Combinatorial Optimization

A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation

  • S.T. DeNegre
  • Ted K. Ralphs
  • S. Tahernejad
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Optimization Software and Modeling Systems Tags , , ,

    In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range … Read more

    A Novel Approach for Solving Convex Problems with Cardinality Constraints

  • Goran Banjac
  • Paul J. Goulart
    • Categories Approximation Algorithms Tags , , , ,

    In this paper we consider the problem of minimizing a convex differentiable function subject to sparsity constraints. Such constraints are non-convex and the resulting optimization problem is known to be hard to solve. We propose a novel generalization of this problem and demonstrate that it is equivalent to the original sparsity-constrained problem if a certain … Read more

    Dantzig Wolfe decomposition and objective function convexification for binary quadratic problems: the cardinality constrained quadratic knapsack case

  • Alberto Ceselli
  • Lucas Létocart
  • Emiliano Traversi
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Quadratic Programming Tags , , ,

    The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig-Wolfe decomposition and Quadratic Convex Reformulation principles. As a representative case study, we apply them to a cardinality constrained quadratic knapsack problem, providing extensive experimental insights. We show that … Read more

    On Matroid Parity and Matching Polytopes

  • Konstantinos Kaparis
  • Adam N. Letchford
  • Ioannis Mourtos
    • Categories Graphs and Matroids, Polyhedra

    The matroid parity (MP) problem is a powerful (and NP-hard) extension of the matching problem. Whereas matching polytopes are well understood, little is known about MP polytopes. We prove that, when the matroid is laminar, the MP polytope is affinely congruent to a perfect b-matching polytope. From this we deduce that, even when the matroid … Read more

    An Augmented Lagrangian Proximal Alternating Method for Sparse Discrete Optimization Problems

  • Xiaoliang Song
  • Yue Teng
  • Li Yang
  • Bo Yu
    • Categories Approximation Algorithms, Constrained Nonlinear Optimization, Finance and Economics

    In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the Mangasarian-Fromovitz and the basic constraint qualification, we show that any … Read more

    Dynamic programming algorithms, efficient solution of the LP-relaxation and approximation schemes for the Penalized Knapsack Problem

  • Federico Della Croce
  • Ulrich Pferschy
  • Rosario Scatamacchia
    • Categories 0-1 Programming, Combinatorial Optimization, Dynamic Programming Tags , , ,

    We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an exact approach relying on a procedure which narrows the relevant range … Read more

    Locality sensitive heuristics for solving the Data Mule Routing Problem

  • Lucia Drummond
  • Luiz Satoru Ochi
  • P.H. González
  • Philippe Michelon
  • P.L.A Munhoz
  • U.S. Souza
    • Categories (Mixed) Integer Linear Programming, Approximation Algorithms, Telecommunications Tags , , , ,

    A usual way to collect data in a Wireless Sensor Network (WSN) is by the support of a special agent, called data mule, that moves between sensor nodes and performs all communication between them. In this work, the focus is on the construction of the route that the data mule must follow to serve all … Read more

    Robust combinatorial optimization with knapsack uncertainty

  • Michael Poss
    • Categories Combinatorial Optimization, Robust Optimization Tags , , ,

    We study in this paper min max robust combinatorial optimization problems for an uncertainty polytope that is defined by knapsack constraints, either in the space of the optimization variables or in an extended space. We provide exact and approximation algorithms that extend the iterative algorithms proposed by Bertismas and Sim (2003). We also study the … Read more

    On the Structure of Linear Programs with Overlapping Cardinality Constraints

  • Tobias Fischer
  • Marc E. Pfetsch
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , , ,

    Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We present the components of a branch-and-cut solution approach, including new branching rules that exploit the structure of the corresponding conflict hypergraph. We also investigate valid … Read more

    Capacitated ring arborescence problems with profits

  • Roberto Baldacci
  • Alessandro Hill
  • Edna Ayako Hoshino
    • Categories Branch and Cut Algorithms, Network Optimization, Transportation Tags

    In this work we introduce profit-oriented capacitated ring arborescence problems and present exact and heuristic algorithms. These combinatorial network design problems ask for optimized bi-level networks taking into account arc costs and node profits. Solutions combine circuits on the inner level with arborescences on the outer level of the networks. We consider the prize-collecting, the … Read more