An Integrated Solver for Multi-index Assignment

We study the axial and planar multi-index assignment problem under the lens of the (k,s)-Assignment problem, i.e., a framework that encompasses all assignment structures. Taking advantage of the complementary strengths of approaches to optimization, we develop for the problem at hand an integrated solver that offers, constraint propagation, problemspecific cuts, SoS-I branching and a new variant of the Feasibility Pump heuristic that uses cutting planes within the pumping cycles of the algorithm. All these components, when combined in a B&C algorithm for the 3-index axial and planar cases, reduce both the time and the number of nodes in the search tree, particularly for larger instances. This effect is more evident in the planar case, where the number of constraints increases quadratically compared to the axial assignment. Apart from literature, non-polynomial, instances we generate and examine large-size instances for which a competitive commercial solver runs out of memory. Further research includes testing this algorithm on the 4-etc-index size axial and planar assignment problems.