相关论文: Mixed integer programming improves comprehensibili…
Integer Quadratic Programming (IQP), $\min\{x^T Q x + c^T x : Ax \le b,\, x\in\Z^n\}$, is a fundamental problem in combinatorial optimization. While the convex and concave special cases admit polynomial-time algorithms for fixed~$n$, the…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In the past decades mathematical optimization has found its way into radiation therapy and has made profound practice changing impact. Today, virtually all advanced treatment delivery methods, such as IMRT, VMAT, tomotherapy, LDR/HDR…
Optimization plays a central role in modern radiation therapy, where it is used to determine optimal treatment machine parameters in order to deliver precise doses adapted to each patient case. In general, solving the optimization problems…
Determining what to eat to satisfy nutritional requirements is one of the oldest optimization problems in operations research, yet existing formulations have two persistent limitations: continuous variables produce impractical fractional…
In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications.…
Inverse optimization (IO) algorithms are used in GYN HDR brachytherapy planning, with user parameter settings embedded in commercial TPS. To examine the dosimetric influence of hidden input parameters in three IO algorithms-IPSA, HIPO, and…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
We consider a real-world chemotherapy scheduling template design problem, where we cluster patient types into groups and find a representative time-slot duration for each group to accommodate all patient types assigned to that group, aiming…
Chemotherapy is one of the primary modalities of cancer treatment. Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens. One way to alleviate this burden and…
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing…
We investigate time-optimal Multi-Robot Coverage Path Planning (MCPP) for both unweighted and weighted terrains, which aims to minimize the coverage time, defined as the maximum travel time of all robots. Specifically, we focus on a…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Most commercially available treatment planning systems for brachytherapy operate based on physical dose and do not incorporate fractionation or tissue-specific response. The purpose of this study is to investigate the potential for…
Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to…
Deep learning (DL) 3D dose prediction has recently gained a lot of attention. However, the variability of plan quality in the training dataset, generated manually by planners with wide range of expertise, can dramatically effect the quality…
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…
Stereotactic body radiotherapy (SBRT) is characterized by delivering a high amount of dose in a short period of time. In SBRT the dose is delivered using open fields (e.g., beam's-eye-view) known as "apertures". Mathematical methods can be…
The steep dose gradients obtained with pencil beam scanning allow for precise tumor targeting at the cost of high sensitivity to uncertainties. Robust optimization is commonly applied to mitigate uncertainties in density and patient setup,…
Purpose: We introduce a novel concept of a compact multiprobe scintillator detector and demonstrate its applicability in HDR-brachytherapy. Our fabricated seven-probe system is sufficiently narrow to be inserted in a brachytherapy needle or…