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In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints,…

Optimization and Control · Mathematics 2024-07-22 Farzin Ahmadi , Todd R. McNutt , Kimia Ghobadi

The authors propose robust adaptive strategies based on stochastic minimax optimization for a series of simulated treatments on a one-dimensional patient phantom. The plan applied during the first fractions should be able to handle…

Optimization and Control · Mathematics 2018-10-01 Michelle Böck , Anders Forsgren , Kjell Eriksson , Björn Hårdemark

In radiation therapy (RT) treatment planning, multi-criteria optimization (MCO) supports efficient plan selection but is usually solved for population-based dosimetric criteria and ignores patient-specific biological risk, potentially…

Medical Physics · Physics 2026-01-09 Mara Schubert , Katrin Teichert , Zhongxing Liao , Thomas Bortfeld , Ali Ajdari

We formalize the concept of Pareto Adaptive Robust Optimality (PARO) for linear Adaptive Robust Optimization (ARO) problems. A worst-case optimal solution pair of here-and-now decisions and wait-and-see decisions is PARO if it cannot be…

Optimization and Control · Mathematics 2022-05-09 Dimitris Bertsimas , Stefan ten Eikelder , Dick den Hertog , Nikolaos Trichakis

We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variations in OAR and tumor sensitivities to…

Tissues and Organs · Quantitative Biology 2015-06-05 Hamidreza Badri , Yoichi Watanabe , Kevin Leder

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the…

Machine Learning · Computer Science 2026-04-21 Dimitris Bertsimas , Cheol Woo Kim

Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust…

Medical Physics · Physics 2019-05-16 Michelle Böck , Kjell Eriksson , Anders Forsgren

Intensity-modulated radiation therapy (IMRT) allows for the design of customized, highly-conformal treatments for cancer patients. Creating IMRT treatment plans, however, is a mathematically complex process, which is often tackled in…

Optimization and Control · Mathematics 2022-03-18 Danielle A. Ripsman , Thomas G. Purdie , Timothy C. Y. Chan , Houra Mahmoudzadeh

This study introduces adaptive robust optimization (ARO) and adaptive robust stochastic optimization (ARSO) approaches to address long- and short-term uncertainties in the optimal sizing and placement of distributed energy resources in…

Optimization and Control · Mathematics 2025-03-25 Fernando García-Muñoz , Cristian Duran-Mateluna

A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii)…

Medical Physics · Physics 2020-09-09 Michelle Böck

A central problem in the field of radiation therapy (RT) is how to optimally deliver dose to a patient in a way that fully accounts for anatomical position changes over time. As current RT is a static process, where beam intensities are…

Medical Physics · Physics 2019-09-04 Rodney D. Wiersma , Xinmin Liu

Radiation Therapy (RT) plays a pivotal role in the treatment of cancer, offering the potential to effectively target and eliminate tumour cells while minimizing harm to surrounding healthy tissues. However, the success of RT heavily depends…

Medical Physics · Physics 2024-02-16 Keshav Kumar K. , NVSL Narasimham , A. Ramakrishna Prasad

Response-Adaptive Randomization (RAR) is recognized for its potential to deliver improvements in patient benefit. However, the utility of RAR is contingent on regularization methods to mitigate early instability and preserve statistical…

Methodology · Statistics 2025-11-27 Lukas Pin , Stef Baas , Gianmarco Caruso , David S. Robertson , Sofía S. Villar

Geometric uncertainty can degrade treatment quality in radiation therapy. While margins and robust optimization mitigate these effects, they provide only implicit control over clinical goal fulfillment probability. We therefore develop a…

Medical Physics · Physics 2026-01-14 Albin Fredriksson , Erik Engwall , Jenneke de Jong , Johan Sundström

Online adaptive radiotherapy (ART) requires accurate and efficient auto-segmentation of target volumes and organs-at-risk (OARs) in mostly cone-beam computed tomography (CBCT) images. Propagating expert-drawn contours from the pre-treatment…

Computer Vision and Pattern Recognition · Computer Science 2023-05-10 Xiao Liang , Jaehee Chun , Howard Morgan , Ti Bai , Dan Nguyen , Justin C. Park , Steve Jiang

Objective: We propose a semiautomatic pipeline for radiation therapy treatment planning, combining ideas from machine learning-automated planning and multicriteria optimization (MCO). Approach: Using knowledge extracted from historically…

Medical Physics · Physics 2022-02-16 Tianfang Zhang , Rasmus Bokrantz , Jimmy Olsson

Beam orientation optimization (BOO) is a key component in the process of IMRT treatment planning. It determines to what degree one can achieve a good treatment plan quality in the subsequent plan optimization process. In this paper, we have…

Medical Physics · Physics 2015-05-27 Xun Jia , Chunhua Men , Yifei Lou , Steve B. Jiang

Radiotherapy (RT) is a critical cancer treatment, with volumetric modulated arc therapy (VMAT) being a commonly used technique that enhances dose conformity by dynamically adjusting multileaf collimator (MLC) positions and monitor units…

Medical Physics · Physics 2025-06-26 Stefanos Achlatis , Efstratios Gavves , Jan-Jakob Sonke

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…

Medical Physics · Physics 2018-10-31 Bram L. Gorissen , Jan Unkelbach , Thomas R. Bortfeld

Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous…

Optimization and Control · Mathematics 2025-11-20 Karl Zhu , Dimitris Bertsimas
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