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.

翻译：投资组合优化是所有主要金融机构都会执行的任务。基数约束均值-方差投资组合优化（CCPO）问题模型在投资组合优化中普遍存在。这类投资组合优化作为混合整数二次规划问题，其挑战源于精确求解器无法在可接受时间内获得解，因此通常采用启发式算法来寻找近似投资组合解。CCPO涉及大量繁琐复杂的工作流程，同时需要在启发式算法开发方面投入大量精力——通过整合多个启发式解可以提升有效前沿的质量。因此，常见方法是开发多种启发式算法。智能体框架作为组合优化领域诸多问题的潜在解决方案崭露头角，研究表明其在自动化大型工作流程方面具有同等效能，在算法开发方面表现卓越，有时甚至超越人类水平。本研究为CCPO实现了一种新型智能体框架，并探索了若干具体架构。在基准问题测试中，所实现的智能体框架达到了最先进算法的性能水平。此外，该框架显著减轻了复杂工作流程和算法开发的工作量，即使在最坏情况下也仅产生较低且可接受的误差。