Abstract

Introduction Exact methods used to solve difficult Combinatorial Optimization problems belong to a generic type. Widely used in Operations Research (OR) and Artificial Intelligence (AI), they consist of exploring a search space : -- the tree of subproblems generated by recursive partitioning of the initial problem (OR : Branch-and-Bound, denoted B&B and Branch-and-Cut algorithms) , -- the graph of transitions between states (AI : A* algorithm, ff \Gamma fi). Exhaustive search of the space is avoided; the acquisition of knowledge during the search allows to prune certain nodes or to eliminate some parts of the space. But as computational requirements (time and space) grow exponentially with the problem size, the possibilities of overflowing storage or consuming too much time can hang the program before reaching the optimal solution. To deal with this type of exploration which tends to create a combinatorial explos

Citations