Combined analytical and empirical learning framework for branch and bound algorithms: the knapsack problem

Optimization methods are being applied to engineering problem solving with increasing frequency as computer hardware and software improves. The configuration of an optimization algorithm can make a significant difference to the efficiency of the solution process. This article examines the use of one such optimization strategy, branch and bound, for the solution of the classic knapsack problem. It is shown that the best configuration of the algorithm can be data dependent and hence that an ‘intelligent’ optimization system will need to automatically configure itself with the control knowledge appropriate to the problems the user is solving. A two-step approach is taken to configuring the algorithm. First, an analytical learning method, explanation based learning is used to derive a provably correct dominance condition for the knapsack problem. Second, the algorithm is configured with and without the condition, and subjected to a rigorous statistical test of performance, on the user's data, to decide which configuration is the best.