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

TL;DR

The paper addresses MO-MAPF under user-defined objective preferences by introducing a lexicographic formulation that orders objectives strictly and seeks a lexicographically minimal joint cost. It presents Lexicographic Conflict-Based Search (LCBS), a two-level CBS framework where the low-level LA$^*$ performs lexicographic optimization and the high-level CBS resolves conflicts via constraint branching, thereby avoiding Pareto-front construction. The authors prove LCBS yields lexicographically optimal solutions on the Pareto frontier and demonstrate linear-in-d to runtime scaling, achieving robust performance up to $d=10$ objectives and large agent counts. Empirical results on standard and randomized MAPF benchmarks show consistently higher success rates for LCBS compared to state-of-the-art baselines, highlighting its scalability and practical impact for real-world, preference-driven multi-agent planning.

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 \textit{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.

Figures (7)

• Figure 1: An illustration of multi-objective planning with user-defined preferences over two objectives. Unlike existing methods, our proposed approach can directly optimize objective preferences and does not require computing a Pareto frontier or determining weights for scalarization.
• Figure 2: LCBS Algorithm Overview. The algorithm starts at the Low-Level Planner, and uses lexicographic A$^*$ (LA$^*$) (Algorithm \ref{['alg:LA*']}) to compute shortest agent-paths to goal following lexicographic ordering over costs, without violating any constraints in $\Omega$ (initially, $\Omega=\emptyset$). At the high level (dotted), LCBS compiles the joint plan $\Pi$ and uses the Conflict Detector module to get information about the conflict (location, time, agent 1, agent 2) if one exists, for example, agents a and b in conflict at vertex $v$ (or edge $e$) at time $t=t_1$ is encoded as $(v,t_1,a,b)$. If $\Pi$ is conflict-free, it is returned, else constraints are imposed on each agent, generated and evaluated using binary branching constraint tree ren2023binary. The constraint set $\Omega$ is updated and returned to the low-level planner that recomputes all agents paths. This process is iteratively done till a conflict-free $\Pi$ is found.
• Figure 3: Success rate trends across MAPF benchmarks for 25 standard scenarios with 3 objectives$(T=2\text{ mins})$.
• Figure 4: Success rate trends across MAPF benchmarks for 10 randomized scenarios for 3 objectives$(T=2\text{ mins})$.
• Figure 5: Success rate trends across MAPF benchmarks for 25 standard scenarios with 4 objectives$(T=2\text{ mins})$.

Theorems & Definitions (5)

• Definition 1: Lexicographic comparison $<_{\text{lex}}$
• Proposition 1
• proof
• Proposition 2
• proof