Integer Programming

Column Generation in Column-and-Constraint Generation for Adjustable Robust Optimization with Interdiction-Type Linking Constraints

  • Henri Lefebvre
  • Martin Schmidt
  • Johannes Thürauf
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , , ,

    Adjustable robust optimization (ARO) is a powerful tool to model problems that have uncertain data and that feature a two-stage decision-making process. Computationally, they are often addressed using the column-and-constraint generation (CCG) algorithm introduced by Zeng and Zhao (2013). While it was empirically shown that the algorithm scales well if all second-stage decisions are continuous, … Read more

    On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints

  • Immanuel M. Bomze
  • Bo Peng
  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Semi-definite Programming Tags , , , ,

    Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, … Read more

    Strengthened MIP Formulations for the Liver Region Redesign Models of Akshat et al.

  • Aysenur Karagoz
  • Ruofeng Liu
  • Hamidreza Validi
  • Andrew J. Schaefer
    • Categories Integer Programming

    Liver transplantation has been a critical issue in the U.S. healthcare system for decades, and the region redesign aims to ameliorate this issue. This paper revisits two mixed integer programming (MIP) formulations of the liver region redesign problem proposed by Akshat et al. We study their first formulation considering two different modeling approaches: one compact … Read more

    Benchmarking Piecewise Linear Reformulations for MINLPs: A Computational Study Based on the Open-Source Framework PWL-T-Rex

  • Kristin Braun
  • Robert Burlacu
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    Solving mixed-integer nonlinear problems by means of piecewise linear relaxations has emerged as a reasonable alternative to the commonly used spatial branch-and-bound. These relaxations have been modeled by various mixed-integer models in recent decades. The idea is to exploit the availability of mature solvers for mixed-integer problems. In this work, we implement a framework that … Read more

    Solving Hard Bi-objective Knapsack Problems Using Deep Reinforcement Learning

  • Hadi Charkhgard
    • Categories Approximation Algorithms, Integer Programming Tags , , ,

    We study a class of bi-objective integer programs known as bi-objective knapsack problems (BOKPs). Our research focuses on the development of innovative exact and approximate solution methods for BOKPs by synergizing algorithmic concepts from two distinct domains: multi-objective integer programming and (deep) reinforcement learning. While novel reinforcement learning techniques have been applied successfully to single-objective … Read more

    A novel Pareto-optimal cut selection strategy for Benders Decomposition

  • Lukas Glomb
  • Frauke Liers
  • Florian Rösel
    • Categories (Mixed) Integer Linear Programming Tags ,

    Decomposition methods can be used to create efficient solution algorithms for a wide range of optimization problems. For example, Benders Decomposition can be used to solve scenario-expanded two-stage stochastic optimization problems effectively. Benders Decomposition iteratively generates Benders cuts by solving a simplified version of an optimization problem, the so-called subproblem. The choice of the generated … Read more

    An Integer Programming Approach To Subspace Clustering With Missing Data

  • Akhilesh Soni
  • Jeff Linderoth
  • James R. Luedtke
  • Daniel Pimentel-Alarcon
    • Categories Data Science Algorithms, Integer Programming Tags , ,

    In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more

    Resilient Relay Logistics Network Design: A k-Shortest Path Approach

  • Onkar Anand Kulkarni
  • Mathieu Dahan
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Production and Logistics Tags , , , ,

    Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more

    DeLuxing: Deep Lagrangian Underestimate Fixing for Column-Generation-Based Exact Methods

  • Yu Yang
    • Categories Branch and Cut Algorithms, Integer Programming, Transportation

    In this paper, we propose an innovative variable fixing strategy called deep Lagrangian underestimate fixing (DeLuxing). It is a highly effective approach for removing unnecessary variables in column-generation (CG)-based exact methods used to solve challenging discrete optimization problems commonly encountered in various industries, including vehicle routing problems (VRPs). DeLuxing employs a novel linear programming (LP) … Read more