About

Michael A. Forbes is an Assistant Professor at the Siebel School of Computing and Data Science at the University of Illinois Urbana-Champaign. His research areas include Theory and Algorithms, with recent courses taught in algorithms, computational complexity, algebra, and geometric theory. Forbes has received recognition for his work, including winning Best Paper at the 2024 Computational Complexity Conference for his work on low-depth algebraic circuit lower bounds over any field. His primary research aims are devoted to algebraic and geometric complexity theory, supported by NSF CAREER Award funding.

Research topics

• Computer Science
• Mathematical optimization
• Mathematics
• Algorithm
• Artificial Intelligence
• Engineering
• Economics
• Chemistry
• Electrical engineering
• Telecommunications
• Discrete mathematics

Selected publications

• Hybrid Restricted Master Problem for Boolean Matrix Factorisation

  Proceedings of the AAAI Conference on Artificial Intelligence · 2026-03-14

  articleOpen access

  We present bfact, a Python package for performing accurate low-rank Boolean matrix factorisation (BMF). bfact uses a hybrid combinatorial optimisation approach based on a priori candidate factors generated from clustering algorithms. It selects the best disjoint factors before performing either a second combinatorial or heuristic algorithm to recover the BMF. We show that bfact does particularly well at estimating the true rank of matrices in simulated settings. In real benchmarks, using a collation of single-cell RNA-sequencing datasets from the Human Lung Cell Atlas, we show that bfact achieves strong signal recovery, with a much lower rank.

  PublisherDOI

• Algorithms for pickup and delivery problems with hours of service constraints

  Computers & Operations Research · 2025-06-14

  articleOpen access
  PublisherDOI

• Puzzle—Queen Puzzles: An Educational Approach to Integer Programming Techniques

  INFORMS Transactions on Education · 2025-08-01

  articleOpen accessSenior author

  Chessboard puzzles involving queens are valuable teaching examples for integer programming. We present the queens domination and peaceable queens problems in an educational format and describe our classroom experience with teaching these problems. We discuss techniques for improving efficiency, such as symmetry breaking, valid inequalities, bounds, and parameters. Funding: This work was supported by the Australian Government (RTP Scholarship).

  PublisherDOI

• Hybrid restricted master problem for Boolean matrix factorisation

  ArXiv.org · 2025-09-07

  preprintOpen access

  We present bfact, a Python package for performing accurate low-rank Boolean matrix factorisation (BMF). bfact uses a hybrid combinatorial optimisation approach based on a priori candidate factors generated from clustering algorithms. It selects the best disjoint factors before performing either a second combinatorial or heuristic algorithm to recover the BMF. We show that bfact does particularly well at estimating the true rank of matrices in simulated settings. In real benchmarks, using a collation of single-cell RNA-sequencing datasets from the Human Lung Cell Atlas, we show that bfact achieves strong signal recovery, with a much lower rank.

  PublisherOA PDFDOI

• A Novel Heuristic for Scenario Approximations of Chance Constrained Programs

  SSRN Electronic Journal · 2025-01-01

  preprintOpen accessSenior author
  PublisherDOI

• A novel strategic planning and sequencing optimisation model for Fully Mobile In-Pit Crusher Conveyor (FMIPCC) systems

  International Journal of Mining Reclamation and Environment · 2025-07-01 · 1 citations

  articleOpen access
  PublisherDOI

• Optimal Phylogenetic Reconstruction of Insertion and Deletion Events

  bioRxiv (Cold Spring Harbor Laboratory) · 2024-01-29

  preprintOpen access

  Abstract Insertions and deletions (indels) influence the genetic code in fundamentally distinct ways from substitutions, significantly impacting gene product structure and function. Despite their influence, the evolutionary history of indels is often neglected in phylogenetic tree inference and ancestral sequence reconstruction, hindering efforts to comprehend biological diversity determinants and engineer variants for medical and industrial applications. We frame determining the optimal history of indel events as a single Mixed-Integer Programming (MIP) problem, across all nodes in a phylogenetic tree adhering to topological constraints, and all sites implied by a given set of aligned, extant sequences. By disentangling the impact on ancestral sequences at each branch point, this approach identifies the minimal indel events that jointly explain the diversity in sequences mapped to the tips of that tree. MIP can recover alternate optimal indel histories, if available. We evaluated MIP for indel inference on a dataset comprising 15 real phylogenetic trees associated with protein families ranging from 165 to 2000 extant sequences, and on 60 synthetic trees at comparable scales of data and reflecting realistic rates of mutation. Across relevant metrics, MIP outperformed alternative parsimony-based approaches and reported the fewest indel events, on par or below their occurrence in synthetic datasets. MIP offers a rational justification for indel patterns in extant sequences; importantly, it uniquely identifies global optima on complex protein data sets without making unrealistic assumptions of independence or evolutionary underpinnings, promising a deeper understanding of molecular evolution and aiding novel protein design.

