John D. Siirola – Optimization Online

An implicit function formulation for optimization of discretized index-1 differential algebraic systems

Published: 2022/04/27

Systems governed by Differential Equations Optimization chemical engineering, Dynamic, implicit, nonlinear

A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) that uses implicit functions to remove algebraic variables and equations from the optimization problem is described. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing … Read more

A covering decomposition algorithm for power grid cyber-network segmentation

Published: 2021/12/13

Applications - OR and Management Sciences defender-attacker-defender, interdiction, mixed-integer programming, power networks, security, trilevel optimization

We present a trilevel interdiction model for optimally segmenting the Supervisory Control and Data Acquisition (SCADA) network controlling an electric power grid. In this formulation, we decide how to partition nodes of the SCADA network in order to minimize the shedding of load from a worst-case cyberattack, assuming that the grid operator has the opportunity … Read more

Scalable Parallel Nonlinear Optimization with PyNumero and Parapint

Published: 2021/09/22

Nonlinear Optimization, Parallel Algorithms nonlinear programming, parallel optimization

We describe PyNumero, an open-source, object-oriented programming framework in Python that supports rapid development of performant parallel algorithms for structured nonlinear programming problems (NLP’s) using the Message Passing Interface (MPI). PyNumero provides three fundamental building blocks for developing NLP algorithms: a fast interface for calculating first and second derivatives with the AMPL Solver Library (ASL), … Read more

Decomposing Optimization-Based Bounds Tightening Problems Via Graph Partitioning

Published: 2021/02/11

Bounds tightening or domain reduction is a critical refinement technique used in global optimization algorithms for nonlinear and mixed-integer nonlinear programming problems. Bounds tightening can strengthen convex relaxations and reduce the size of branch and bounds trees. An effective but computationally intensive bounds tightening technique is optimization-based bounds tightening (OBBT). In OBBT, each variable is … Read more

A Parallel Hub-and-Spoke System for Large-Scale Scenario-Based Optimization Under Uncertainty

Published: 2020/11/02, Updated: 2022/09/09

Stochastic Programming decomposition, parallel computing, progressive hedging, stochastic programming

Efficient solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We describe the overall architecture and provide computational examples and results showing scalability to the largest instances that we know of for the … Read more

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

Published: 2020/09/13

Applications - Science and Engineering, Energy decomposition, generation transmission expansion, mixed-integer programming, power systems, renewable

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

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

Published: 2016/05/25

Modeling Languages and Systems, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization algebraic modeling language, dae constrained optimization, dynamic programming, mathematical modeling, pde-constrained optimization

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