Integer Programming

Strengthening Dual Bounds for Multicommodity Capacitated Network Design with Unsplittable Flow Constraints

  • Lacy M. Greening
  • Santanu S. Dey
  • Alan L. Erera
    • Categories Integer Programming, Network Optimization, Production and Logistics Tags , , ,

    Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and destination follow the same transfer path. This unsplittable flow requirement complicates the MCND problem, requiring integer programming (IP) formulations with binary variables replacing continuous … Read more

    Lagrangian Duality for Mixed-Integer Semidefinite Programming: Theory and Algorithms

  • Frank de Meijer
  • Renata Sotirov
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , ,

    This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous relaxation of the MISDP problem. We present a hierarchy of Lagrangian dual bounds by exploiting the theory of integer positive semidefinite matrices … Read more

    Risk-Averse Antibiotics Time Machine Problem

  • Deniz Tuncer
  • Burak Kocuk
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Stochastic Programming Tags , , ,

    Antibiotic resistance, which is a serious healthcare issue, emerges due to uncontrolled and repeated antibiotic use that causes bacteria to mutate and develop resistance to antibiotics. The Antibiotics Time Machine Problem aims to come up with treatment plans that maximize the probability of reversing these mutations. Motivated by the severity of the problem, we develop … Read more

    New Dynamic Discretization Discovery Strategies for Continuous-Time Service Network Design

  • Shengnan Shu
  • Zhou Xu
  • Roberto Baldacci
    • Categories Applications - OR and Management Sciences, Integer Programming, Network Optimization Tags , , ,

    Service Network Design Problems (SNDPs) are prevalent in the freight industry. While the classic SNDP is defined on a discretized planning horizon with integral time units, the Continuous-Time SNDP (CTSNDP) uses a continuous-time horizon to avoid discretization errors. Existing CTSNDP algorithms primarily rely on the Dynamic Discretization Discovery (DDD) framework, which iteratively refines discretization and … Read more

    A Single-Level Reformulation of Integer Bilevel Programs using Decision Diagrams

  • Sebastian Vasquez
  • Leonardo Lozano
  • Willem-Jan van Hoeve
    • Categories Combinatorial Optimization, Integer Programming Tags , ,

    Integer bilevel programs are notoriously difficult to solve due to the absence of strong and efficiently computable relaxations. In this work, we introduce a novel single-level reformulation of these programs by leveraging a network flow-based representation of the follower’s value function, utilizing decision diagrams and linear programming duality. This approach enables the development of scalable … Read more

    Mixed Integer Linear Programming Formulations for Robust Surgery Scheduling

  • Ankit Bansal
    • Categories (Mixed) Integer Linear Programming, Robust Optimization, Scheduling

    We introduce Mixed Integer Linear Programming (MILP) formulations for the two-stage robust surgery scheduling problem (2SRSSP). We derive these formulations by modeling the second-stage problem as a longest path problem on a layered acyclic graph and subsequently converting it into a linear program. This linear program is then dualized and integrated with the first-stage, resulting … Read more

    Improved Approximation Algorithms for Low-Rank Problems Using Semidefinite Optimization

  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Linear Programming, Approximation Algorithms, Semi-definite Programming

    Inspired by the impact of the Goemans-Williamson algorithm on combinatorial optimization, we construct an analogous relax-then-sample strategy for low-rank optimization problems. First, for orthogonally constrained quadratic optimization problems, we derive a semidefinite relaxation and a randomized rounding scheme, which obtains provably near-optimal solutions, mimicking the blueprint from Goemans and Williamson for the Max-Cut problem. We … Read more

    Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs

  • Sumin Kang
  • Manish Bansal
    • Categories Integer Programming, Network Optimization, Stochastic Programming Tags , , , ,

    We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated L-shaped (\(L^2\)) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage … Read more

    Proximity results in convex mixed-integer programming

  • Burak Kocuk
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Cone Programming Tags , , , ,

    We study proximity (resp. integrality gap), that is, the distance (resp. difference) between the optimal solutions (resp. optimal values) of convex integer programs (IP) and the optimal solutions (resp. optimal values) of their continuous relaxations. We show that these values can be upper bounded in terms of the recession cone of the feasible region of … Read more

    The Edge-based Contiguous p-median Problem with Connections to Logistics Districting

  • Zeyad Kassem
  • Adolfo Escobedo
    • Categories Applications - OR and Management Sciences, Branch and Cut Algorithms, Cutting Plane Approaches Tags , , , ,

    This paper introduces the edge-based contiguous p-median (ECpM) problem to partition the roads in a network into a given number of compact and contiguous territories. Two binary programming models are introduced, both of which incorporate a network distance. The first model requires an exponential number of cut set-based constraints to model contiguity; it is paired … Read more