  PublisherOA PDFDOI

• The Value of Drilling—A Chance-Constrained Optimization Approach

  Mining Metallurgy & Exploration · 2024-08-22 · 1 citations

  articleOpen accessSenior author

  Abstract Managing uncertainty is a core challenge in mine planning. Mine planners often represent various planning variables, such as equipment performance and geological parameters, as random variables due to inherent uncertainties. This paper looks at geological uncertainty and its impact on mine planning. Some traditional approaches to manage this uncertainty include using conditional simulations or mathematical programming in the planning process. Drilling additional holes, despite its cost, is a common method to reduce uncertainty using additional samples to reduce deposit variance. In this paper, we first outline an ore blending optimization model which uses chance-constrained programming to manage property limit risk when selecting the order of ore feed into a processing facility. In coal mining, in tactical planning horizons, the order of coal seam removal is usually predetermined, allowing a blending model to ensure optimal feed properties. Using chance-constrained programming allows us to blend the uncertainties from geological models to maximize plant output while adhering to property constraints. We use the chance-constrained blending model to determine the value of additional information from infill drilling. The model prioritizes drilling locations that reduce uncertainty and improve blending outcomes. A case study on a coking coal mine in Queensland, Australia, demonstrates the model’s application, highlighting significant improvements in blending by reducing the variance of high-quality blocks. The study concludes that targeting high-quality blocks for variance reduction can better accommodate lower-quality material, offering a more valuable approach than the traditional focus of reducing uncertainty in low-quality blocks. This approach provides insights for improving mine planning strategies and showcases the potential of chance constraints in optimizing ore blending under uncertainty.

  PublisherOA PDFDOI

• Enhancements of Fragment Based Algorithms for Vehicle Routing Problems

  arXiv (Cornell University) · 2024-11-20 · 1 citations

  preprintOpen accessSenior author

  The method of fragments was recently proposed, and its effectiveness has been empirically shown for three specialised pickup and delivery problems. We propose an enhanced fragment algorithm that for the first time, effectively solves the Pickup and Delivery Problem with Time Windows. Additionally, we describe the approach in general terms to exemplify its theoretical applicability to vehicle routing problems without pickup and delivery requirements. We then apply it to the Truck-Based Drone Delivery Routing Problem Problem with Time Windows. The algorithm uses a fragment formulation rather than a route one. The definition of a fragment is problem specific, but generally, they can be thought of as enumerable segments of routes with a particular structure. A resource expanded network is constructed from the fragments and is iteratively updated via dynamic discretization discovery. Additionally, we introduce two new concepts called formulation leveraging and column enumeration for row elimination that are crucial for solving difficult problems. These use the strong linear relaxation of the route formulation to strengthen the fragment formulation. We test our algorithm on instances of the Pickup and Delivery Problem with Time Windows and the Truck-Based Drone Delivery Routing Problem with Time Windows. Our approach is competitive with, or outperforms the state-of-the-art algorithm for both.

  PublisherOA PDFDOI

• Optimal phylogenetic reconstruction of insertion and deletion events

  Bioinformatics · 2024-05-09 · 3 citations

  articleOpen access

  MOTIVATION: Insertions and deletions (indels) influence the genetic code in fundamentally distinct ways from substitutions, significantly impacting gene product structure and function. Despite their influence, the evolutionary history of indels is often neglected in phylogenetic tree inference and ancestral sequence reconstruction, hindering efforts to comprehend biological diversity determinants and engineer variants for medical and industrial applications. RESULTS: We frame determining the optimal history of indel events as a single Mixed-Integer Programming (MIP) problem, across all branch points in a phylogenetic tree adhering to topological constraints, and all sites implied by a given set of aligned, extant sequences. By disentangling the impact on ancestral sequences at each branch point, this approach identifies the minimal indel events that jointly explain the diversity in sequences mapped to the tips of that tree. MIP can recover alternate optimal indel histories, if available. We evaluated MIP for indel inference on a dataset comprising 15 real phylogenetic trees associated with protein families ranging from 165 to 2000 extant sequences, and on 60 synthetic trees at comparable scales of data and reflecting realistic rates of mutation. Across relevant metrics, MIP outperformed alternative parsimony-based approaches and reported the fewest indel events, on par or below their occurrence in synthetic datasets. MIP offers a rational justification for indel patterns in extant sequences; importantly, it uniquely identifies global optima on complex protein data sets without making unrealistic assumptions of independence or evolutionary underpinnings, promising a deeper understanding of molecular evolution and aiding novel protein design. AVAILABILITY AND IMPLEMENTATION: The implementation is available via GitHub at https://github.com/santule/indelmip.

  PublisherOA PDFDOI

Recent grants

• CRII: AF: Linear-Algebraic Pseudorandomness

  NSF · $175k · 2018–2021

• AF: Small: Challenges in Unconditional Pseudorandomness for Boolean Computation

  NSF · $350k · 2018–2022

Frequent coauthors

• Amir Shpilka

  Tel Aviv University

  32 shared

• Alessandro Chiesa

  22 shared

• Raghu N. Kacker

  National Institute of Standards and Technology

  19 shared

• D. Richard Kuhn

  Information Technology Laboratory

  18 shared

• Jim Lawrence

  George Mason University

  17 shared

• Nicholas Spooner

  New York University

  17 shared

• Yu Lei

  The University of Texas at Arlington

  17 shared

• Ramprasad Saptharishi

  11 shared

Education

• PhD, Mathematics

  The University of Queensland

Awards & honors

• Best Paper for "Low-depth algebraic circuit lower bounds ove…