Improving coalition structure search with an imperfect algorithm: analysis and evaluation results

Optimal Coalition Structure Generation (CSG) is a significant research problem in multi-agent systems that remains difficult to solve. This problem has many important applications in transportation, eCommerce, distributed sensor networks and others. The CSG problem is NP-complete and finding the optimal result for n agents needs to check $$O (n^n)$$ O ( n n ) possible partitions. The ODP–IP algorithm (Michalak et al. in Artif Intell 230:14–50, 2016) achieves the current lowest worst-case time complexity of $$O (3^n)$$ O ( 3 n ) . In the light of its high computational time complexity, we devise an Imperfect Dynamic Programming (ImDP) algorithm for the CSG problem with runtime $$O (n2^n)$$ O ( n 2 n ) given n agents. Imperfect algorithm means that there are some contrived inputs for which the algorithm fails to give the optimal result. We benchmarked ImDP against ODP–IP and proved its efficiency. Experimental results confirmed that ImDP algorithm performance is better for several data distributions, and for some it improves dramatically ODP–IP. For example, given 27 agents, with ImDP for agent-based uniform distribution time gain is 91% (i.e. 49 min).