A double oracle approach to minmax regret optimization problems with interval data

In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk [2]. The validity of the bound is based on game theoretic arguments and its computation is performed via a double oracle algorithm [6] that we specify. The lower bound can be efficiently computed for any minmax regret optimization problem whose standard version is “easy”. We describe how to efficiently embed this lower bound in a branch and bound procedure. Finally we apply our approach to the robust shortest path problem. Our numerical results show a significant gain in the computation times.