About

Illya V. Hicks is a Trustee Professor and Department Chair of Computational Applied Mathematics and Operations Research at Rice University. He joined the Department of Computational and Applied Mathematics at Rice in 2007, after serving as a faculty member in the Industrial and Systems Engineering Department at Texas A&M University from 2000 to 2006. Hicks received his MA and PhD in Computational and Applied Mathematics from Rice University in 2000, and his bachelor’s degree in mathematics from Southwest Texas State University (currently Texas State University at San Marcos). His research interests include combinatorial optimization, graph theory, and integer programming, with applications in big data, imaging, social networks, cancer treatment, and logistics. He has conducted extensive research in finding cohesive groups in data networks and utilizing graph decomposition techniques to solve complex discrete optimization problems. In addition to his research, Hicks teaches courses in operations research, graph theory, combinatorial optimization, linear and integer optimization, engineering computation, and real analysis. He is actively involved in mentoring and student organizations, serving as the faculty advisor to the undergraduate chapter of the National Society of Black Engineers and the Black Graduate Student Association at Rice. Hicks has also served as a faculty senator and as a faculty advisor to the university president. His contributions have been recognized through honors such as being named an INFORMS Fellow, receiving the Presidential Mentoring Award, the Moving Spirit Award from INFORMS, and the Optimization Prize for Young Researchers from the Optimization Society of INFORMS.

Research topics

• Computer Science
• Mathematics
• Combinatorics
• Discrete mathematics
• Mathematical optimization
• Machine Learning
• Artificial Intelligence
• Pure mathematics
• Algorithm

Selected publications

• Mixed Integer Linear Optimization Formulations for Learning Optimal Binary Classification Trees

  INFORMS journal on computing · 2026-03-12

  articleSenior author

  Decision trees are powerful supervised machine learning tools for classification and regression that attract many academic researchers and industry professionals. In particular, decision trees provide interpretability, which is often preferred over other higher-accuracy methods that are relatively uninterpretable. An optimal binary classification tree has two types of vertices and is obtainable by solving a bi-objective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. In this paper, we propose two mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees: a maximum flow-based formulation and a minimum cut-based formulation, both of which share a common base model. The formulations enforce connected feasible paths for training datapoints through flow-based or cut-based connectivity constraints while maintaining computational tractability without the need for decomposition techniques commonly used to combat scaling concerns. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available data sets to demonstrate our models’ ability to scale, strength against traditional branch-and-bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This research was supported by the Office of Naval Research [Grant N000142412648]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0068 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0068 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

  PublisherDOI

• Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions

  Operations Research · 2025-04-24

  article

  We study mixed-integer programming formulations for the piecewise linear lower and upper bounds (in other words, piecewise linear relaxations) of nonlinear functions that can be modeled by a new class of combinatorial disjunctive constraints (CDCs), generalized nD-ordered CDCs. We first introduce a general formulation technique to model piecewise linear lower and upper bounds of univariate nonlinear functions concurrently so that it uses fewer binary variables than modeling bounds separately. Next, we propose logarithmically sized ideal nonextended formulations to model the piecewise linear relaxations of univariate and higher-dimensional nonlinear functions under the CDC and independent branching frameworks. We also perform computational experiments for the approaches modeling the piecewise linear relaxations of nonlinear functions and show significant speed-ups of our proposed formulations. Furthermore, we demonstrate that piecewise linear relaxations can provide strong dual bounds of the original problems with less computational time by an order of magnitude. Funding: This work was supported by the Office of Naval Research [Grant N000142412648] for Rice University. Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2023.0187 .

  PublisherDOI

• Compact Mixed Integer Programming Formulations for the Minimum Biclique Cover Problem

  Networks · 2025-12-20

  articleSenior author

  ABSTRACT Given a simple graph with vertex set and edge set , the minimum biclique cover problem seeks to cover all edges of the graph with a minimum number of bicliques (i.e., complete bipartite subgraphs). This paper proposes two compact mixed integer programming (MIP) formulations for solving the minimum biclique cover problem on general graphs: (i) A natural formulation in the edge space and (ii) an extended formulation in the edge and vertex spaces. While the natural MIP formulation of Cornaz and Fonlupt ( Discrete Mathematics , 2006) has exponentially many constraints, our natural formulation enjoys only a polynomial number of their exponential “no‐good” cuts, along with another set of polynomial valid inequalities. We also employ bounding and variable fixing procedures that help solve most of our social network instances, which are not solvable to optimality in a one‐hour time limit without the bounding and fixing procedures. The instances that are not solved in the one‐hour time limit are submitted to the 2024 Mixed Integer Programming Library (MIPLIB 2024).

