combinatorial optimization

Recycling Valid Inequalities for Robust Combinatorial Optimization with Budget Uncertainty

  • Christina Büsing
  • Timo Gersing
  • Arie M.C.A. Koster
    • Categories 0-1 Programming, Polyhedra, Robust Optimization Tags , , , ,

    Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more

    Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

  • Yu Hin (Gary) Au
  • Levent Tunçel
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Semi-definite Programming Tags , , , ,

    We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator \( \text{LS}_+\), with a particular focus on a search for relatively small graphs with high \( \text{LS}_+\)-rank (the least number of iterations of the \( \text{LS}_+\) operator on the fractional stable set polytope to compute the … Read more

    The Hamiltonian p-median Problem: Polyhedral Results and Branch-and-Cut Algorithm

  • Michele Barbato
  • Luís Gouveia
    • Categories Branch and Cut Algorithms, Combinatorial Optimization, Polyhedra Tags , , , ,

    In this paper we study the Hamiltonian \(p\)-median problem, in which a weighted graph on \(n\) vertices is to be partitioned into \(p\) simple cycles of minimum total weight. We introduce two new families of valid inequalities for a formulation of the problem in the space of natural edge variables. Each one of the families … Read more

    A Combinatorial Flow-based Formulation for Temporal Bin Packing Problems

  • John Martinovic
  • Nico Strasdat
  • José Valério de Carvalho
  • Fabio Furini
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization Tags , , , ,

    We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To … Read more

    Temporal Bin Packing with Half-Capacity Jobs

  • Christopher Muir
  • Luke Marshall
  • Alejandro Toriello
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Scheduling Tags , , , ,

    Motivated by applications in cloud computing, we study a temporal bin packing problem with jobs that occupy half of a bin’s capacity. An instance is given by a set of jobs, each with a start and end time during which it must be processed, i.e., assigned to a bin. A bin can accommodate two jobs … Read more

    On Aligning Non-Order-Associated Binary Decision Diagrams.

  • Alexey Bochkarev
  • Cole Smith
    • Categories Combinatorial Optimization, Network Optimization Tags , , ,

    Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, i.e., transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to … Read more

    Dendrograms, Minimum Spanning Trees and Feature Selection

  • Martine Labbé
  • Mercedes Landete
  • Marina Leal
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Combinatorial Optimization Tags , , , ,

    Feature selection is a fundamental process to avoid overfitting and to reduce the size of databases without significant loss of information that applies to hierarchical clustering. Dendrograms are graphical representations of hierarchical clustering algorithms that for single linkage clustering can be interpreted as minimum spanning trees in the complete network defined by the database. In … Read more

    Minimum-Link Covering Trails for any Hypercubic Lattice

  • Marco Ripà
    • Categories Combinatorial Optimization, Graphs and Matroids Tags , , , ,

    In 1994, Kranakis et al. published a conjecture about the minimum link-length of every rectilinear covering path for the \(k\)-dimensional grid \(P(n,k) := \{0,1, \dots, n-1\} \times \{0,1, \dots, n-1\} \times \cdots \times \{0,1, \dots, n-1\}\). In this paper we consider the general, NP-complete, Line-Cover problem, where the edges are not required to be axis-parallel, … Read more

    CliSAT: a SAT-based exact algorithm for hard maximum clique problems

  • Pablo San Segundo
  • Fabio Furini
  • David Alvarez
  • Panos M. Pardalos
    • Categories Combinatorial Optimization, Game Theory Tags , , ,

    Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a … Read more

    An Efficient Tabu Search Algorithm for the Tool Indexing Problem

  • Deepti Mohan
  • Diptesh Ghosh
    • Categories Meta Heuristics, Production and Logistics Tags , , ,

    In this paper, we look at the tool indexing problem in which a single copy of each tool is allowed in the tool magazine. We develop problem specific methods to search the neighborhood efficiently and design a Tabu Search algorithm based on them. Computational experiments show that our algorithm is competent. CitationIndian Institute of Management … Read more