Generative Heuristics for Hard- and Soft-Criteria Optimization: Integrating LLMs Within Metaheuristics

Miguel Saiz, A. Juan, J. Panadero

Abstract

In many real-world domains, optimization problems involve both quantitative objectives and qualitative criteria that cannot be directly formulated as mathematical functions. While recent research has integrated large language models (LLMs) into optimization algorithms, these approaches primarily use LLMs to guide the search process, generate heuristics, or tune optimization strategies, rather than to evaluate semantic objectives. This paper introduces generative heuristics, a methodology that combines traditional metaheuristics with LLM-based semantic evaluation to address ‘soft optimization’ problems containing both hard quantitative constraints and soft qualitative objectives. The proposed methodology first applies a metaheuristic algorithm to generate a shortlist of high-quality candidate solutions satisfying the quantitative objectives. These candidates are then evaluated by an LLM according to a user-defined qualitative rubric, and the resulting semantic scores are incorporated into the optimization process through a weighted soft objective. The methodology is illustrated through a constrained portfolio optimization problem in which financial risk is minimized while simultaneously promoting strategic objectives related to sector diversification, geographic exposure, environmental-social-governance quality, and overall portfolio coherence. Experimental results show that the proposed methodology consistently improves strategic alignment while producing solutions that remain close to those obtained from the hard optimization formulation.

Source: semanticscholar · PDF

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