Efficient Stochastic Programming in Julia

TL;DR

This paper introduces StochasticPrograms.jl, a Julia-based framework for stochastic programming that offers expressive modeling, interactive analysis, and scalable distributed optimization algorithms, demonstrated through numerical benchmarks.

Contribution

The paper presents a new open-source Julia framework with structure-exploiting solvers and distributed computing capabilities for stochastic programming.

Findings

Framework scales effectively on multi-node setups

Solvers based on L-shaped and progressive-hedging algorithms

Demonstrated strong scaling properties on benchmarks

Abstract

We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms. Stochastic programming models can be efficiently formulated using expressive syntax and models can be instantiated, inspected, and analyzed interactively. The framework scales seamlessly to distributed environments. Small instances of a model can be run locally to ensure correctness, while larger instances are automatically distributed in a memory-efficient way onto supercomputers or clouds and solved using parallel optimization algorithms. These structure-exploiting solvers are based on variations of the classical L-shaped and progressive-hedging algorithms. We provide a concise mathematical background for the various tools and constructs available in the framework, along with code listings exemplifying their usage. Both software innovations related to the implementation of the framework and algorithmic innovations related to the structured solvers are highlighted. We conclude by demonstrating strong scaling properties of the distributed algorithms on numerical benchmarks in a multi-node setup.