A Pruning-Based Algorithm for Computing Optimal Coalition Structures in Linear Production Domains

Computing optimal coalition structures is an important research problem in multi-agent systems. It has rich application in real world problems, including logistics and supply chains. We study computing optimal coalition structures in linear production domains. The common goal of the agents is to maximize the system’s profit. Agents perform two steps: i) deliberate profitable coalitions, and ii) exchange computed coalitions and compute optimal coalition structures. In our previous studies, agents keep growing their coalitions from the singleton ones in the deliberation step. This work takes opposite approach that agents keep pruning unlikely profitable coalitions from the grand coalition. It also relaxes the strict condition of coalition center, which yields the minimal cost to the coalition, that agents merely keep generating profitable coalitions. Furthermore, we discuss relevant concept, i.e., integer partition, that draw into concept in our algorithm and provide an example of how it can work. Lastly, we show that our algorithm outperforms exhaustive search in generating optimal coalition structures in terms of elapses time and number of coalition structures generated.