Searching for overlapping coalitions in multiple virtual organizations

Coalition formation is an active and essential component for multi-agent systems (MAS) in task-oriented domains in which tasks can be too complicated to be accomplished by a single agent with insufficient resources. By forming a coalition, agents are able to cooperate and combine resources to complete tasks that are impossible to accomplish alone within a given time bound. For example, in virtual enterprises, small and agile enterprises can provide more services and make more profits than an individual can. In many multi-task environments, especially in parallel multi-task environments, an individual abundant in resources is inclined to undertake more than one task to make more profits and participate in multiple virtual organizations (MVOs) at the same time, where every member has to decide how to allocate different parts of its resources to serve multiple different project tasks. Such overlapping property is a very intractable problem in practical decision making, and to the best of our knowledge, current coalition formation algorithms typically exclude the possibility of having overlapping coalitions, that is an agent can only be a member of one coalition at any given time, leading to waste of resources, preventing the system from efficiently allocating all agents’ resources, and limiting the scope of their applications in real-world scenarios. Indeed, overlapping coalition formation (OCF) is an important research question, because MVOs are very crucial and beneficial in parallel multi-task domains where only a few selected individuals have rare, but highly demanded, resources. With this in mind, we develop a discrete particle swarm optimization based algorithm to solve the OCF problem in MVOs, applicable for more complex virtual enterprises environments. We introduce a two-dimensional binary encoding scheme and propose a novel repairing strategy for resolving conflicts over the usage of joint resources among overlapping coalitions. With this novel strategy for cooperative conflict resolution, any invalid encoding can be adjusted into a valid one without any resource conflict. Finally, simulations are conducted to show the efficiency of the proposed algorithm.