Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the … Read more

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

Model-Free Assortment Pricing with Transaction Data

We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase … Read more

A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Chance Constraints

Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a large range of … Read more

Dynamic Scheduling of Home Health Care Patients to Medical Providers

Home care provides personalized medical care and social support to patients within their own home. Our work proposes a dynamic scheduling framework to assist in the assignment of patients to health practitioners (HPs) at a single home care agency. We model the decision of which patients to assign to HPs as a discrete-time Markov decision … Read more

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in … Read more

Network-based Approximate Linear Programming for Discrete Optimization

We develop a new class of approximate linear programs (ALPs) that project the high-dimensional value function of dynamic programs onto a class of basis functions, each defined as a network that represents aggregrations over the state space. The resulting ALP is a minimum-cost flow problem over an extended variable space that synchronizes flows across multiple … Read more

Modeling with Metaconstraints and Semantic Typing of Variables

Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise … Read more