Without trying all 2,000! possible combinations of dorm room assignments, we would like to find the combination where everyone is the happiest. To do this we need a way to quantify how bad a configuration is, that is, how unhappy the students are likely to be. We define an objective function, , to capture as much knowledge as possible regarding preferences and policy choices. Our goal is to find the set of assignments with the smallest value of , thereby minimizing mismatches.