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Researcher profile

J. Kyle Brubaker

J. Kyle Brubaker contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial Intelligencemath.OCcond-mat.dis-nnMachine LearningNeural and Evolutionary Computingquant-ph

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Published work

3 published item(s)

preprint2026arXiv

A Constraint Programming Approach for n-Day Lookahead Playoff Clinching in the NHL

In professional sports, a team has clinched the playoffs if they are guaranteed a postseason spot, regardless of the outcomes of any remaining games. As the season progresses, sports fans and other stakeholders are interested in precisely when, and under what conditions, their team will clinch the playoffs. In this paper, we investigate playoff clinching in the context of the National Hockey League (NHL), where it is computationally challenging to produce clinching scenarios due, in part, to complex tie-breakers. We present an algorithm that determines under which combinations of game outcomes in the next $n$ days a team will clinch the playoffs (i.e., "$n$-day lookahead clinching"). Our approach is a custom tree search which employs various preprocessing techniques, pruning strategies, and node ordering heuristics to efficiently explore the space of possible outcomes. The tree search leverages a constraint programming (CP)-based subroutine for inference that determines if a team has clinched the playoffs for some snapshot in time of the regular season (i.e., "0-day lookahead clinching"). This CP subroutine aims to find a counter-example in which the team being evaluated is eliminated, taking into account qualification rules and the NHL's extensive list of tie-breakers. We validate the efficacy of our algorithm using hundreds of scenarios based on public NHL data for the seasons 2021-22 through 2024-25. The methods introduced can be readily extended to other metrics of interest, including mathematical proof of playoff elimination, clinching the President's Trophy, as well as clinching (or being eliminated from clinching) any other seed in the standings.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

A Random-Key Optimizer for Combinatorial Optimization

This paper introduces the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys that are subsequently decoded into feasible solutions via problem-specific decoders. The RKO framework is able to combine a plethora of classic metaheuristics, each capable of operating independently or in parallel, with solution sharing facilitated through an elite solution pool. This modular approach allows for the adaptation of various metaheuristics, including simulated annealing, iterated local search, and greedy randomized adaptive search procedures, among others. The efficacy of the RKO framework, implemented in C++ and publicly available (Github public repository: github.com/RKO-solver), is demonstrated through its application to three NP-hard combinatorial optimization problems: the alpha-neighborhood p-median problem, the tree of hubs location problem, and the node-capacitated graph partitioning problem. The results highlight the framework's ability to produce high-quality solutions across diverse problem domains, underscoring its potential as a robust tool for combinatorial optimization.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Combinatorial Optimization with Physics-Inspired Graph Neural Networks

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical physics is still outstanding. Here we demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial unconstrained binary optimization problems. We apply a relaxation strategy to the problem Hamiltonian to generate a differentiable loss function with which we train the graph neural network and apply a simple projection to integer variables once the unsupervised training process has completed. We showcase our approach with numerical results for the canonical maximum cut and maximum independent set problems. We find that the graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables.

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