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

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 LLMs (LLM) has led to substantial improvements in their language understanding and code generation capabilities. Consequently, the design of optimization algorithms leveraging LLMs 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 LLM(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 LLMs. 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.