Cost Propagation - Numerical Propagation for Optimization Problems

Abstract: In this thesis, we investigate Cost Propagation, an approach to numerical propagation for optimization problems, where we combine ideas from both Constraint Programming and Combinatorial Optimization. We consider discrete optimization problems with binary variables that can be expressed in the model max_x sum_k g_k(x^k) where the terms g_k(x^k) are distinct arbitrary functions over subsets x^k of x. The problem is iteratively solved by propagation, i.e. by updates for single constraints or terms in the optimization model. We formalize a theory of updates in terms of equivalent problems with notions of consistency, local optimality, convergence and bounds, and with links to Linear Programming theory. We discuss some specific updates and analyse their behavior in propagation. Further, we introduce a special update, the non-conflicting update,that guarantees optimality if a solution is found by propagation. Finally, we perform computational experiments on three sample problems, the Assignment problem, a crossword puzzle and the Set Partitioning problem, illustrating advantages and limitations of the approach. The experiments also show that Cost Propagation can by itself solve non-trivial problems even without a top level search, which is otherwise needed to create a complete algorithm.