## Positions:

Professor

## Education:

Ph.D., Cornell University

## Research Area:

Discrete Optimization

Polyhedral Theory

Combinatorial Optimization

Design and Implementation of Algorithms

Parallel Algorithms

Graphs and Network Flows

## Classes Taught:

Integer Programming

Linear Programming

Non-linear Programming

Algorithms in Systems Engineering

Computation in Operations Research

Introduction to Engineering Practice

Systems Engineering Design

## Interests:

Discrete Optimization

Combinatorial Optimization

Logistics Problems

Routing and Packing Problems

Electronic Auctions

Graphs and Network Flows

Design and Analysis of ALgorithms

Parallel Algorithms

Computational Biology

Dr. Ralphs is a co-founder and co-director of the Computational Optimization Research at Lehigh (COR@L) Laboratory and chairs Lehigh's High-performance Computing Steering Committee. Dr. Ralphs' research focuses on theoretical and computational aspects of the solution and analysis of mixed-integer linear programs, including the implementation of parallel algorithms and the use of high-performance computing platforms. Courses taught by Dr. Ralphs include an introduction to mathematical programming, integer programming, nonlinear programming, and algorithms in systems engineering. Dr. Ralphs has been with the faculty since 2000.

## Publications:

M. V. Galati and T. K. Ralphs, "DIP: A Framework for Decomposition in Integer Programming," COR@L Laboratory, Lehigh University, 2014 (working paper).

A. Hassanzadeh, T. K. Ralphs, and M. Güzelsoy, "On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for Its Construction," COR@L Laboratory, Lehigh University, 2014 (available by request).

A. Bulut and T. K. Ralphs, "Inverse Integer Programming," COR@L Laboratory, Lehigh University, 2014 (working paper).

A. Bulut and T. K. Ralphs, "On the Complexity of Optimization Problems," COR@L Laboratory, Lehigh University, 2014 (working paper).

A. Hassanzadeh and T. K. Ralphs, "A Generalized Benders’ Algorithm for Two-Stage Stochastic Program with Mixed Integer Recourse," CRO@L Laboratory, Lehigh University, 2014 (available by request).

A. Lodi, T. K. Ralphs, and G. Woeginger, "Bilevel Programming and the Separation Problem," Mathematical Programming, 2013 (to appear).

P. Belotti, J. C. Goez, I. Polik, T. K. Ralphs, and T. Terlaky, "On Families of Quadratic Surfaces Having Fixed Intersection with Two Hyperplanes," Discrete Applied Mathematics, vol. 161, p. 2778, 2013.

T. K. Ralphs, M. Guzelsoy, and A. Mahajan, "SYMPHONY Version 5.5 User’s Manual," COR@L Laboratory, Lehigh University, 2013

K. L. Hoffman and T. K. Ralphs, "Integer and Combinatorial Optimization," COR@L Laboratory, Lehigh University, 2013 (to appear).

J. Wang and T. K. Ralphs, "Computational Experience with Hypergraph-based Methods for Automatic Decomposition in Discrete Optimization," in Proceedings of the Conference on Constraint Programming, Artificial Intelligence, and Operations Research, 2013, p. 394.

P. Belotti, J. C. Goez, I. Polik, T. K. Ralphs, and T. Terlaky, "A Conic Representation of the Convex Hull of Disjunctive Sets and Conic Cuts for Integer Second Order Cone Optimization," COR@L Laboratory Report 12T-009, Lehigh University, 2012

J. Wang and T. K. Ralphs, "Computational Experience with Hypergraph-based Methods for Automatic Decomposition in Discrete Optimization," COR@L Laboratory Report 12T-014, Lehigh University, 2012

T. Koch, T. Ralphs, and Y. Shinano, "Could We Use a Millon Cores to Solve an Integer Program?," Mathematical Methods of Operations Research, vol. 76, pp. 67-93, 2012.

M. V. Galati, T. K. Ralphs, and J. Wang, "Computational Experience with Generic Decomposition using the DIP Framework," in Proceedings of RAMP 2012, 2012.

M. Güzelsoy and T. K. Ralphs, "Warm-starting for Real-time Vehicle Routing," COR@L Laboratory, Lehigh University, 2011 (available by request).

T. K. Ralphs, M. Güzelsoy, and A. Mahajan, "SYMPHONY Version 5.3 User’s Manual," COR@L Laboratory, Lehigh University, 2011

T. K. Ralphs, M. Güzelsoy, and A. Mahajan, "SYMPHONY Version 5.4 User’s Manual," COR@L Laboratory, Lehigh University, 2011

T. Koch, T. Achterburg, E. Andersen, O. Bastert, T. Berthold, R. E. Bixby, E. Danna, G. Gamrath, A. Gleixner, S. Heinz, A. Lodi, H. Mittelmann, T. K. Ralphs, D. Salvagnin, D. Steffy, and K. Wolter, "MIPLIB 2010," Mathematical Programming Computation, vol. 3, pp. 103-163, 2011.

A. Lodi, T. K. Ralphs, F. Rossi, and S. Smriglio, "Interdiction Branching," COR@L Laboratory, Lehigh University, 2011

S. DeNegre and T. K. Ralphs, "A Branch-and-Cut Algorithm for Bilevel Integer Programming," in Proceedings of the Eleventh INFORMS Computing Society Meeting, 2009, pp. 65-78.

A. Mahajan and T. K. Ralphs, "Experiments with Branching using General Disjunctions," in Proceedings of the Eleventh INFORMS Computing Society Meeting, 2009, pp. 101-118.

Z. Akca, R. T. Berger, and T. K. Ralphs, "A Branch-and-Price Algorithm for Combined Location and Routing Problems Under Capacity Restrictions," in Proceedings of the Eleventh INFORMS Computing Society Meeting, 2009, pp. 309-330.