Coalition Calculation in a Dynamic Agent Environment Ted Scully Edward.Scully@nuigalway.ie Michael G. Madden Michael.Madden@nuigalway.ie Gerard Lyons Gerard.Lyons@nuigalway.ie Department of Information Technology, National University of Ireland, Galway, Ireland. Abstract We consider a dynamic market-place of self- interested agents with differing capabilities. A task to be completed is proposed to the agent population. An agent attempts to form a coalition of agents to perform the task. Be- fore proposing a coalition, the agent must determine the optimal set of agents with whom to enter into a coalition for this task; we refer to this activity as coalition calcu- lation. To determine the optimal coalition, the agent must have a means of calculating the value of any given coalition. Multiple metrics (cost, time, quality etc.) determine the true value of a coalition. However, be- cause of conflicting metrics, differing metric importance and the tendency of metric im- portance to vary over time, it is difficult to obtain a true valuation of a given coalition. Previous work has not addressed these issues. We present a solution based on the adapta- tion of a multi-objective optimization evolu- tionary algorithm. In order to obtain a true valuation of any coalition, we use the con- cept of Pareto dominance coupled with a dis- tance weighting algorithm. We determine the Pareto optimal set of coalitions and then use an instance-based learning algorithm to se- lect the optimal coalition. We show through empirical evaluation that the proposed tech- nique is capable of eliciting metric impor- tance and adapting to metric variation over time. Appearing in Proceedings of the 21 st International Confer- ence on Machine Learning, Banff, Canada, 2004. Copyright 2004 by the authors. 1. INTRODUCTION A coalition is a set of self-interested agents that agree to cooperate to execute a task or achieve a goal (Tsve- tovat et al., 2000). Coalition formation is currently an active area of research in multiagent systems. This paper considers coalition formation in the context of a market-place where organizations (represented by agents) can cooperate to bid for and perform a task. While the techniques proposed in this paper are gen- erally applicable, we provide context for the work by considering a simplified model of a real world transport market-place. Each agent represents a transportation firm, and its abilities relate to the routes its firm can service. A task involves the transportation of an item from a collection point to a delivery point. The task is broken into subtasks, which are the routes that consti- tute a complete journey. Because different firms have different abilities, their representative agents may form coalitions to service a transportation task. In this domain, a transportation task consisting of sev- eral subtasks is proposed in the market-place. Each agent attempts to form a coalition with other agents to bid for the task. Thus, multiple coalitions are pro- posed and these compete to be awarded the task. We examine the problem from the perspective of an indi- vidual agent; we are not concerned with overall sys- tem performance and we do not make any assump- tions about other agents’ strategies for coalition for- mation. We assume an agent can provide assessments of the abilities of all other agents in the market, but that these assessments are based on personal beliefs rather than objective information. Based on these as- sessments and the task proposed, it must determine the optimal coalition to propose. We define coalition calculation as the determination of the optimal set of agents with which to enter into coalition. Dutta and Sen (2002) observe that in real-life scenarios, multi- ple objectives like time, quality, dependability, etc., will be involved when an agent evaluates the benefit of interacting with another agent. This statement also