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.
Agentic Large Language Models (LLM) are emerging as critical elements in automating large workflows and decision support systems in many fields, such as logistics [Xu et al., 2021], management [Chen et al., 2025a], healthcare [Liu et al., 2025], urban planning [Yu and Hyland, 2025], and transportation [Yu, 2025]. Hence, LLM agents have consequently been cast as tools for algorithm development in relevant combinatorial optimization problems such as scheduling [Romera-Paredes et al., 2024]. They have been studied extensively in natural language processing for optimization [Ramamonjison et al., 2022], where natural-language problem descriptions have been effectively translated into valuable mathematical formulations. Language model agents are equally proficient at generating algorithmic solutions to optimization problems when presented with natural-language descriptions and mathematical formulations [Xiao et al., 2024], and their performance has also been shown to exceed that of human experts in time-constrained scenarios [Sun et al., 2025].
Researchers and industry alike have been very interested in these frameworks, as they serve as valuable benchmarks for some of the foremost applications of LLMs. These applications stimulate two crucial facets of LLM performance: Natural-Language Processing (NLP) and coding [Xi et al., 2025]. However, application of language model agents to combinatorial optimization problems has been limited to academic cases, where problem framing and descriptions are taken directly or inspired by textbooks used in human education [Mostajabdaveh et al., 2025]. Although these studies present structured benchmarks for LLM agents, they are limited to problems with single objectives and are tractable to exact solution approaches.
Limited work has been conducted on combinatorial optimization that reflects real life. Problems that reflect real life are rarely transcribed into textbooks and can seldom be solved exactly, either due to computational resource constraints or problem uncertainty. Furthermore, real-life problems rarely come without trade-offs [Deb, 2014], and real-life decision makers often require knowledge of those trade-offs’ implications, i.e., the Pareto fronts resulting from multi-objective optimization tasks. Studies have applied LLM agents to develop heuristic algorithms for problems intractable to exact solvers [ İbrahim Oguz Çetinkaya et al., 2026]. Still, limited work has been conducted on LLM agent solutions for multi-objective optimization problems.
This study’s focus is on the development of a language model framework capable of generating algorithm solutions to combinatorial optimization problems, reflecting real-life worst-case scenarios (opposite to several benchmark studies, where problem framing is a best-case scenario). Combinatorial optimization problems are frequently intractable due to their NP-hardness and due to the combinatorial explosion of subsets [Hoffman, 2000], rendering exact solutions exploring all subsets intractable. Furthermore, real-life problems are often multi-objective, where decision makers are faced with competing business needs, etc.
An agentic framework capable of heuristic algorithm development presents itself as a valuable tool in such instances. Problems intractable to exact solvers often require approximate solutions from metaheuristics [Peres and Castelli, 2021]. Furthermore, multi-objective optimization problems have been shown to sometimes greatly benefit from the pooling of heuristic solutions, where pooled heuristic solutions form non-dominated frontiers with greater convergence and coverage [Calderín et al., 2015]. For example, the Cardinality-Constrained Mean-Variance Portfolio Optimization (CCPO) [Chang et al., 2000] fits this description very well. Unlike standard Markowitz meanvariance portfolio optimization [Markowitz, 1952], which can be solved trivially with exact dynamic programming, CCPO is an NP-hard problem [Moral-Escudero et al., 2006] with a non-convex and discontinuous efficient frontier. The subject of metaheuristic CCPO solutions has been studied extensively in the literature [Kalayci et al., 2019], and the performance of pooled heuristics in this case has been shown to greatly improve performance beyond singular heuristics [Woodside-Oriakhi et al., 2011].
Following this rationale, this study contributes several findings:
• This study presents an agentic language model framework that serves in the construction of algorithm portfolios for multi-objective combinatorial optimization problems with NPhardness. The agent framework not only trivializes the immense developmental burden associated with the construction of algorithm portfolios but also has the added benefit of the potential discovery of novel algorithms. • This study validates the agentic framework, along with its produced algorithm portfolio, in a series of challenging multi-objective investment portfolio optimization benchmark problems studied extens
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