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 remain still unsolved with it. We present an improving technique for branch-and-bound methods applied to Brucker et al.'s algorithm for Open-Shop problems. Our technique is based on intelligent backtracking. An adaptation of a generic explanation system we have initially developed in the constraint programming scheme is used to develop that technique. We tested our approach on Open-Shop problems from the literature (benchmarks of Taillard). The search is definitely improved: on some square problems of size 10, the number of backtracks is reduced by more than 90% and we even solved an open problem of that size.