Combinatorial Optimization

A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

  • Brian Dandurand
  • Kibaek Kim
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Robust Optimization Tags , , ,

    We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … Read more

    Hub Location and Route Dimensioning: Strategic and Tactical Intermodal Transportation Hub Network Design

  • Oya Ekin Karasan
  • Hande Yaman
  • Barış Yıldız
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Transportation Tags , , , , ,

    We propose a novel hub location model that jointly eliminates the traditional assumptions on the structure of the network and on the discount due to economies of scale in an effort to better reflect real-world logistics and transportation systems. Our model extends the hub literature in various facets: instead of connecting non-hub nodes directly to … Read more

    Integer Programming Formulations for Minimum Spanning Tree Interdiction

  • Foad Mahdavi Pajou
  • Jose L. Walteros
  • Ningji Wei
    • Categories Branch and Cut Algorithms, Integer Programming, Network Optimization Tags , , ,

    We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … 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

    An exact algorithm for robust influence maximization

  • Giacomo Nannicini
  • Roberto Wolfler Calvo
  • Giorgio Sartor
  • Emiliano Traversi
    • Categories Branch and Cut Algorithms, Robust Optimization Tags , ,

    We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with … Read more

    Relating Single-Scenario Facets to the Convex Hull of the Extensive Form of a Stochastic Single-Node Flow Polytope

  • Victor A. Gonzalez
  • Andrew J. Schaefer
  • Mehdi Hemmati
  • David T. Mildebrath
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Stochastic Programming Tags , ,

    Stochastic mixed-integer programs (SMIPs) are a widely-used modeling paradigm for sequential decision making under uncertainty. One popular solution approach to solving SMIPs is to solve the so-called “extensive form” directly as a large-scale (deterministic) mixed-integer program. In this work, we consider the question of when a facet-defining inequality for the convex hull of a deterministic, … Read more

    Arc routing with electric vehicles: dynamic charging and speed-dependent energy consumption

  • Elena Fernandez
  • Markus Leitner
  • Ivana Ljubić
  • Mario Ruthmair
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Production and Logistics Tags , , , , , ,

    Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These … Read more

    Globalized Robust Optimization with Gamma-Uncertainties

  • Andreas Bärmann
  • Christina Büsing
  • Frauke Liers
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Robust Optimization Tags , , ,

    Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its … 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

    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