# Genetic Algorithms with Optimization Guided Operators

arXiv: https://arxiv.org/abs/2606.12279 · HTML: https://mlsanity.com/paper/2606.12279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning](https://mlsanity.com/paper/1712.06567/) (2017)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [Evolving Deeper LLM Thinking](https://mlsanity.com/paper/2501.09891/) (2025)
- [Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning](https://mlsanity.com/paper/2509.24372/) (2025)
- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [Fast Learning Requires Good Memory: A Time-Space Lower Bound for Parity Learning](https://mlsanity.com/paper/1602.05161/) (2016)
- [Reinforced Generation of Combinatorial Structures: Ramsey Numbers](https://mlsanity.com/paper/2603.09172/) (2026)
- [Generalizing and Unifying Gray-box Combinatorial Optimization Operators](https://mlsanity.com/paper/2407.06742/) (2024)
- [The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses](https://mlsanity.com/paper/1801.10087/) (2018)
- [Flow-based Extremal Mathematical Structure Discovery](https://mlsanity.com/paper/2601.18005/) (2026)
- [How Population Diversity Influences the Efficiency of Crossover](https://mlsanity.com/paper/2404.12268/) (2024)

## Abstract (arXiv)

Recent work in ML applies genetic algorithms at inference time to iteratively improve solutions to optimization problems. The basic mutation and recombination operators involved are qualitatively different from those studied classically. Mutations are no longer random; an ML algorithm mutates a solution with the goal of improving an objective. Similarly, recombination is not based on random collages of parent solutions. Instead, it is an ML optimization-based operator whose goal is to synthesize improved solutions from its inputs. Thus, these mutation and recombination operators are more likely to improve the objective, but their computational cost is much higher. We introduce a general model of genetic algorithms and formulate optimization in this model as a query complexity problem, using the language of reinforcement learning. We demonstrate three fundamental phenomena. First, we show that diversity of the solution pool can be necessary: for parity learning, viewed in our framework, we show that with pool size w and vectors of length n, the optimal query complexity is Theta(w+2n-w). We further show that this phenomenon persists under general memory constraints: Theta(n2) bits of memory are necessary for efficient success. Second, we show that generation, mutation, and recombination can all be simultaneously necessary to reach a nearly optimal solution. Finally, we give a phase transition for Gaussian distributions, showing that a positive em drift of the operators yields exponential speedup.