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.