Multistage Stochastic Fractionated Intensity Modulated Radiation Therapy Planning

Intensity modulated radiation therapy (IMRT) is a widely used cancer treatment technique designed to target malignant cells. To enhance its effectiveness on tumors and reduce side effects, radiotherapy plans are usually divided into consecutive treatments, or fractions, that are delivered over multiple weeks. However, typical planning approaches have focused on finding the full sequence of … Read more

A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning

Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof such that target tissues receive prescribed doses in a reasonable amount of treatment time, while healthy tissues nearby are spared. We … Read more

Copositive Duality for Discrete Energy Markets

Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have strong duality if a … Read more

Stochastic RWA and Lightpath Rerouting in WDM Networks

In a telecommunication network, Routing and Wavelength Assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity due to stranded bandwidth. At this … Read more

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter’s co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles … Read more

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g., (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain … Read more

Routing and Wavelength Assignment with Protection: A Quadratic Unconstrained Binary Optimization Approach

The routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant maximum number of requests by assigning lightpaths at minimum network resource usage level, while ensuring the provided services remain functional in case of a … Read more

Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization – determining parameters of an optimization problem that render a given solution optimal – has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, … Read more

Generation Expansion Planning with Revenue Adequacy Constraints

Generation capacity expansion models have traditionally taken the vantage point of a centralized planner seeking to find cost-optimal generation capacity to reliably meet load over decadal time scales. Often assuming perfectly competitive players, these models attempt to provide guidance for system planners without necessarily ensuring that individual generators are adequately remunerated for their generation, flexibility, … Read more

Stochastic Last-mile Delivery with Crowd-shipping and Mobile Depots

This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more