Integer Programming

Polynomial-Time Algorithms for Setting Tight Big-M Coefficients in Transmission Expansion Planning with Disconnected Buses

  • Behnam Jabbari Marand
  • Adolfo Escobedo
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Energy Tags , , ,

    The increasing penetration of renewable energy into power systems necessitates the development of effective methodologies to integrate initially disconnected generation sources into the grid. This paper introduces the Longest Shortest-Path-Connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of Transmission Expansion Planning (TEP) using valid inequalities (VIs). Traditional approaches for … Read more

    Neural Embedded Mixed-Integer Optimization for Location-Routing Problems

  • Waquar Kaleem
  • Anirudh Subramanyam
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Production and Logistics Tags , , ,

    We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical yet NP-hard problem that integrates strategic facility location with operational vehicle routing decisions, aiming to simultaneously minimize both fixed and variable costs. The proposed method first trains a permutationally invariant neural … Read more

    Mixed-Integer Bilevel Optimization with Nonconvex Quadratic Lower-Level Problems: Complexity and a Solution Method

  • Immanuel M. Bomze
  • Martin Schmidt
  • Horländer Andreas
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , ,

    We study bilevel problems with a convex quadratic mixed-integer upper-level and a nonconvex quadratic, purely continuous lower-level problem. We prove $\Sigma_p^2$-hardness of this class of problems, derive an iterative lower- and upper-bounding scheme, and show its finiteness and correctness in the sense that it computes globally optimal points or proves infeasibility of the instance. To … Read more

    On parametric formulations for the Asymmetric Traveling Salesman Problem

  • Gustavo Angulo
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Linear Programming, Linear Programming, Polyhedra

    The traveling salesman problem is a widely studied classical combinatorial problem for which there are several integer linear formulations. In this work, we consider the Miller-Tucker-Zemlin (MTZ), Desrochers-Laporte (DL) and Single Commodity Flow (SCF) formulations. We argue that the choice of some parameters of these formulations is arbitrary and, therefore, there are families of formulations … Read more

    An Efficient Algorithm to the Integrated Shift and Task Scheduling Problem

  • G S R Murthy
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Scheduling Tags , , , , ,

    Abstract   This paper deals with operational models for integrated shift and task scheduling problem. Staff scheduling problem is a special case of this with staff requirements as given input to the problem. Both problems become hard to solve when the problems are considered with flexible shifts. Current literature on these problems leaves good scope … Read more

    Approximating the Gomory Mixed-Integer Cut Closure Using Historical Data

  • Berkay Becu
  • Santanu S. Dey
  • Feng Qiu
  • Alinson S. Xavier
    • Categories (Mixed) Integer Linear Programming

    Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of this paper is to generate good cutting-planes for such instances using historical data. Gomory mixed integer cuts (GMIC) for a general MILP can be parameterized … Read more

    Closest Assignment Constraints for Hub Disruption Problems

  • Saikat Mukherjee
  • Prasanna Ramamoorthy
    • Categories Integer Programming Tags , , ,

    Supply chains and logistics can be well represented with hub networks. Operations of these hubs can be disrupted due to unanticipated occurrences or attacks. This study includes Closest assignment Constraints related to hub disruption problems, which can be used in single-level reformulation of the bilevel model. In this study, We propose new sets of constraints … Read more

    A Branch-and-Price-and-Cut Algorithm for Discrete Network Design Problems Under Traffic Equilibrium

  • David
  • Michael Levin
    • Categories (Mixed) Integer Nonlinear Programming, Game Theory, Transportation Tags , , , ,

    This study addresses discrete network design problems under traffic equilibrium conditions or DNDPs. Given a network and a budget, DNDPs aim to model all-or-nothing decisions such as link addition to minimize network congestion effects. Congestion is measured using traffic equilibrium theory where link travel times are modeled as convex flow-dependent functions and where users make … Read more

    Unboundedness in Bilevel Optimization

  • Bárbara Rodrigues
  • Margarida Carvalho
  • Miguel F. Anjos
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Polyhedra Tags , , ,

    Bilevel optimization has garnered growing interest over the past decade. However, little attention has been paid to detecting and dealing with unboundedness in these problems, with most research assuming a bounded high-point relaxation. In this paper, we address unboundedness in bilevel optimization by studying its computational complexity and developing algorithmic approaches to detect it. We … Read more

    An analytical lower bound for a class of minimizing quadratic integer optimization problems

  • Christian Schmitt
  • Bismark Singh
    • Categories Combinatorial Optimization, Integer Programming, Quadratic Programming Tags , , ,

    Lower bounds on minimization problems are essential for convergence of both branching-based and iterative solution methods for optimization problems. They are also required for evaluating the quality of feasible solutions by providing conservative optimality gaps. We provide an analytical lower bound for a class of quadratic optimization problems with binary decision variables. In contrast to … Read more