New commodity representations for multicommodity network flow problems: An application to the fixed-charge network design problem

by   Ahmad Kazemi, et al.

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The conventional approach to improve the solve time of the LP relaxation of a Mixed Integer Programming (MIP) model that encodes such an instance is to aggregate all commodities that have the same origin or the same destination. However, the bound of the resulting LP relaxation can significantly worsen, which tempers the efficiency of aggregating techniques. In this paper, we introduce the concept of partial aggregation of commodities that aggregates commodities over a subset of the network instead of the conventional aggregation over the entire underlying network. This offers a high level of control on the trade-off between size of the aggregated MIP model and quality of its LP bound. We apply the concept of partial aggregation to two different MIP models for the multicommodity network design problem. Our computational study on benchmark instances confirms that the trade-off between solve time and LP bound can be controlled by the level of aggregation, and that choosing a good trade-off can allow us to solve the original large-scale problems faster than without aggregation or with full aggregation.


page 1

page 2

page 3

page 4


Towards Efficient Large-Scale Network Slicing: An LP Rounding-and-Refinement Approach

In this paper, we propose an efficient algorithm for the network slicing...

The Invisible Hand Heuristic for Origin-Destination Integer Multicommodity Network Flows

Origin-destination integer multicommodity flow problems differ from clas...

Recursive McCormick Linearization of Multilinear Programs

Linear programming (LP) relaxations are widely employed in exact solutio...

On Partial Opimality by Auxiliary Submodular Problems

In this work, we prove several relations between three different energy ...

Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers

Formal verification of neural networks (NNs) is a challenging and import...

A scaleable projection-based branch-and-cut algorithm for the p-center problem

The p-center problem (pCP) is a fundamental problem in location science,...

MIPaaL: Mixed Integer Program as a Layer

Machine learning components commonly appear in larger decision-making pi...

Please sign up or login with your details

Forgot password? Click here to reset