Abstract

This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a well-known optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear equalities and inequalities. The state of the art in solvers for this problem is the “branch and bound ” approach. The performance of such solvers depends crucially on four types of in-built heuristics: primal, improvement, branching, and cut-separation or, more generally, bounding heuristics. Such heuristics in general-purpose solvers have not, until recently, exploited structure in integer linear programs beyond the recognition of certain types of single-row constraints. Many alternative approaches to integer linear programming can be cast in the following, novel framework. “Structure” in any integer linear program

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