Cutting Plane Generation Through Sparse Principal Component Analysis

  • Santanu S. Dey
  • Aleksandr M. Kazachkov
  • Andrea Lodi
  • Gonzalo Muñoz
    • Categories Cutting Plane Approaches, Quadratic Programming Tags , , ,

    Quadratically-constrained quadratic programs (QCQPs) are optimization models whose remarkable expressiveness has made them a cornerstone of methodological research for nonconvex optimization problems. However, modern methods to solve a general QCQP fail to scale, encountering computational challenges even with just a few hundred variables. Specifically, a semidefinite programming (SDP) relaxation is typically employed, which provides strong … Read more

    Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

  • Hatim Djelassi
  • Alexander Mitsos
  • Oliver Stein
    • Categories Global Optimization Applications, Semi-infinite Programming

    The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

    Scaling Up Exact Neural Network Compression by ReLU Stability

  • Abhinav Kumar
  • Srikumar Ramalingam
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Combinatorial Optimization

    We can compress a neural network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons in networks with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. … Read more

    Edge Minimizing the Student Conflict Graph

  • Joshua S. Friedman
    • Categories Scheduling

    In many schools, courses are given in sections. Prior to timetabling students need to be assigned to individual sections. We give a hybrid approximation sectioning algorithm that minimizes the number of edges (potential conflicts) in the student conflict graph (SCG). We start with a greedy algorithm to obtain a starting solution and then continue with … Read more

    An adaptive robust optimization model for parallel machine scheduling

  • Izack Cohen
  • Krzysztof Postek
  • Shimrit Shtern
    • Categories Robust Optimization, Scheduling Tags , ,

    Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is completed and a machine becomes idle. Robust optimization is the natural methodology to cope with the first characteristic of duration … Read more

    Masking Primal and Dual Models for Data Privacy in Network Revenue Management

  • Utku Karaca
  • Ş. İlker Birbil
  • Nursen Aydin
  • Gizem Mullaoğlu
    • Categories Applications - OR and Management Sciences Tags , , ,

    We study a collaborative revenue management problem where multiple decentralized parties agree to share some of their capacities. This collaboration is performed by constructing a large mathematical programming model available to all parties. The parties then use the solution of this model in their own capacity control systems. In this setting, however, the major concern … Read more

    Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

  • Prasanna Balaprakash
  • Sven Leyffer
  • Jongeun Kim
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , ,

    In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as … Read more

    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