  PublisherDOI

• A folding preprocess for the max k-cut problem

  Optimization Letters · 2025-04-28

  articleOpen access

  Abstract Given graph $$G=(V,E)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> with vertex set V and edge set E , the max k -cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This paper proposes a graph folding procedure (i.e., a procedure that reduces the number of the vertices and edges of graph G ) for the weighted max k -cut problem that may help reduce the problem’s dimensionality. While our theoretical results hold for any $$k \ge 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , our computational results show the effectiveness of the proposed preprocess only for $$k=2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> and on two sets of instances. Furthermore, we observe that the preprocess improves the performance of a MIP solver on a set of large-scale instances of the max cut problem.

  PublisherOA PDFDOI

• Optimizing Cost Hamiltonian Compilation for Max-Cut QAOA on Unweighted Graphs Using Global Controls and Qubit Bit Flips

  ArXiv.org · 2025-08-29

  preprintOpen accessSenior author

  We study a cost Hamiltonian compilation problem for the quantum approximate optimization algorithm (QAOA) applied to the Max-Cut problem, focusing on trapped-ion quantum computers. Instead of standard compilation with CNOT and Rz gates, we employ global coupling operations and single-qubit bit flips. Prior work by Rajakumar et al. established that such a compilation is always possible. Minimizing operational error requires short operation sequences. The problem reduces to a low-rank semi-discrete decomposition of the graph's adjacency matrix, where the minimum achievable rank, the graph coupling number gc(G), represents the number of global control layers. Rajakumar et al. introduced the Union of Stars construction, proving gc(G) &lt;= 3n - 2 for unweighted graphs with n vertices, and gave an O(m)-rank construction for weighted graphs. We concentrate on unweighted graphs. We derive structural properties of the compilation problem and show the Union of Stars method is order-optimal by proving a lower bound of gc(G) &gt;= n - 1 for a family of graphs. We also improve the general upper bound to 2.5n + 2. For particular graph families -- cliques, perfect matchings, paths, and cycles -- we provide sharper bounds. Further, we reveal a link between the problem and Hadamard matrix theory. Finally, we introduce a compact mixed-integer programming (MIP) formulation that outperforms the previously studied exponential-size MIP.

  PublisherOA PDFDOI

• Characterizing QUBO Reformulations of the Max-k-Cut Problem for Quantum Computing

  ArXiv.org · 2025-11-02

  preprintOpen access

  Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a quadratic unconstrained binary optimization (QUBO) problem. The solution of the QUBO reformulation can then be addressed using adiabatic quantum computing devices or appropriate quantum computing algorithms on gate-based quantum computing devices. In general, QUBO reformulations of combinatorial problems can be readily obtained by properly penalizing the violation of the problem's constraints in the original problem's objective. However, characterizing tight (i.e., minimal but sufficient) penalty coefficients for this purpose is important and non-trivial for enabling the solution of the resulting QUBO in current and near-term quantum computing devices. Along these lines, we present closed-form characterizations of tight penalty coefficients for two distinct QUBO reformulations of the max $k$-cut problem whose values depend on the (weighted) degree of the vertices of the graph defining the problem. These findings contribute to the ongoing effort to make quantum computing a viable tool for solving combinatorial problems at scale. We support our theoretical results with illustrative examples and simple numerical results.

  PublisherOA PDFDOI

• The AGEP Engineering Alliance: A Model to Advance Historically URM Postdoctoral Scholars and Early-Career Faculty in Engineering

