ROmodel: modeling robust optimization problems in Pyomo

This paper introduces ROmodel, an open source Python package extending the modeling capabilities of the algebraic modeling language Pyomo to robust optimization problems. ROmodel helps practitioners transition from deterministic to robust optimization through modeling objects which allow formulating robust models in close analogy to their mathematical formulation. ROmodel contains a library of commonly used uncertainty sets which can be generated using their matrix representations, but it also allows users to define custom uncertainty sets using Pyomo constraints. ROmodel supports adjustable variables via linear decision rules. The resulting models can be solved using ROmodels solvers which implement both the robust reformulation and cutting plane approach. ROmodel is a platform to implement and compare custom uncertainty sets and reformulations. We demonstrate ROmodel’s capabilities by applying it to six case studies. We implement custom uncertainty sets based on (warped) Gaussian processes to show how ROmodel can integrate data-driven models with optimization.

SDDP.jl: A Julia Package for Stochastic Dual Dynamic Programming

We present SDDP.jl, an open-source library for solving multistage stochastic programming problems using the stochastic dual dynamic programming algorithm. SDDP.jl is built on JuMP, an algebraic modeling language in Julia. JuMP provides SDDP.jl with a solver-agnostic, user-friendly interface. In addition, we leverage unique features of Julia, such as multiple dispatch, to provide an extensible framework for practitioners to build on our work. SDDP.jl is well tested, and accessible documentation is available at https://github.com/odow/SDDP.jl .

High-Performance Prototyping of Decomposition Methods in GAMS

Prototyping algorithms in algebraic modeling languages has a long tradition. Despite the convenient prototyping platform that modeling languages offer, they are typically seen as rather inefficient with regard to repeatedly solving mathematical programming problems, a concept on which many algorithms are based. The most prominent examples of such algorithms are decomposition methods, such as the Benders decomposition, column generation, and the Dantzig–Wolfe decomposition. In this work, we discuss the underlying reasons for repeated solve deficiency with regard to speed in detail and provide an insider’s look into the algebraic modeling language GAMS. Further, we present recently added features in GAMS that mitigate some of the efficiency drawbacks inherent to the way modeling languages represent model data and ultimately solve a model. In particular, we demonstrate the grid-enabled gather-update-solve-scatter facility and the GAMS object-oriented application programming interface on a large-scale case study that involves a Benders decomposition–type algorithm for a power-expansion planning problem.

An integrated platform for intuitive mathematical programming modeling using LaTeX

This paper presents a novel prototype platform that uses the same LaTeX mark-up language, commonly used to typeset mathematical content, as an input language for modeling optimization problems of various classes. The platform converts the LaTeX model into a formal Algebraic Modeling Language (AML) representation based on Pyomo through a parsing engine written in Python and solves by either via NEOS server or locally installed solvers, using a friendly Graphical User Interface (GUI). The distinct advantages of our approach can be summarized in (i) simplification and speed-up of the model design and development process (ii) non-commercial character (iii) cross-platform support (iv) easier typo and logic error detection in the description of the models and (v) minimization of working knowledge of programming and AMLs to perform mathematical programming modeling. Overall, this is a presentation of a complete workable scheme on using LaTeX for mathematical programming modeling which assists in furthering our ability to reproduce and replicate scientific work.

Commercial Impact and Optimum Capacity Determination of Pumped Storage Hydro Plant for a Practical Power System

This paper attempts to study the commercial impact of pumped storage hydro plant on the operation of a stressed power system. The paper further attempts to compute the optimum capacity of the pumped storage scheme that can be provided on commercial basis for a practical power system. Unlike the analysis of commercial aspects of pumped storage scheme attempted in several papers, this paper is presented from the point of view of power system management of a practical system considering the impact of the scheme on the economic operation of the system. A realistic case study is presented as the many factors that influence the pumped storage operation vary widely from one system to another. The suitability of pumped storage for the particular generation mix of a system is well explored in the paper. To substantiate the economic impact of pumped storage on the system, the problem is formulated as a short-term hydrothermal scheduling problem involving power purchase which optimizes the quantum of power to be scheduled and the duration of operation. The optimization model is formulated using an algebraic modeling language, AMPL, which is then solved using the advanced MILP solver CPLEX.