LLM Agents for Combinatorial Efficient Frontiers: Investment Portfolio Optimization
Simon Paquette-Greenbaum, Jiangbo Yu
TL;DR
The paper addresses the NP-hard CCPO problem by introducing MoCo--Agent, an LLM-driven framework that iteratively generates and refines a portfolio of metaheuristic algorithms for multi-objective optimization. By training on a Hang Seng CCPO instance and evaluating on multiple asset universes, the approach produces an algorithm portfolio that frequently matches or surpasses state-of-the-art baselines and demonstrates improved frontier quality through pooling. The work provides evidence that agentic LLMs can automate complex algorithm design and frontier exploration, reducing development effort while enhancing convergence and coverage of Pareto fronts. The practical impact lies in scalable, automated generation of diverse metaheuristics for real-world MO optimization tasks such as portfolio optimization, with potential applicability to broader combinatorial problems.
Abstract
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.