Multi-Objective Multi-Agent Path Finding with Lexicographic Cost Preferences

2025-10-08

AI Summary

Multi-objective multi-agent pathfinding (MO-MAPF) faces a fundamental trade-off between accommodating user preferences and ensuring scalability. Traditional Pareto-optimality approaches suffer from computational intractability and poor scalability as the number of objectives grows. Method: This paper proposes a novel lexicographic-preference framework for MO-MAPF, replacing Pareto-front computation with explicit objective prioritization. We introduce LCBS—a lightweight, lexicographically constrained best-first search algorithm—integrating priority-aware A* with conflict-driven hierarchical search and sequential objective constraints at the底层 level. Contribution/Results: LCBS guarantees optimality under lexicographic ordering while avoiding combinatorial explosion in high-dimensional objective spaces. Experiments on standard and random MAPF benchmarks demonstrate significantly higher success rates and unprecedented scalability: LCBS solves instances with up to ten objectives—far exceeding the capabilities of existing MO-MAPF methods in both efficiency and scalability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Multiagent Systems: Multiagent Planning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Many real-world scenarios require multiple agents to coordinate in shared environments, while balancing trade-offs between multiple, potentially competing objectives. Current multi-objective multi-agent path finding (MO-MAPF) algorithms typically produce conflict-free plans by computing Pareto frontiers. They do not explicitly optimize for user-defined preferences, even when the preferences are available, and scale poorly with the number of objectives. We propose a lexicographic framework for modeling MO-MAPF, along with an algorithm extit{Lexicographic Conflict-Based Search} (LCBS) that directly computes a single solution aligned with a lexicographic preference over objectives. LCBS integrates a priority-aware low-level $A^*$ search with conflict-based search, avoiding Pareto frontier construction and enabling efficient planning guided by preference over objectives. We provide insights into optimality and scalability, and empirically demonstrate that LCBS computes optimal solutions while scaling to instances with up to ten objectives -- far beyond the limits of existing MO-MAPF methods. Evaluations on standard and randomized MAPF benchmarks show consistently higher success rates against state-of-the-art baselines, especially with increasing number of objectives.

Problem

• Optimizing multi-agent path planning with user-defined cost preferences
• Avoiding Pareto frontier construction for improved computational efficiency
• Scaling path finding algorithms to handle numerous competing objectives

Innovation

• Lexicographic framework models multi-objective multi-agent path finding
• LCBS algorithm computes single solution with lexicographic preferences
• Priority-aware A* search avoids Pareto frontier construction