Applications – Science and Engineering

A Novel Cooperative Multi-search Benders Decomposition for Solving the Hydrothermal Unit-Commitment Problem

  • Felipe Beltrán
  • Bruno Colonetti
  • Erlon Finardi
  • Paulo Larroyd
    • Categories Applications - Science and Engineering, Parallel Algorithms, Scheduling

    Renewable energy and modernization of power operation demand Independent System Operators (ISOs) to solve ever more complex and larger programming problems to securely and economically schedule power resources. A key step in the scheduling process is the unit commitment (UC). In a hydro-dominated system, this process also involves managing reservoirs and is called hydrothermal UC … Read more

    Optimizing Active Surveillance for Prostate Cancer Using Partially Observable Markov Decision Processes

  • Brian T. Denton
  • Todd Morgan
  • Weiyu Li
    • Categories Applications - OR and Management Sciences, Biomedical Applications, Dynamic Programming Tags , , , ,

    We describe a finite-horizon partially observable Markov decision process (POMDP) approach to optimize decisions about whether and when to perform biopsies for patients on active surveillance for prostate cancer. The objective is to minimize a weighted combination of two criteria, the number of biopsies to conduct over a patient’s lifetime and the delay in detecting … Read more

    UAV Formation Shape Control via Decentralized Markov Decision Processes

  • Md Ali Azam
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering

    In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region … Read more

    Implicit Regularization of Sub-Gradient Method in Robust Matrix Recovery: Don’t be Afraid of Outliers

  • Salar Fattahi
  • Jianhao Ma
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Statistics Tags , ,

    It is well-known that simple short-sighted algorithms, such as gradient descent, generalize well in the over-parameterized learning tasks, due to their implicit regularization. However, it is unknown whether the implicit regularization of these algorithms can be extended to robust learning tasks, where a subset of samples may be grossly corrupted with noise. In this work, … Read more

    Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees

  • Salar Fattahi
  • Andrés Gómez
    • Categories Combinatorial Optimization, Statistics Tags , ,

    In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying MRFs rely on the regularized maximum likelihood estimation (MLE), that typically suffer from weak statistical guarantees and high … Read more

    On the Structure of Decision Diagram-Representable Mixed Integer Programs with Application to Unit Commitment

  • Hosseinali Salemi
  • Danial Davarnia
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Energy Tags , , ,

    Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their extension to model mixed integer programs (MIPs) such as those appearing in energy applications has been lacking. More broadly, the question on which … Read more

    Strong Optimal Classification Trees

  • Sina Aghaei
  • Andrés Gómez
  • Phebe Vayanos
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Statistics Tags , , ,

    Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees with univariate splits. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality … Read more

    Fairness over Time in Dynamic Resource Allocation with an Application in Healthcare

  • Andrea Lodi
  • Philippe Olivier
  • Gilles Pesant
  • Sriram Sankaranarayanan
    • Categories Branch and Cut Algorithms, Facility Planning and Design, Scheduling

    Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations … Read more

    Random-Sampling Monte-Carlo Tree Search Methods for Cost Approximation in Long-Horizon Optimal Control

  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering, Control Applications Tags , , ,

    We develop Monte-Carlo based heuristic approaches to approximate the objective function in long horizon optimal control problems. In these approaches, to approximate the expectation operator in the objective function, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the average (or weighted average) … Read more

    Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

  • Mark Brooke
  • Yair Censor
  • Aviv Gibali
    • Categories Biomedical Applications, Nonlinear Optimization Tags , , , , , , ,

    We study a feasibility-seeking problem with percentage violation constraints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to … Read more