On the application of explanation-based learning to acquire control knowledge for branch and bound algorithms

The goal of this article is to present a methodology for the automatic acquisition of new control knowledge in the form of dominance and equivalence conditions, using an explanation-based learning algorithm from artificial intelligence. The acquisition of new control knowledge proceeds through the following stages: 1) Analysis of the problem-solving activity, generated from the application of a branch and bound algorithm on specific instance(s) of a class of problems. 2) Interpretation of the problem-solving activity and synthesis of new control knowledge, which can lead to more efficient solution of future problems. The generated control knowledge is provably correct within the theory of the given class of problems and the employed branch and bound strategy. Consequently, the number of nodes evaluated by a specific branch and bound algorithm is guaranteed to be reduced, as new control knowledge is continuously acquired from the solution of specific problems. The article presents the theoretical foundations for the handling of the above two tasks. It concludes with an application of the proposed approach to a mixed integer linear programming formulation of a batch scheduling problem.