Are Language Models Up to Sequential Optimization Problems? From Evaluation to a Hegelian-Inspired Enhancement

Large Language Models (LLMs) have demonstrated impressive capabilities across numerous fields, presenting an opportunity to revolutionize optimization problem-solving, a crucial, ubiquitous, and complex domain. This paper explores the proficiency of LLMs in handling Sequential Optimization Problems (SOPs). We introduce WorldGen, a dynamic framework for generating unseen SOPs with controllable complexities, to evaluate LLM performance. Our initial observations reveal that while LLMs perform well on simple SOPs, their performance significantly degrades with increased complexity. Motivated by this, we revisit philosophical hypotheses on reasoning to enhance LLM performance. Inspired by the influential framework of Hegelian Dialectics, we propose ACE, demonstrating how the performance of LLMs in SOP contexts can be significantly improved without any retraining or further fine-tuning.