arXiv subjects

Natalie M. Isenberg

Publications and source records attributed to Natalie M. Isenberg.

4 recordsLinked to original sources

arXiv2026

ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs

Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly identify high-quality solutions within a short amount of time. Recently, a growing body of research has also used machine learning to accelerate solution methods for challenging combinatorial optimization problems. Despite the increasing popularity of these ML-guided methods, a large body of work has focused on Mixed-Integer Linear Programs (MILPs). MBQPs are challenging to solve due to the combinatorial complexity coupled with nonlinearities. This work proposes ML-guided primal heuristics for Mixed Binary Quadratic Programs (MBQPs) by adapting and extending existing work on ML-guided MILP solution prediction to MBQPs. We introduce a new neural network architecture for MBQP solution prediction and a new training data collection procedure. Moreover, we extend existing loss functions in solution prediction and propose to combine contrastive and weighted cross-entropy losses. We evaluate the methods on standard and real-world MBQP benchmarks and show that the developed ML-guided methods significantly outperform existing primal heuristics and state-of-the-art solvers. Furthermore, models trained with our proposed extension with combined losses outperform other ML-based methods adapted from MILPs and improve generalization in cross-regional inference on a real-world wind farm layout optimization problem.

cs.LG↗

arXiv2025

Efficient Primal Heuristics for Mixed Binary Quadratic Programs Using Suboptimal Rounding Guidance

Mixed Binary Quadratic Programs (MBQPs) are a class of NP-hard problems that arise in a wide range of applications, including finance, machine learning, and chemical and energy systems. Large-scale MBQPs are challenging to solve with exact algorithms due to the combinatorial search space and nonlinearity. Primal heuristics have been developed to quickly identify high-quality solutions to challenging combinatorial optimization problems. In this paper, we propose an extension for two well-established rounding-based primal heuristics, RENS and Undercover. Instead of using the optimal solution to a relaxation for variable rounding and search as in RENS, we use a suboptimal relaxation solution of the MBQP as the basis for rounding and guidance for searching over a restricted subproblem where a certain percentage of binary variables are free. We apply a similar idea to the Undercover heuristic that fixes a variable cover to the rounded relaxation values. Instead, we relax a subset of the cover variables based on the suboptimal relaxation and search over a larger restricted subproblem. We evaluate our proposed methods on synthetic MBQP benchmarks and real-world wind farm layout optimization problem instances. The results show that our proposed heuristics identify high-quality solutions within a small time limit and significantly reduce the primal gap and primal integral compared to RENS, Undercover, and solvers with additional primal heuristics integrated inside Branch-and-Bound.

math.OC↗

arXiv2024

Bayesian Optimization Algorithms for Accelerator Physics

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques towards solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design.

physics.acc-ph↗

arXiv2023

Identifying Bayesian Optimal Experiments for Uncertain Biochemical Pathway Models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

q-bio.MN↗