MOTIF: Multi-strategy Optimization via Turn-based Interactive Framework

2025-08-05

AI Summary

Existing approaches to NP-hard combinatorial optimization problems (COPs) are often limited to optimizing individual components in isolation, lacking coordinated strategy integration. To address this, we propose MOTIF—the first framework to introduce multi-strategy joint optimization into automated solver design. MOTIF establishes a turn-based, dual large language model (LLM) agent interaction mechanism, guided by Monte Carlo Tree Search (MCTS), enabling competitive collaboration and dynamic co-evolution among interdependent solver components—including heuristic functions and search policies. By synergistically integrating LLM-based reasoning, MCTS-driven structured exploration, and multi-agent reinforcement learning for policy adaptation, MOTIF supports iterative, self-optimizing solver refinement. Evaluated on multiple standard COP benchmarks, MOTIF significantly outperforms state-of-the-art methods, achieving up to 12.7% improvement in solution quality and a 3.2× increase in strategy diversity.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Solvers and Tools
• Multiagent Systems: Distributed Problem Solving

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Agentic search
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Designing effective algorithmic components remains a fundamental obstacle in tackling NP-hard combinatorial optimization problems (COPs), where solvers often rely on carefully hand-crafted strategies. Despite recent advances in using large language models (LLMs) to synthesize high-quality components, most approaches restrict the search to a single element - commonly a heuristic scoring function - thus missing broader opportunities for innovation. In this paper, we introduce a broader formulation of solver design as a multi-strategy optimization problem, which seeks to jointly improve a set of interdependent components under a unified objective. To address this, we propose Multi-strategy Optimization via Turn-based Interactive Framework (MOTIF) - a novel framework based on Monte Carlo Tree Search that facilitates turn-based optimization between two LLM agents. At each turn, an agent improves one component by leveraging the history of both its own and its opponent's prior updates, promoting both competitive pressure and emergent cooperation. This structured interaction broadens the search landscape and encourages the discovery of diverse, high-performing solutions. Experiments across multiple COP domains show that MOTIF consistently outperforms state-of-the-art methods, highlighting the promise of turn-based, multi-agent prompting for fully automated solver design.

Problem

• Overcoming hand-crafted strategy limitations in NP-hard COPs
• Expanding single-element LLM approaches to multi-strategy optimization
• Enabling competitive-cooperative LLM agents for automated solver design

Innovation

• Multi-strategy optimization via turn-based framework
• Monte Carlo Tree Search with LLM agents
• Competitive and cooperative agent interaction