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Covariance Matrix Adaptation Evolution Strategy

Technique

Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a continuous optimization evolutionary algorithm that has been applied to program synthesis by reformulating program generation as a continuous search problem. The Genesys tool implements CMA-ES for program synthesis, mapping continuous solutions to programs, while CMA-ES has also been used in related work on one-class constraint synthesis.

First seen 7/1/2026
Last seen 7/2/2026
Evidence 12 chunks
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Covariance Matrix Adaptation Evolution Strategy

Overview

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a continuous optimization technique drawn from the family of evolutionary algorithms. It is a stochastic, derivative-free method that adapts a multivariate normal distribution's covariance matrix to capture dependencies between candidate solutions and efficiently search continuous parameter spaces.

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RELATIONSHIPS

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Genesys ← uses 100% 2e
GENESYS uses CMA-ES as its core optimization algorithm to solve the continuous program synthesis problem.
Neural Program Optimization ← uses 100% 2e
NPO also uses CMA-ES to solve the optimization problem.
Evolutionary Algorithm implements → 97% 1e
CMA-ES is an evolutionary algorithm used for continuous optimization.
Continuous Optimization uses → 97% 1e
CMA-ES operates in the continuous optimization domain.
Multivariate Normal Distribution uses → 100% 1e
CMA-ES samples points from a multivariate normal distribution in each generation.
Genesys ← implements 99% 1e
Genesys uses CMA-ES as its core evolutionary optimization technique for program synthesis.
Cumulative Step-Size Adaptation uses → 100% 1e
CMA-ES updates step size using cumulative step-size adaptation.
CMA-ES for one-class constraint synthesis ← uses 97% 1e
The CMA-ES for one-class constraint synthesis paper applies CMA-ES for constraint synthesis.

LINKED ENTITIES

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Genesys IMPLEMENTS Extracted graph relationship
CMA-ES for one-class constraint synthesis USES Extracted graph relationship
Evolutionary Algorithm IMPLEMENTS Extracted graph relationship
Continuous Optimization USES Extracted graph relationship

CITATIONS

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6 citations — click to expand
[1] Genesys formulates program synthesis as a continuous optimization problem using CMA-ES as the evolutionary approach. Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization
[2] Genesys synthesizes 28% more programs of length 10 than existing schemes within the same time budget. Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization
[3] Genesys is the first work to demonstrate feasibility of the continuous approach for synthesizing complex, non-toy programs. Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization
[4] Genesys proposes mapping schemes to convert continuous CMA-ES solutions into actual programs and several restart policies. Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization
[5] CMA-ES has been used in the paper 'CMA-ES for one-class constraint synthesis' by Karmelita and Pawlak (GECCO 2020). Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization
[6] Genesys is a tool that implements CMA-ES for program synthesis. Genesys: A Novel Evolutionary Program Synthesis Tool with Continuous Optimization