Integer Programming

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

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    Strategic Network Design for Parcel Delivery with Drones under Competition

  • Gohram Baloch
  • Fatma Gzara
    • Categories (Mixed) Integer Nonlinear Programming, Supply Chain Management, Transportation

    This paper studies the economic desirability of UAV parcel delivery and its e ect on e-retailer distribution network while taking into account technological limitations, government regulations, and customer behavior. We consider an e-retailer o ering multiple same day delivery services including a fast UAV service and develop a distribution network design formulation under service based competition where … 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

    Anomalous Behaviour of Dual-Based Heuristics

  • Trivikram Dokka
  • Adam N. Letchford
  • M. Hasan Mansoor
    • Categories 0-1 Programming, Combinatorial Optimization, Meta Heuristics Tags , , ,

    Some popular heuristics for combinatorial optimisation start by constructing a feasible solution to a dual of the problem. We show that such dual-based heuristics can exhibit highly counter-intuitive behaviour. In particular, for some problem classes, solving the dual exactly invariably leads to much worse primal solutions than solving the dual with a simple greedy heuristic. … 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

    A Generic Exact Solver for Vehicle Routing and Related Problems

  • Artur Alves Pessoa
  • Ruslan Sadykov
  • Eduardo Uchoa
  • François Vanderbeck
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Modeling Languages and Systems Tags , ,

    Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This … Read more

    Theorems of the Alternative for Conic Integer Programming

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Varun Suriyanarayana
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Farkas’ Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested … Read more

    Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

  • Tanveer Hossain Bhuiyan
  • Mahantesh Halappanavar
  • Hugh R. Medal
  • Apurba Nandi
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Stochastic Programming Tags , , , ,

    Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more

    Solving Multiobjective Mixed Integer Convex Optimization Problems

  • Marianna De Santis
  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , ,

    Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, … Read more