Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

Generalizing Backdoors

A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of \Backdoor" variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo- Backdoors and Heuristic-Backdoors are formally introduced and then applied ¯rstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the e®ectiveness of these approaches that are able to produce very low run times and | in the case of Heuristic-Backdoors | high quality solutions by employing very simple heuristic rules such as greedy local search strategies

Modelling dynamic programming-based global constraints in constraint programming

Dynamic Programming (DP) can solve many complex problems in polynomial or pseudo-polynomial time, and it is widely used in Constraint Programming (CP) to implement powerful global constraints. Implementing such constraints is a nontrivial task beyond the capability of most CP users, who must rely on their CP solver to provide an appropriate global constraint library. This also limits the usefulness of generic CP languages, some or all of whose solvers might not provide the required constraints. A technique was recently introduced for directly modelling DP in CP, which provides a way around this problem. However, no comparison of the technique with other approaches was made, and it was missing a clear formalisation. In this paper we formalise the approach and compare it with existing techniques on MiniZinc benchmark problems, including the flow formulation of DP in Integer Programming. We further show how it can be improved by state reduction methods