Large Language Model for Multi-objective Evolutionary Optimization (2310.12541v3)

Abstract: Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful LLM to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.To foster reproducibility and accessibility, the source code is https://github.com/FeiLiu36/LLM4MOEA.

LLM for Multi-objective Evolutionary Optimization

The integration of machine learning techniques into the domain of multi-objective optimization is a burgeoning field of research, as exemplified by the paper "LLM for Multi-objective Evolutionary Optimization." The paper explores the application of LLMs, particularly in the context of multi-objective evolutionary algorithms (MOEAs), to address multi-objective optimization problems (MOPs). This work primarily investigates the use of pre-trained LLMs as black-box optimizers and proposes an innovative approach for employing LLMs to enhance MOEAs.

Summary of Contributions

The research articulates a novel technique where LLMs are leveraged in the decomposition-based MOEA framework, MOEA/D, serving as black-box search operators. Through the use of prompt engineering, the authors demonstrate how LLMs can be scripted to function effectively as search operators in a zero-shot manner—a significant advancement since these models do not require extensive domain-specific retraining. The paper advances the following key contributions:

• Decomposition-based MOEA framework with LLMs: By redefining the role of LLMs within a decomposition-based MOEA/D framework, the authors propose using LLMs to tackle subproblems derived from the decomposition of original MOPs. This approach not only utilizes LLMs as optimizers but also introduces the capacity for robust generalization across unseen problems with varying patterns.
• Development of a White-box Operator: Alongside the black-box use of LLMs, the authors introduce MOEA/D-LO, a white-box version of the framework. It draws from the observed LLM behavior to produce a straightforward, explainable operator by treating it as an approximate weighted linear operator incorporating randomness—a pivotal step to increase transparency and elucidate LLM behavior in evolutionary optimization contexts.
• Experimental Validation: The efficacy of the proposed approaches is validated against standard test problems where MOEA/D-LO showcased competitive and even superior performance metrics when compared with state-of-the-art MOEAs like MOEA/D and NSGA-II. The robust performance across varied test cases strongly suggests the potential that inherently lies in deploying LLMs within MOEAs.

Implications and Future Directions

The paper pushes forward the frontiers on how LLMs can be employed beyond conventional text processing, demonstrating potential benefits when applied to multi-objective optimization. Two significant implications are evident:

1. Automating Search Operator Design: By utilizing LLMs within the MOEA framework, search operator design becomes less reliant on human-expert knowledge and more on algorithmic learning, thus facilitating democratized access to optimization tools for practitioners from diverse domains.
2. Behavioral Interpretability of LLMs in Optimization: The transition from black-box to white-box approaches using simplified models can improve our understanding of LLMs' decision-making processes, offering better insights and possibly shaping future improvements in model design and application efficacy.

The paper alludes to several future research avenues. There is potential to refine prompt engineering techniques further, exploring more sophisticated interactions that guide LLMs effectively during the optimization process. Furthermore, the exploration of LLM application across more complex multi-objective problems that offer high-dimensional and potentially constrained environments represents a logical progression. Finally, examining LLM integration within other MOEA paradigms, such as Pareto-dominance and indicator-based methods, could further widen the spectrum of LLM utility.

In conclusion, this research illuminates an intriguing path forward in the landscape of evolutionary algorithms by synthesizing LLM capabilities with MOEA frameworks, heralding a promising confluence of disciplines with practical and theoretical significance.