Module cmsa_es 

Covariance Matrix Self-Adaptation Evolution Strategy (CMSA-ES).

CMSA-ES (Beyer & Sendhoff, 2008) is the path-free cousin of CMA-ES. It drops the evolution paths and Cumulative Step-size Adaptation entirely and instead:

• self-adapts the step size per individual with the classical log-normal rule σᵢ = σ̄ · exp(τ · N(0, 1)), then recombines the selected σᵢ into the next σ̄ (the same σ-self-adaptation mechanism as crate::algorithms::es_classical, so the two ES σ-adaptation families share one mutation rule);
• blends the covariance toward the rank-μ maximum-likelihood estimate of the selected mutation steps with time constant τ_c = 1 + D(D+1)/(2μ): C ← (1 − 1/τ_c) C + (1/τ_c) · (1/μ) Σ s_{(i)} s_{(i)}ᵀ.

Sampling needs only a Cholesky factor of C (no eigendecomposition, no C^{-1/2}), so each generation is cheaper than CMA-ES.

On the τ constant

The canonical CMSA-ES learning rate is τ = 1/√(2D) (Beyer & Sendhoff, 2008), used here. Note this differs from EsConfig’s 1/√(2√D): the two strategies share the log-normal σ-self-adaptation mechanism (ADR 0021 §5), but CMSA-ES keeps its own algorithm-faithful constant.

Relationship to the EDA / ProbabilityModel family

Like CmaEs, this is a self-contained Strategy; per ADR 0021 it does not instantiate ProbabilityModel. The rank-μ covariance blend is closer to an EMNA-style maximum-likelihood update than CMA-ES’s path-driven adaptation, but the per-individual σ self-adaptation keeps it on the ES side of the boundary (research note eda-vs-cma-es-boundary).

References

• Beyer, H.-G. & Sendhoff, B. (2008), Covariance Matrix Adaptation Revisited — The CMSA Evolution Strategy, PPSN X, LNCS 5199.

Structs

CmsaEs

Covariance Matrix Self-Adaptation Evolution Strategy.

CmsaEsConfig

Static configuration for a CMSA-ES run.

CmsaEsState

Generation state for CmsaEs.