# LLM Agents for Combinatorial Efficient Frontiers: Investment Portfolio Optimization

arXiv: https://arxiv.org/abs/2601.00770 · HTML: https://mlsanity.com/paper/2601.00770/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 2 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://mlsanity.com/paper/2504.04310/) (2025)
- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [Evaluating LLM Reasoning in the Operations Research Domain with ORQA](https://mlsanity.com/paper/2412.17874/) (2024)
- [Will bots take over the supply chain? Revisiting Agent-based supply chain automation](https://mlsanity.com/paper/2109.01703/) (2021)
- [The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems](https://mlsanity.com/paper/1908.01181/) (2019)
- [Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling](https://mlsanity.com/paper/2510.24013/) (2025)

## Abstract (arXiv)

Investment portfolio optimization is a task conducted in all major financial institutions. The Cardinality Constrained Mean-Variance Portfolio Optimization (CCPO) problem formulation is ubiquitous for portfolio optimization. The challenge of this type of portfolio optimization, a mixed-integer quadratic programming (MIQP) problem, arises from the intractability of solutions from exact solvers, where heuristic algorithms are used to find approximate portfolio solutions. CCPO entails many laborious and complex workflows and also requires extensive effort pertaining to heuristic algorithm development, where the combination of pooled heuristic solutions results in improved efficient frontiers. Hence, common approaches are to develop many heuristic algorithms. Agentic frameworks emerge as a promising candidate for many problems within combinatorial optimization, as they have been shown to be equally efficient with regard to automating large workflows and have been shown to be excellent in terms of algorithm development, sometimes surpassing human-level performance. This study implements a novel agentic framework for the CCPO and explores several concrete architectures. In benchmark problems, the implemented agentic framework matches state-of-the-art algorithms. Furthermore, complex workflows and algorithm development efforts are alleviated, while in the worst case, lower but acceptable error is reported.