Jean-Paul Watson

pyomo.dae: A Modeling and Automatic Discretization Framework for Optimization with Differential and Algebraic Equations

  • Lorenz T. Biegler
  • Jean-Paul Watson
  • Victor M. Zavala
  • Bethany Nicholson
  • John D. Siirola
    • Categories Modeling Languages and Systems, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more

    Distributionally Robust Optimization with Principal Component Analysis

  • Richard Chen
  • Habib Najm
  • Jean-Paul Watson
  • Jianqiang Cheng
  • Ali Pinar
  • Cosmin Safta
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more

    Obtaining Lower Bounds from the Progressive Hedging Algorithm for Stochastic Mixed-Integer Programs

  • Dinakar Gade
  • Jean-Paul Watson
  • Gabriel Hackebeil
  • Sarah M. Ryan
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming

    We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using … Read more

    Toward Scalable Stochastic Unit Commitment – Part 1: Load Scenario Generation

  • Yonghan Feng
  • Jean-Paul Watson
  • Ignacio Rios
  • Sarah M. Ryan
  • Kai Spurkel
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories Stochastic Programming

    Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. … Read more

    Toward Scalable Stochastic Unit Commitment – Part 2: Solver Configuration and Performance Assessment

  • Kwok Cheung
  • Dinakar Gade
  • Cesar Silva-Monroy
  • Jean-Paul Watson
  • Sarah M. Ryan
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories Stochastic Programming

    In this second portion of a two-part analysis of a scalable computational approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets’ progressive hedging algorithm, a scenario-based decomposition strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we … Read more

    PySP: Modeling and Solving Stochastic Programs in Python

  • William E. Hart
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags , , ,

    Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its wide-spread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic … Read more

    Python Optimization Modeling Objects (Pyomo)

  • William E. Hart
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories (Mixed) Integer Linear Programming, Modeling Languages and Systems, Parallel Algorithms

    We describe Pyomo, an open source tool for modeling optimization applications in Python. Pyomo can be used to de fine symbolic problems, create concrete problem instances, and solve these instances with standard solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS, but Pyomo’s modeling objects are … Read more

    Progressive Hedging Innovations for a Class of Stochastic Resource Allocation Problems

  • David Strip
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories Production and Logistics, Stochastic Programming Tags , ,

    Progressive hedging (PH) is a scenario-based decomposition technique for solving stochastic programs. While PH has been successfully applied to a number of problems, a variety of issues arise when implementing PH in practice, especially when dealing with very difficult or large-scale mixed-integer problems. In particular, decisions must be made regarding the value of the penalty … Read more

    Scalable Heuristics for Stochastic Programming with Scenario Selection

  • Jean-Paul Watson
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories Stochastic Programming Tags , , ,

    We describe computational procedures to solve a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets’ progressive hedging algorithm. Experiments demonstrate the … Read more