Augmentation search for integer programming over a polyhedron

Abstract

This paper describes a primal search algorithm to optimise an integer programme defined over a polyhedron. The search is conducted on the lattice described by the linear constraints of the model, where search directions are derived in the spirit of Graver bases and extracted dynamically using a feasibility-seeking black-box. Computational results show potential particularly on 0-1 programming formulations with complex objective functions when compared with state-of-the-art solvers.