Integer Programming

Cluster branching for vehicle routing problems

  • Joao Marcos P Silva
  • Eduardo Uchoa
  • Anand Subramanian
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming Tags , , ,

    This article introduces Cluster Branching, a novel branching strategy for exact algorithms solving Vehicle Routing Problems (VRPs). While branching is crucial for the efficiency of branch-and-bound-based algorithms, existing branching types such as Edge Branching, CutSet Branching, and Ryan&Foster Branching have their limitations. The proposed branching strategy aggregates multiple edge variables into higher-level decision structures corresponding … Read more

    Interdiction of minimum spanning trees and other matroid bases

  • Noah Weninger
  • Ricardo Fukasawa
    • Categories 0-1 Programming, Dynamic Programming, Graphs and Matroids Tags , , , , , ,

    \(\) In the minimum spanning tree (MST) interdiction problem, we are given a graph \(G=(V,E)\) with edge weights, and want to find some \(X\subseteq E\) satisfying a knapsack constraint such that the MST weight in \((V,E\setminus X)\) is maximized. Since MSTs of \(G\) are the minimum weight bases in the graphic matroid of \(G\), this … Read more

    Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

  • Yiling Zhang
    • Categories Integer Programming, Robust Optimization, Stochastic Programming

    We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of … Read more

    Computational Methods for the Household Assignment Problem

  • Ulf Friedrich
  • Lucas Moschen
  • Ralf Münnich
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Integer Programming Tags , , , ,

    We consider the household assignment problem as it occurs in the geo-referencing step of spatial microsimulation models. The resulting model is a maximum weight matching problem with additional side constraints. For real-world instances such as the one for the city of Trier in Germany, the number of binary variables exceeds 10^9, and the resulting instances … Read more

    Granularity for mixed-integer polynomial optimization problems

  • Carl Eggen
  • Oliver Stein
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , , ,

    Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sos-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sos-hierarchy is hereby used to solve those … Read more

    BOBILib: Bilevel Optimization (Benchmark) Instance Library

  • Johannes Thürauf
  • Thomas Kleinert
  • Ivana Ljubić
  • Ted K. Ralphs
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Optimization Software Benchmark Tags , , , ,

    In this report, we present the BOBILib, a collection of more than 2500~instances of mixed integer linear bilevel optimization problems. The goal of this library is to make a large and well-curated set of test instances freely available for the research community so that new and existing algorithms in bilevel optimization can be tested and … Read more

    Exact Augmented Lagrangian Duality for Nonconvex Mixed-Integer Nonlinear Optimization

  • Henri Lefebvre
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , ,

    In the context of mixed-integer nonlinear problems (MINLPs), it is well-known that strong duality does not hold in general if the standard Lagrangian dual is used. Hence, we consider the augmented Lagrangian dual (ALD), which adds a nonlinear penalty function to the classic Lagrangian function. For this setup, we study conditions under which the ALD … Read more

    Inverse of the Gomory Corner Relaxation of Integer Programs

  • George Lyu
  • Fatemeh Nosrat
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Linear Programming, Integer Programming, Other Topics Tags , ,

    \(\) We analyze the inverse of integer programs (IPs) using the Gomory corner relaxation (GCR). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We propose a linear program formulation for the inverse GCR under \(L_1\) and \(L_\infty\) norms.The inverse … Read more

    Routing a fleet of unmanned aerial vehicles: a trajectory optimisation-based framework

  • Walton P. Coutinho
  • Jörg Fliege
  • Maria Battarra
  • Anand Subramanian
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Systems governed by Differential Equations Optimization Tags , ,

    We consider an aerial survey operation in which a fleet of unmanned aerial vehicles (UAVs) is required to visit several locations and then land in one of the available landing sites while optimising some performance criteria, subject to operational constraints and flight dynamics. We aim to minimise the maximum flight time of the UAVs. To … Read more

    A Toll-Setting Problem with Robust Wardrop Equilibrium Conditions Under Budgeted Uncertainty

  • Yasmine Beck
  • Martine Labbé
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Transportation Tags , , , ,

    We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop’s user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented … Read more