ES

Introduction

Addressing Numerical Black-Box Optimization:
CMA-ES (Tutorial)

Abstract

Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. Evolution strategies (ES) are stochastic, derivative-free methods for numerical optimization of non-linear or non-convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation. An evolutionary algorithm is broadly based on the principle of biological evolution, namely the repeated interplay of variation (via recombination and mutation) and selection: in each generation (iteration) new individuals (candidate solutions, denoted as $x$) are generated by variation, usually in a stochastic way, of the current parental individuals. Then, some individuals are selected to become the parents in the next generation based on their fitness or objective function value $f(x)$. Like this, over the generation sequence, individuals with better and better $f$-values are generated.

Usage

E.g. PYTHONPATH='./' python examples/CMAES/rosenbrock_cma-es.py

benchmark

Modify the following section of comparison/xbbo_benchmark.py :

test_algs = ["cma-es"]

And run PYTHONPATH='./' python comparison/xbbo_benchmark.py in the command line.

Results

Branin

Method	Minimum	Best minimum	Mean f_calls to min	Std f_calls to min	Fastest f_calls to min
XBBO(cma-es)	0.398+/-0.000	0.398	180.9	29.28	97