A Grid-enabled Branch and Bound Algorithm for Solving Challenging Combinatorial Optimization Problems

摘要

Solving optimally large instances of combinatorial optimization problems requires a huge amount of computational resources. In this paper, we propose an adaptation of the parallel branch and bound algorithm for computational grids. Such gridification is based on new ways to efficiently deal with some crucial issues, mainly dynamic adaptive load balancing, fault tolerance, global information sharing and termination detection of the algorithm. A new efficient coding of the work units (search sub-trees) distributed during the exploration of the search tree is proposed to optimize the involved communications. The algorithm has been implemented following a large scale idle time stealing paradigm (Farmer-Worker). It has been experimented on a flow-shop problem instance (Ta056) that has never been optimally solved. The new algorithm allowed to realize a success story as the optimal solution has been found with proof of optimality, within 25 days using about 1900 processors belonging to 9 Nation-wide distinct clusters (administration domains). During the resolution, the worker processors were exploited with an average of 97% while the farmer processor was exploited only 1.7% of the time. These two rates are good indicators on the efficiency of the proposed approach and its scalability.