Fault-Tolerant Mechanism for Hierarchical Branch and Bound Algorithm

Solving exactly large instances of Combinatorial Optimization Problems emph{(COPs)} using Branch and Bound emph{(B&B) }algorithms requires a huge amount of computing resources. These resources can be offered by computational grids and the scalability can be achieved using Hierarchical Master/Worker-based B&B pushing the limits of the traditional Master/Worker paradigm. However, the resources offered by grids are most of the time unreliable, volatile, and heterogeneous. Therefore, they must take into account fault tolerance. In this paper, we present FTH-B&B, a fault tolerant hierarchical B&B, in order to deal with the fault tolerance issue. It is composed of several fault tolerant Master/Worker-based sub-B&Bs organized hierarchically into groups and perform independently fault tolerant mechanism. Beside, a fault recovery mechanism is introduced to recover and avoid redundant exploration of sub-problems in case of failures. In addition, we propose a mechanism to maintain the hierarchy safe and balanced during the lifetime of the algorithm. Our algorithm is applied to the Flow-Shop scheduling problem emph{(FSP)} and implemented on top of the ProActive grid middleware. It has been promisingly experimented on the Grid´5000 French nation-wide grid and shows its ability to remain efficient even in presence of failures.