Network Optimization

A Catalog of Formulations for the Multi-Follower Discrete Bilevel Network Design Problem

  • Vladimir Stadnichuk
    • Categories Bilevel Optimization, Branch and Cut Algorithms, Network Optimization Tags , , ,

    Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and … Read more

    Designing Autonomous Aerial Cable Car Networks for Sustainable Urban Logistics

  • Zeynep Çınar
  • Mehmet Ali Silgu
  • Barış Yıldız
    • Categories Network Optimization, Other Topics, Transportation Tags , , , ,

    This paper investigates the emerging autonomous aerial cableway technology to reduce the negative impacts of urban freight transportation. We focus on the infrastructure design problem to minimize the road-transportation externalities, taking pricing, investment costs, and the physical footprint into account. The network design problem is formulated as a mixed-integer linear programming (MILP) model that explicitly … Read more

    A cut-based mixed integer programming formulation for the hop-constrained cheapest path problem

  • Hamidreza Validi
    • Categories Combinatorial Optimization, Integer Programming, Network Optimization Tags , ,

    Given a simple graph G = (V, E) with edge cost c ∈ ℝ^|E|, a positive integer h, source s ∈ V and terminal t ∈ V, the hop-constrained cheapest path problem (HCCP) seeks to find an s–t path of length at most h hops with the cheapest cost. This paper proposes a cut-based mixed … Read more

    Adaptive Subproblem Selection in Benders Decomposition for Survivable Network Design Problems

  • Tim Donkiewicz
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Network Optimization

    Scenario-based optimization problems can be solved via Benders decomposition, which separates first-stage (master problem) decisions from second-stage (subproblem) recourse actions and iteratively refines the master problem with Benders cuts. In conventional Benders decomposition, all subproblems are solved at each iteration. For problems with many scenarios, solving only a selected subset can reduce computation. We quantify … Read more

    On the Single-Multi-Commodity Gap: Lifting Single- to Multicommodity Flow Instances

  • Felix P. Broesamle
  • Stefan Nickel
    • Categories Applications - OR and Management Sciences, Linear Programming, Network Optimization Tags , , , , ,

    Benchmark instances for multicommodity flow problems frequently lack the structural nuances of real-world networks or fail to maintain a rigorous mathematical relationship with their single-commodity counterparts. This paper introduces a formal meta-generation framework that addresses these limitations by lifting single-commodity minimum-cost flow instances into the multicommodity space while strictly preserving the underlying network topology, capacity … Read more

    Finding Minimal Discretizations in Dynamic Discretization Discovery for Continuous-Time Service Network Design

  • Tom Wüllner
  • Alexander Helber
    • Categories Combinatorial Optimization, Network Optimization, Transportation Tags , , ,

    The dynamic discretization discovery framework is a powerful tool for solving network design problems with a temporal component by iteratively refining a time-discretized model. Existing approaches refine the time discretization in ways that guarantee eventual termination. However, refinement choices are not unique, and better choices can yield smaller and easier-to-solve time-discretized models. We pose the … Read more

    Water network design and operation optimization: Leveraging approximations

  • Sourabh Kumar Choudhary
  • Santanu S. Dey
  • Nikolaos Sahinidis
    • Categories Network Optimization Tags , ,

    This study concerns the optimal design and operation of produced water and urban water networks. The optimization formulations of these problems have inherent nonconvexity, making them hard to solve. We address a key source of nonconvexity and difficulty in solving these problems: the representation of frictional pressure changes across network nodes using nonlinear constraints, typically … Read more

    Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks

  • Wencheng Bao
  • Chrysafis Vogiatzis
  • Eleftheria Kontou
    • Categories Network Optimization, Robust Optimization, Transportation Tags , , , , ,

    Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic … Read more

    Potential-Based Flows – An Overview

  • Marc E. Pfetsch
  • Martin Schmidt
  • Martin Skutella
  • Johannes Thürauf
    • Categories Energy, Network Optimization

    Potential-based flows provide an algebraic way to model static physical flows in networks, for example, in gas, water, and lossless DC power networks. The flow on an arc in the network depends on the difference of the potentials at its end-nodes, possibly in a nonlinear way. Potential-based flows have several nice properties like uniqueness and … Read more

    The Generalized Group Steiner Tree Problem with Logical Side Constraints

  • Chrysafis Vogiatzis
    • Categories Network Optimization Tags , , ,

    In this work, we study a recent extension to the well-known Steiner tree problem: the Generalized Group Steiner Tree problem with logical side constraints. In this variant, we aim to identify a tree of minimum total cost, that spans a given set of groups of nodes, like in the traditional Group Steiner Tree problem. However, … Read more