  2021 ASEE Virtual Annual Conference Content Access Proceedings · 2024-02-20 · 1 citations

  articleOpen access

  Abstract The AGEP Engineering Alliance brings together Georgia Institute of Technology, Florida Agricultural and Mechanical University, William Marsh Rice University, and the University of Colorado Colorado Springs to develop, implement, study, evaluate, and disseminate a model focused on the career development of historically underrepresented minority (URM) engineering postdoctoral scholars who eventually successfully transition into tenure-track faculty positions. Funding for this Alliance was procured from The National Science Foundation (NSF) Alliances for Graduate Education and the Professoriate (AGEP) program (award numbers: 1821298, 1821019, 1821052, and 1821008). Presently, approximately 10% of postdoctoral scholars (Yadav et al., 2020) and 6% of engineering professors (Roy, 2019) identify as racial/ethnic minorities, and this disproportionality will continue until URMs are more effectively engaged and embraced in the discipline (NSF, 2018). To address increasing the effective engagement and embracement of URM postdoctoral scholars, the AGEP Engineering Alliance project team employs an asset-based approach to meeting the career development needs of the project participants by offering both prescribed and customized personal and professional development sessions. This poster details survey evidence of the effectiveness attributed to the sessions presented between 2019-2020 from the point of view of the 11 postdoctoral scholars participating in the project. Sessions included topics on the tenure-track faculty hiring process; expectations for research, teaching, and service in academia; and more nuanced, personal topics such as parenting as a postdoctoral scholar/early-career faculty member. Survey results indicate nearly 100% of participants rated the sessions as relevant to their academic career intentions and beneficial to their academic career planning process. Additionally, results indicate the postdoctoral scholars found conversations amongst themselves and with the AGEP project team members to be valuable as they were able to use the session time to connect, network, and quell individual anxieties as they embarked on tenure-track faculty job searches. Participants also report feeling more informed on teaching responsibilities, academic entrepreneurship prospects, start-up packages, the importance of networking, and pursuing employment at various institutional types because of the sessions. They also recommend additional sessions involving conversations with URM faculty in which they share their tenure-track hiring and faculty experiences; ways to create and optimize mentoring relationships; grant-funding advice; personal branding; effectively managing a lab; and additional guidance on hiring, such as developing well-crafted application packages, preparing for interviews, and negotiating start-up packages. Suggestions on improving the sessions include facilitating more structured rather than organic discussions and meeting more frequently to leverage the project opportunities offered.

  PublisherOA PDFDOI

• Exploring the Mentoring Needs of Engineering Postdoctoral Scholars of Color: Is Systematic Change Required in the Postdoctoral Training Environment? (Research)

  2021 ASEE Virtual Annual Conference Content Access Proceedings · 2024-02-20

  articleOpen access

  This phenomenological study (Moustakas, 1994) explores the mentoring needs of 11 engineering postdoctoral scholars of color with an adaptation of the ideal mentoring model (Zambrana et al., 2015) used as the conceptual framework.A critical theory lens (Morrow & Brown, 1994) is applied to Moustakas' (1994) four-stage process of phenomenological data analysis to examine the interview data: epoch, horizontalization, imaginative variation, and synthesis.The essence of the phenomenon is engineering postdoctoral scholars of color have primary and secondary mentoring needs pertaining to their immediate career acquisition of a tenure-track faculty position.Primary mentoring needs include expanding professional networks for the tenure-track faculty job search and receiving guidance on work-life balance and enhancing technical skills.Secondary needs consist of refining research directions

  PublisherOA PDFDOI

• The Many Face(t)s of Zero Forcing

  Notices of the American Mathematical Society · 2024-01-10 · 2 citations

  articleOpen access1st authorCorresponding

  In this article, we outline several different settings where the zero forcing problem arose independently, and then discuss some of the solution techniques and remaining challenges related to the problem.

  PublisherDOI

• Optimal Mixed Integer Linear Optimization Trained Multivariate Classification Trees

  arXiv (Cornell University) · 2024-08-02

  preprintOpen accessSenior author

  Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have exactly two children and where datapoints are assessed on a set of discrete features and (ii) leaf vertices at which datapoints are given a prediction, and can be obtained by solving a biobjective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. Branching vertices are linear combinations of training features and therefore can be thought of as hyperplanes. In this paper, we propose two cut-based mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees (leaf vertices assign discrete classes). Our models leverage on-the-fly identification of minimal infeasible subsystems (MISs) from which we derive cutting planes that hold the form of packing constraints. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available datasets to show our models' ability to scale, strength against traditional branch and bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub.

  PublisherOA PDFDOI

Recent grants

• Innovative Techniques for Constructing Branch Decompositions

  NSF · $117k · 2006–2009

• Collaborative Research: Zero Forcing on Graphs: Computation and Applications

  NSF · $204k · 2017–2021

• Innovative Techniques to Optimally Distribute and Package Healthcare Services for Rural and Remote Areas

  NSF · $250k · 2013–2017

• Collaborative Research: Risk-Averse Cluster Detection in Network Models of Bigdata Under Measurement Uncertainty

  NSF · $175k · 2014–2018

• Branch Decomposition Techniques for Submodular Optimization

  NSF · $261k · 2009–2013

Frequent coauthors

• Hamidreza Validi

  Texas Tech University

  76 shared

• Stuart Baxley

  IBM (United States)

  65 shared

• Deniz Gurkan

  University of Houston

  65 shared

• Taras Lykhenko

  Temple College

  64 shared

• Y. Charlie Hu

  64 shared

• Ning Liu

  State Grid Corporation of China (China)

  64 shared

• Jason Liu

  64 shared

• Ruizhe Jiang

  Qingdao University

  64 shared

Awards & honors

• INFORMS Fellow
• Presidential Mentoring Award
• Moving Spirit Award from the Institute for Operations Resear…
• Optimization Prize for Young Researchers from the Optimizati…