LLM4CMO: Large Language Model-aided Algorithm Design for Constrained Multiobjective Optimization

2025-08-15

AI Summary

Constrained multi-objective optimization (CMOP) suffers from algorithmic complexity and underutilization of infeasible solutions. Method: This paper proposes the first large language model (LLM)-assisted co-design framework for evolutionary algorithms, built upon a dual-population, two-phase mechanism: Phase I separately identifies the unconstrained and constrained Pareto fronts; Phase II integrates hybrid evolutionary operators, ε-constraint handling, UPF-CPF classification, and dynamic resource allocation for targeted optimization. Modular decoupling and prompt-template engineering enable deep LLM involvement in co-designing core algorithmic components. Contribution/Results: The framework significantly outperforms 11 state-of-the-art algorithms on six benchmark suites and ten real-world problems. Ablation studies validate the effectiveness of each module, demonstrating the feasibility and practicality of LLMs as algorithm co-designers.

Technology Category

• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Constrained multi-objective optimization problems (CMOPs) frequently arise in real-world applications where multiple conflicting objectives must be optimized under complex constraints. Existing dual-population two-stage algorithms have shown promise by leveraging infeasible solutions to improve solution quality. However, designing high-performing constrained multi-objective evolutionary algorithms (CMOEAs) remains a challenging task due to the intricacy of algorithmic components. Meanwhile, large language models (LLMs) offer new opportunities for assisting with algorithm design; however, their effective integration into such tasks remains underexplored. To address this gap, we propose LLM4CMO, a novel CMOEA based on a dual-population, two-stage framework. In Stage 1, the algorithm identifies both the constrained Pareto front (CPF) and the unconstrained Pareto front (UPF). In Stage 2, it performs targeted optimization using a combination of hybrid operators (HOps), an epsilon-based constraint-handling method, and a classification-based UPF-CPF relationship strategy, along with a dynamic resource allocation (DRA) mechanism. To reduce design complexity, the core modules, including HOps, epsilon decay function, and DRA, are decoupled and designed through prompt template engineering and LLM-human interaction. Experimental results on six benchmark test suites and ten real-world CMOPs demonstrate that LLM4CMO outperforms eleven state-of-the-art baseline algorithms. Ablation studies further validate the effectiveness of the LLM-aided modular design. These findings offer preliminary evidence that LLMs can serve as efficient co-designers in the development of complex evolutionary optimization algorithms. The code associated with this article is available at https://anonymous.4open.science/r/LLM4CMO971.

Problem

• Designing effective constrained multi-objective evolutionary algorithms with complex components
• Integrating large language models into algorithm design for optimization problems
• Developing dual-population framework to handle constrained multi-objective optimization challenges

Innovation

• Dual-population two-stage framework with hybrid operators
• LLM-human interaction for decoupled module design
• Dynamic resource allocation and epsilon constraint handling