Using intelligent backtracking to improve branch-and-bound methods: An application to Open-Shop problems

Only two branch-and-bound methods have been published so far for the Open-Shop problem. The best one has been proposed by Brucker et al. But some square problems from size 7 are still unsolved by it. We present an improving technique for branch-and-bound methods applied to Brucker et al. algorithm for Open-Shop problems. Our technique is based on intelligent backtracking. Intelligent backtracking techniques involve the computation of explanations when encountering a contradiction in the search. We present here an adaptation of a generic explanation system we have initially developed in the constraint programming scheme. We tested our approach on Open-Shop problems from the literature (benchmarks of Taillard). The search is de nitely improved : on some square problems of size 10, the number of explored nodes is reduced by more than 90% and we solved an open problem of size 10. We applied our technique on Open-Shop problems, but it can easily be adapted to solve any other shop problems with a Branch-and-Bound in which the branching scheme consists in xing disjunctions.