Network Optimization

Exact Decentralized Optimization via Explicit $\ell_1$ Consensus Penalties

  • Hong Wang
    • Categories Network Optimization, Nonlinear Optimization Tags ,

    Consensus optimization enables autonomous agents to solve joint tasks through peer-to-peer exchanges alone. Classical decentralized gradient descent is appealing for its minimal state but fails to achieve exact consensus with fixed stepsizes unless additional trackers or dual variables are introduced. We revisit penalty methods and introduce a decentralized two-layer framework that couples an outer penalty-continuation … Read more

    generalizing the successive shortest path algorithm to solve the multi-objective assignment problem

  • Antonio Sedeño-Noda
    • Categories Multi-Criteria Optimization, Network Optimization, Other Topics Tags , ,

    We introduce a novel characterization of the efficient solutions to the Multi-objective Assignment Problem (MAP), relying solely on Network Flow theory. This result establishes that the set of efficient assignments restricted to the first $k$ origin-destination pairs in the associated bipartite graph can be derived incrementally from the efficient solutions corresponding to the first $k-1$ … Read more

    Column Generation for Generalized Min-Cost Flows with Losses

  • Jonas Alker
  • Marc E. Pfetsch
    • Categories Combinatorial Optimization, Linear Programming, Network Optimization Tags ,

    The generalized flow problem deals with flows through a network with losses or gains along the arcs. Motivated by energy networks, this paper concentrates on the case with losses along cycles. Such networks can become extremely large, mostly because they are considered over large time horizons. We therefore develop a column generation approach for a … Read more

    Effective Solution Algorithms for Bulk-Robust Optimization Problems

  • Christoph Buchheim
  • Enrico Malaguti
  • Michele Monaci
  • Paolo Paronuzzi
  • Pia Schreynemackers
    • Categories 0-1 Programming, Network Optimization, Robust Optimization Tags , , , ,

    Bulk-robust optimization is a recent paradigm for addressing problems in which the structure of a system is affected by uncertainty. It considers the case in which a finite and discrete set of possible failure scenarios is known in advance, and the decision maker aims to activate a subset of available resources of minimum cost so … Read more

    Optimizing Expeditionary Logistics: Dynamic Discretization for Fleet Management

  • Haden Boone
  • Mathieu Dahan
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Production and Logistics Tags , , ,

    We introduce the Expeditionary Logistics Network Design Problem (ELNDP), a new formulation for operational-level planning in expeditionary environments where multi-modal vehicle coordination is critical and penalties for unmet demand dominate transportation costs. ELNDP extends the classical Scheduled Service Network Design Problem by incorporating flexible commodity sourcing and heterogeneous vehicle capabilities, both essential in military logistics. … Read more

    Investment and Operational Planning for an electric market with massive entry of renewable energy

  • Matías Vera
  • Alejandro Jofré
  • Nicolas Hernández-Santibáñez
    • Categories Dynamic Programming, Network Optimization, Stochastic Programming Tags

    In this paper, we study a joint problem in which the Independent System Operator (ISO) intends to minimize the joint cost of operation and investment in a network structure. The problem is formulated through operational and investment control variables; we discuss the hierarchy between them and use the so-called Day Ahead Problem to find an … Read more

    Arc-Based Dynamic Discretization Discovery for Continuous-Time Service Network Design

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

    In the continuous time service network design problem, a freight carrier decides the path of shipments in their network as well as the dispatch times of the vehicles transporting the shipments. State-of-the-art algorithms to solve this problem are based on the dynamic discretization discovery framework. These algorithms solve a relaxation of the problem using a … Read more

    The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms

  • Wenjin Yan
  • Elena Fernandez
  • Ivana Ljubić
    • Categories Branch and Cut Algorithms, Combinatorial Optimization, Network Optimization Tags , , ,

    We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more

    Direct-search methods for decentralized blackbox optimization

  • Elhoucine Bergou
  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • Clément W. Royer
    • Categories Network Optimization, Nonlinear Optimization, Unconstrained Optimization

    Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. … Read more

    Optimal Control of Semilinear Graphon Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more