# Latent Heuristic Search: Continuous Optimization for Automated Algorithm Design

arXiv: https://arxiv.org/abs/2605.17137 · HTML: https://mlsanity.com/paper/2605.17137/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 16 May 2026.

## Builds on (most cited first, 15 of 15)

- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Learning to Synthesize Programs as Interpretable and Generalizable Policies](https://mlsanity.com/paper/2108.13643/) (2021)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [Controllable Text Generation via Probability Density Estimation in the Latent Space](https://mlsanity.com/paper/2212.08307/) (2022)
- [Searching Latent Program Spaces](https://mlsanity.com/paper/2411.08706/) (2024)

## Abstract (arXiv)

The integration of Large Language Models (LLMs) into evolutionary frameworks has established a new paradigm for automated heuristic discovery. Despite their promise, these methods typically search in the discrete space of program syntax, relying on stochastic sampling to navigate a highly non-convex optimization landscape. This work proposes a continuous heuristic discovery framework that shifts optimization to a learned latent manifold. We employ an encoder to map discrete programs into continuous embeddings and train a differentiable surrogate model to predict performance, enabling gradient-based search. To regularize the optimization trajectory, an invertible normalizing flow maps these embeddings to a structured Gaussian prior, where we perform gradient ascent. The resulting optimized latent vectors are projected through a learned mapper into soft prompts, which condition a frozen LLM to synthesize novel executable heuristics. We evaluate the proposed method on the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP), the Knapsack Problem (KSP), and Online Bin Packing (OBP). Empirical results demonstrate that continuous latent-space optimization achieves performance competitive with state-of-the-art discrete evolutionary baselines while offering a complementary methodological alternative for automated algorithm design. The implementation code is available at urlhttps://github.com/cheikh025/LHS.