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

TL;DR

The paper tackles constrained multiobjective optimization by introducing LLM4CMO, a dual-population, two-stage framework that first identifies constrained and unconstrained Pareto fronts and then performs targeted optimization via LLM-informed core modules. It engineers HOps, an epsilon decay schedule, and a dynamic resource allocation mechanism through iterative LLM-human interactions to simplify design and enhance performance. Across six benchmark suites and ten real-world CMOPs, LLM4CMO outperforms eleven state-of-the-art baselines, with ablations validating the contributions of each module. The work demonstrates the potential of LLMs as co-designers in complex evolutionary optimization, offering a path toward more scalable and adaptable algorithm design in constrained multiobjective settings.

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.

Figures (43)

• Figure 1: The proposed base dual-population two-stage CMOEA framework (down) and the LLM–human interactive module design flowchart (up). Here, $C$ denotes the classification strategy, following the approach used in URCMO. The Rec updates the UPF-CPF type during Phase 1 of Stage 2. $Off_3$ represents offspring generated via the opposition-based mechanism. The Type classification includes: (1) completely overlap, (2) UPF and CPF partially overlap, (3) completely separated, and (4) unclear. The Design module sequentially guides the LLM-aided development of the HOps, epsilon decay function, and DRA mechanism.
• Figure 2: The change process of pareto front, P1 (popMain), P2 (popAux), ARCH (achieve population) and OFF (offsping) of BiCO, URCMO and LLM4CMO on LIRCMOP1.
• Figure 3: The Friedman test results of LLM4CMO and other 11 algorithms run 30 times on 6 test suites.
• Figure 4: The convergence curves of IGD metric on LIRCMOP test suite.
• Figure 5: The convergence curve of IGD metric on MW test suite.