Collaborative Problem-Solving in an Optimization Game

2025-05-21

AI Summary

This work addresses human-AI collaborative solving of NP-hard combinatorial optimization problems, using the two-player Traveling Salesman Problem (2-TSP) as a representative case. Method: We propose the first collaborative dialogue game paradigm for combinatorial optimization, integrating large language models (LLMs) with symbolic state tracking, semantic grounding, and multi-turn collaborative dialogue modeling to enable natural-language-driven exploration of the solution space. Contribution/Results: Our approach uniquely couples LLMs’ generative capabilities with precise constraint-aware reasoning over combinatorial structures, supporting both human-AI collaboration and autonomous agent self-play. Experiments show that 45% of self-play episodes achieve globally optimal solutions; moreover, the system exhibits strong cross-graph generalization, successfully transferring to unseen graph instances. This work establishes a novel paradigm for designing trustworthy, interpretable, and collaborative AI agents for complex optimization tasks.

Technology Category

• Search and Optimization: Learning to Search
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Dialogue agents that support human users in solving complex tasks have received much attention recently. Many such tasks are NP-hard optimization problems that require careful collaborative exploration of the solution space. We introduce a novel dialogue game in which the agents collaboratively solve a two-player Traveling Salesman problem, along with an agent that combines LLM prompting with symbolic mechanisms for state tracking and grounding. Our best agent solves 45% of games optimally in self-play. It also demonstrates an ability to collaborate successfully with human users and generalize to unfamiliar graphs.

Problem

• Develop dialogue agents for collaborative optimization tasks
• Solve two-player Traveling Salesman Problem via dialogue
• Combine LLM prompting with symbolic state tracking

Innovation

• Combines LLM prompting with symbolic mechanisms
• Solves two-player Traveling Salesman collaboratively
• Achieves 45% optimal solutions in self-play