Coalition Formation For Distributed Constraint Optimization Problems

This dissertation presents our research on coalition formation for Distributed Constraint Optimization Problems (DCOP). In a DCOP, a problem is broken up into many disjoint sub-problems, each controlled by an autonomous agent and together the system of agents have a joint goal of maximizing a global utility function. In particular, we study the use of coalitions for solving distributed k-coloring problems using iterative approximate algorithms, which do not guarantee optimal results, but provide fast and economic solutions in resource constrained environments. The challenge in forming coalitions using iterative approximate algorithms is in identifying constraint dependencies between agents that allow for effective coalitions to form. We first present the Virtual Structure Reduction (VSR) Algorithm and its integration with a modified version of an iterative approximate solver. The VSR algorithm is the first distributed approach for finding structural relationships, called strict frozen pairs, between agents that allows for effective coalition formation. Using coalition structures allows for both more efficient search and higher overall utility in the solutions. Secondly, we relax the assumption of strict frozen pairs and allow coalitions to form under a probabilistic relationship. We identify probabilistic frozen pairs by calculating the propensity between two agents, or the joint probability of two agents in a k-coloring problem having the same value in all satisfiable instances. Using propensity, we form coalitions in sparse graphs where strict frozen pairs may not exist, but there is still benefit to forming coalitions. Lastly, we present a cooperative game theoretic approach where agents search for Nash stable coalitions under the conditions of additively separable and symmetric value functions