Combinatorial Optimization

Computational evaluation of cut-strengthening techniques in logic-based Benders’ decomposition

  • Aigerim Saken
  • Emil Karlsson
  • Stephen J. Maher
  • Elina Rönnberg
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Scheduling Tags , , , , ,

    Cut-strengthening techniques have a significant impact on the computational effectiveness of the Logic-based Benders’ decomposition (LBBD) scheme. While there have been numerous cut-strengthening techniques proposed, very little is understood about which techniques achieve the best computational performance for the LBBD scheme. This is typically due to implementations of LBBD being problem specific and thus, no … Read more

    On solving the MAX-SAT using sum of squares

  • Lennart Sinjorgo
  • Renata Sotirov
    • Categories 0-1 Programming, Branch and Cut Algorithms, Semi-definite Programming Tags , , , ,

    We consider semidefinite programming (SDP) approaches for solving the maximum satisfiabilityproblem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suitedto approximate the (MAX-)2-SAT. Our work shows the potential of SDP also for other satisfiabilityproblems, by being competitive with some of the best solvers in the yearly MAX-SAT competition.Our solver combines … Read more

    Stochastic programming for an integrated assignment, routing, and scheduling problem

  • Syu-Ning Johnn
  • Andrés Miniguano-Trujillo
  • Yiran Zhu
  • Akshay Gupte
  • Joerg Kalcsics
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Stochastic Programming Tags , , ,

    We study a two-stage stochastic combinatorial optimization problem that integrates fleet-sizing, assignment, routing, and scheduling problems. Although this problem has wide applicability, it arises in particular in the home healthcare industry where a service team of caregivers have to be assigned to patients and put in vehicle fleet that have to be routed amongst the … Read more

    An easily computable upper bound on the Hoffman constant for homogeneous inequality systems

  • Javier F. Peña
    • Categories Linear Programming, Polyhedra, Second-Order Cone Programming Tags , ,

    \(\)Let $A\in \mathbb{R}^{m\times n}\setminus \{0\}$ and $P:=\{x:Ax\le 0\}$. This paper provides a procedure to compute an upper bound on the following {\em homogeneous Hoffman constant} \[ H_0(A) := \sup_{u\in \mathbb{R}^n \setminus P} \frac{\text{dist}(u,P)}{\text{dist}(Au, \mathbb{R}^m_-)}. \] In sharp contrast to the intractability of computing more general Hoffman constants, the procedure described in this paper is entirely … Read more

    Approximation Algorithms for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

  • Jannis Kurtz
    • Categories Approximation Algorithms, Robust Optimization Tags , , ,

    In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It … Read more

    Toward Efficient Transportation Electrification of Heavy-Duty Trucks: Joint Scheduling of Truck Routing and Charging

  • Mikhail Bragin
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Transportation Tags

    The timely transportation of goods to customers is an essential component of economic activities. However, heavy-duty diesel trucks that deliver goods contribute significantly to greenhouse gas emissions within many large metropolitan areas, including Los Angeles, New York, and San Francisco. To facilitate freight electrification, this paper proposes joint routing and charging (JRC) scheduling for electric … Read more

    Semi-Infinite Mixed Binary and Disjunctive Programs: Applications to Set-Covering with Infinite Demand Points and Implicit Hitting Set Problems

  • Manish Bansal
    • Categories Combinatorial Optimization, Integer Programming, Semi-infinite Programming

    Sherali and Adams [Discrete Applied Math. 157: 1319-1333, 2009] derived convex hull of semi-infinite mixed binary linear programs (SIMBLPs) using Reformulation-Linearization Technique (RLT). In this paper, we study semi-infinite disjunctive programs (SIDPs — a generalization of SIMBLPs) and present linear programming equivalent and valid inequalities for them. We utilize these results for deriving a hierarchy … Read more

    Recognizing Series-Parallel Matrices in Linear Time

  • Matthias Walter
    • Categories Graphs and Matroids Tags ,

    \(\) A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of an existing row/column or have at most one 1-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We … Read more

    The min-Knapsack Problem with Compactness Constraints and Applications in Statistics

  • Alberto Santini
  • Enrico Malaguti
    • Categories Branch and Cut Algorithms, Dynamic Programming, Statistics Tags , ,

    In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper we introduce an extension of the min-Knapsack problem with additional … 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 … Read more