Valuation-based systems for discrete optimisation

This paper describes valuation-based systems for representing and solving discrete optimization problems. The information in an optimization problem is represented using variables, sample spaces of variables, a set of values, and func­ tions that map sample spaces of sets of variables to the set of values. The func­ tions, called valuations, represent the factors of an objective function. Solving the optimization problem involves using two operations called combination and marginalization. The combination operation tells us how to combine the factors of the objective function to form the global objective function. Marginalization is either maximization or minimization. Solving an optimization problem can be simply described as finding the marginal of the joint objective function for the empty set. We state some simple axioms that combination and marginalization need to satisfy to enable us to solve an optimization problem using local compu­ tation.