# MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization

arXiv: https://arxiv.org/abs/2203.12675 · HTML: https://mlsanity.com/paper/2203.12675/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 64 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Convex Sparse Spectral Clustering: Single-view to Multi-view](https://mlsanity.com/paper/1511.06860/) (2015)
- [LM-CMA: an Alternative to L-BFGS for Large Scale Black-box Optimization](https://mlsanity.com/paper/1511.00221/) (2015)
- [Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions](https://mlsanity.com/paper/1608.04813/) (2016)

## Built on by (most cited first, 9 of 9)

- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (2024)
- [Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN](https://mlsanity.com/paper/2412.17629/) (2024)
- [DesignX: Human-Competitive Algorithm Designer for Black-Box Optimization](https://mlsanity.com/paper/2505.17866/) (2025)
- [Advancing CMA-ES with Learning-Based Cooperative Coevolution for Scalable Optimization](https://mlsanity.com/paper/2504.17578/) (2025)
- [Sharpness-Aware Black-Box Optimization](https://mlsanity.com/paper/2410.12457/) (2024)
- [A Novel Two-Phase Cooperative Co-evolution Framework for Large-Scale Global Optimization with Complex Overlapping](https://mlsanity.com/paper/2503.21797/) (2025)
- [A Learning-Based Cooperative Coevolution Framework for Heterogeneous Large-Scale Global Optimization](https://mlsanity.com/paper/2604.01241/) (2026)
- [Physics-Informed Evolution: An Evolutionary Framework for Solving Quantum Control Problems Involving the Schr"odinger Equation](https://mlsanity.com/paper/2502.05228/) (2025)

## Abstract (arXiv)

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.