A Multiagent Path Search Algorithm for Large-Scale Coalition Structure Generation

TL;DR

This work addresses the coalition structure generation problem by recasting it as a scalable MAPF-like path search on a graph of coalition structures. It introduces SALDAE, a multiagent, anytime algorithm that uses bridging-path strategies, memory-guided search, and conflict-resolution to rapidly produce high-quality solutions for large-scale instances. Empirical results across diverse value distributions show SALDAE often surpasses state-of-the-art methods in solution quality and optimality, and remains effective when scaling to hundreds or thousands of agents. The approach offers practical impact for real-world large-scale coalition formation problems in domains like disaster response and vehicle allocation.

Abstract

Coalition structure generation (CSG), i.e. the problem of optimally partitioning a set of agents into coalitions to maximize social welfare, is a fundamental computational problem in multiagent systems. This problem is important for many applications where small run times are necessary, including transportation and disaster response. In this paper, we develop SALDAE, a multiagent path finding algorithm for CSG that operates on a graph of coalition structures. Our algorithm utilizes a variety of heuristics and strategies to perform the search and guide it. It is an anytime algorithm that can handle large problems with hundreds and thousands of agents. We show empirically on nine standard value distributions, including disaster response and electric vehicle allocation benchmarks, that our algorithm enables a rapid finding of high-quality solutions and compares favorably with other state-of-the-art methods.

Figures (14)

• Figure 1: An illustration of the three phases of our algorithm. The numbers represent the agents. For example, $1$ represents agent $a_{1}$. In the first iteration, the start node is the bottom node. The child nodes are represented by the nodes that are directly connected to the bottom node. All of these child nodes are candidates to become the new start node. However, the coalition structure $\{\{a_{1},a_{4}\},\{a_{2},a_{3}\}\}$ in level 2 has, we assume, the highest value and hence it is selected and becomes the new start node. The newly generated child nodes of this coalition structure are $\{\{a_{1}\},\{a_{4}\},\{a_{2},a_{3}\}\}$ and $\{\{a_{2}\},\{a_{3}\},\{a_{1},a_{4}\}\}$. We assume that $\{\{a_{1}\},\{a_{4}\},\{a_{2},a_{3}\}\}$ is the highest valued coalition structure between the child nodes and hence it becomes the new start node. For the third iteration, there are child nodes that can be generated by merging coalitions through the blue edges, which are $\{\{a_{1}\},\{a_{2},a_{3},a_{4}\}\}$ and $\{\{a_{4}\},\{a_{1},a_{2},a_{3}\}\}$, but these are already generated. Hence, the only new child node generated is $\{\{a_{1}\},\{a_{2}\},\{a_{3}\},\{a_{4}\}\}$, which results from splitting a coalition. The algorithm then selects the coalition structure $\{\{a_{1}\},\{a_{2},a_{3},a_{4}\}\}$, which is, we assume, the highest valued one, and so on. Of course, after each selection, the best coalition structure is updated.
• Figure 2: An illustration of the 3 strategies with a partial graph of 6 agents. The numbers represent the agents. For example, $1$ represents agent $a_{1}$. The last best solution is the red node and the new best one is the green node. The nodes of the path between the two current best solutions of the SPLIT-THEN-MERGE, MERGE-THEN-SPLIT and APPROACH-THEN-SWAP strategies are represented by the orange, purple, and blue nodes, respectively.
• Figure 3: An illustration of the APPROACH-THEN-SWAP strategy.
• Figure 4: Solution quality of SALDAE, PICS and CSG-UCT for sets of agents between 4 and 20.
• Figure 5: Success rate of the SALDAE, PICS and CSG-UCT algorithms on 2000 executions per distribution.

Theorems & Definitions (5)

• Theorem 1
• proof
• proof : Proof of Observation 1
• proof : Proof of Observation 2
• Theorem 2