How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems

TL;DR

This paper introduces a multimodal large language model framework that combines textual and visual prompts to improve optimization performance, demonstrated through a case study on capacitated vehicle routing problems.

Contribution

The paper presents a novel multimodal LLM-based optimization framework that integrates visual and textual data to enhance problem understanding and solution quality.

Findings

Multimodal approach outperforms text-only LLM methods in optimization tasks.

Significant improvement in solution quality for capacitated vehicle routing problems.

Framework simulates human problem-solving for better insights.

Abstract

Recently, large language models (LLMs) have notably positioned them as capable tools for addressing complex optimization challenges. Despite this recognition, a predominant limitation of existing LLM-based optimization methods is their struggle to capture the relationships among decision variables when relying exclusively on numerical text prompts, especially in high-dimensional problems. Keeping this in mind, we first propose to enhance the optimization performance using multimodal LLM capable of processing both textual and visual prompts for deeper insights of the processed optimization problem. This integration allows for a more comprehensive understanding of optimization problems, akin to human cognitive processes. We have developed a multimodal LLM-based optimization framework that simulates human problem-solving workflows, thereby offering a more nuanced and effective analysis. The efficacy of this method is evaluated through extensive empirical studies focused on a well-known combinatorial optimization problem, i.e., capacitated vehicle routing problem. The results are compared against those obtained from the LLM-based optimization algorithms that rely solely on textual prompts, demonstrating the significant advantages of our multimodal approach.