Cutting Plane Approaches

Logic-based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room Scheduling

  • Dionne M. Aleman
  • Merve Bodur
  • Cheng Guo
  • David R. Urbach
    • Categories Cutting Plane Approaches, Scheduling, Stochastic Programming

    The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample … Read more

    Visible points, the separation problem, and applications to MINLP

  • Felipe Serrano
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization Tags , , , ,

    In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require … Read more

    New facets and facet-generating procedures for the orientation model for vertex coloring problems

  • Diego Delle Donne
  • Javier Marenco
    • Categories Cutting Plane Approaches, Polyhedra Tags , ,

    In this work, we study the \emph{orientation model} for vertex coloring problems with the aim of finding partial descriptions of the associated polytopes. We present new families of valid inequalities, most of them supported by paths of the input graph. We develop facet-generating procedures for the associated polytopes, which we denominate \emph{path-lifting procedures}. Given a … Read more

    A Unified Approach to Mixed-Integer Optimization Problems With Logical Constraints

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal component analysis and sparse learning problems. These problems exhibit logical relationships between continuous and discrete variables, which are usually reformulated linearly … Read more

    Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs

  • Huiwen Jia
  • Siqian Shen
    • Categories Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification … Read more

    Generalized Chvatal-Gomory closures for integer programs with bounds on variables

  • Sanjeeb Dash
  • Oktay Gunluk
  • Dabeen Lee
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvatal-Gomory inequalities obtained by strengthening Chvatal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvatal-Gomory inequalities is … Read more

    Decorous Combinatorial Lower Bounds for Row Layout Problems

  • Mirko Dahlbeck
  • Anja Fischer
  • Frank Fischer
    • Categories Cutting Plane Approaches, Facility Planning and Design

    In this paper we consider the Double-Row Facility Layout Problem (DRFLP). Given a set of departments and pairwise transport weights between them the DRFLP asks for a non-overlapping arrangement of the departments along both sides of a common path such that the weighted sum of the center-to-center distances between the departments is minimized. Despite its … Read more

    On the depth of cutting planes

  • Laurent Poirrier
  • James Yu
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Cutting Plane Approaches Tags , ,

    We introduce a natural notion of depth that applies to individual cutting planes as well as entire families. This depth has nice properties that make it easy to work with theoretically, and we argue that it is a good proxy for the practical strength of cutting planes. In particular, we show that its value lies … Read more

    Submodularity in conic quadratic mixed 0-1 optimization

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , , , , , ,

    We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and … Read more

    Consistency for 0-1 programming

  • Danial Davarnia
  • John Hooker
    • Categories Cutting Plane Approaches, Integer Programming

    Concepts of consistency have long played a key role in constraint programming but never developed in integer programming (IP). Consistency nonetheless plays a role in IP as well. For example, cutting planes can reduce backtracking by achieving various forms of consistency as well as by tightening the linear programming (LP) relaxation. We introduce a type … Read more