A heuristic for constrained set partitioning in the light of heterogeneous objectives

Abstract

The set partitioning problem (SPP) is at the heart of the formation of several organizational structures in multi-agent systems. Essentially, such structures can improve scalability and enable cooperation between agents with limited resources and capabilities. We present a discrete Particle Swarm Optimizer that solves the NP-hard SPP in the presence of partitioning constraints which restrict valid partitionings in terms of acceptable ranges for the number and the size of partitions. To be applicable to a broad range of applications, our algorithm relies on basic set operations to come to a solution and is thus independent of the characteristics of a specific objective function. Among other things, it can be used for coalition structure generation, strict partitioning clustering, anticlustering, and, combined with an additional control loop, even for the creation of hierarchical partitionings. Our evaluation confirms that it finds high-quality solutions in different scenarios and for various objectives in short time.