Using Multi-modal Large Language Model to Boost Fireworks Algorithm's Ability in Settling Challenging Optimization Tasks

TL;DR

This paper introduces a novel multi-modal large language model-assisted fireworks algorithm to improve solving complex, high-dimensional optimization problems like TSP and EDA, achieving state-of-the-art results.

Contribution

It proposes integrating multi-modal large language models with the fireworks algorithm, extending its capability to complex high-dimensional tasks through the Critical Part concept.

Findings

Achieved or surpassed SOTA results on multiple problem instances.

Enhanced FWA performance in complex high-dimensional optimization tasks.

Demonstrated effectiveness on TSP and EDA problems.

Abstract

As optimization problems grow increasingly complex and diverse, advancements in optimization techniques and paradigm innovations hold significant importance. The challenges posed by optimization problems are primarily manifested in their non-convexity, high-dimensionality, black-box nature, and other unfavorable characteristics. Traditional zero-order or first-order methods, which are often characterized by low efficiency, inaccurate gradient information, and insufficient utilization of optimization information, are ill-equipped to address these challenges effectively. In recent years, the rapid development of large language models (LLM) has led to substantial improvements in their language understanding and code generation capabilities. Consequently, the design of optimization algorithms leveraging large language models has garnered increasing attention from researchers. In this study, we choose the fireworks algorithm(FWA) as the basic optimizer and propose a novel approach to assist the design of the FWA by incorporating multi-modal large language model(MLLM). To put it simply, we propose the concept of Critical Part(CP), which extends FWA to complex high-dimensional tasks, and further utilizes the information in the optimization process with the help of the multi-modal characteristics of large language models. We focus on two specific tasks: the \textit{traveling salesman problem }(TSP) and \textit{electronic design automation problem} (EDA). The experimental results show that FWAs generated under our new framework have achieved or surpassed SOTA results on many problem instances.