Graph-Based Optimization Modeling Language

Abstract

Mathematical optimization has come to play a key role in numerous disciplines in recent years. In this work, we focus on a class of problems involving the optimization of linear discrete-time dynamical systems over a finite time horizon and possessing a natural block structure. Such problems arise in a number of fields, including energy systems planning and supply chain management. The typical workflow of optimization practitioners includes four basic steps, namely formulating the model, encoding it in a computer, solving it and post-processing it. The dominant approach for the second step makes use of algebraic modeling languages (AMLs), which make it possible to write problems in a form close to the typical mathematical notation. However, AMLs are usually ill-suited for exploiting the block structure that a problem may display. A second approach, the object-oriented modeling languages (OOMLs), possess a block structure implementation of problems but lacks of the easy mathematical encoding. To alleviate this, we design and implement a language, named the Graph-Based Modeling Language (GBOML), that natively supports the definition of problems with such structure, and exploits it to facilitate their encoding and post-processing. GBOML also possesses a formulation close to the mathematical one. This language can be viewed as a hybrid language, somewhere between AMLs and OOMLs. In addition, we implemented a method to retrieve a solution for problems encoded in GBOML. In this work, we formally introduce GBOML, explain its implementation and demonstrate its usefulness with an energy system planning example.