decomposition

A Novel Solution Methodology for Wasserstein-based Data-Driven Distributionally Robust Problems

  • Carlos Gamboa
  • Tito Homem-de-Mello
  • Alexandre Street
  • Davi Valladão
    • Categories Stochastic Programming Tags , ,

    Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for their sound mathematical properties. For right-hand-sided uncertainty, however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, … Read more

    Risk-Averse Multistage Stochastic Programs with Expected Conditional Risk Measures

  • Maryam Khatami
  • Lewis Ntaimo
  • Bernardo K. Pagnoncelli
  • Thuener Silva
    • Categories Stochastic Programming Tags , ,

    We study decomposition algorithms for risk-averse multistage stochastic programs with expected conditional risk measures (ECRMs). ECRMs are attractive because they are time-consistent, which means that a plan made today will not be changed in the future if the problem is re-solved given a realization of the random variables. We show that solving risk-averse problems based … Read more

    Mixed-integer Linear Programming Models and Algorithms for Generation and Transmission Expansion Planning of Power Systems

  • Antonio Conejo
  • Ignacio E. Grossmann
  • Can Li
  • Peng Liu
  • Benjamin Omell
  • John D. Siirola
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    With the increasing penetration of renewable generating units, especially in remote areas not well connected with load demand, there are growing interests to co-optimize generation and transmission expansion planning (GTEP) in power systems. Due to the volatility in renewable generation, a planner needs to include the operating decisions into the planning model to guarantee feasibility. … Read more

    Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories Cutting Plane Approaches, Polyhedra, Scheduling Tags , , , ,

    Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to … Read more

    Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

  • Merve Bodur
  • Timothy C.Y. Chan
  • Ian Yihang Zhu
    • Categories Integer Programming Tags , , , , ,

    Inverse optimization – determining parameters of an optimization problem that render a given solution optimal – has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, … Read more

    Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games

  • Pedro Borges de Melo
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many … Read more

    A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

  • Suresh Bolusani
  • Stefano Coniglio
  • Ted K. Ralphs
  • Sahar Tahernejad
    • Categories (Mixed) Integer Linear Programming, Game Theory, Stochastic Programming Tags , , , , ,

    We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, … Read more

    Stochastic Last-mile Delivery with Crowd-shipping and Mobile Depots

  • Merve Bodur
  • Kianoush Mousavi
  • Matthew J. Roorda
    • Categories Stochastic Programming, Transportation Tags , , , , , ,

    This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more

    Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems

  • Merve Bodur
  • Moira MacNeil
    • Categories Branch and Cut Algorithms, Integer Programming, Other Topics Tags , , , ,

    Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called … Read more

    A Decomposition Heuristic for Mixed-Integer Supply Chain Problems

  • Lars Schewe
  • Martin Schmidt
  • Dieter Weninger
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management Tags , , , ,

    Mixed-integer supply chain models typically are very large but are also very sparse and can be decomposed into loosely coupled blocks. In this paper, we use general-purpose techniques to obtain a block decomposition of supply chain instances and apply a tailored penalty alternating direction method, which exploits the structural properties of the decomposed instances. We … Read more