Algebraic Modeling and Optimization

Introduction The aim of this chapter is to provide an overview on algebraic modeling systems and their application in Chemical Engineering. Algebraic modeling systems are a class of computational modeling tools that are mainly oriented for the development of optimization models. One important characteristic of these systems is the representation of the model using a mathematical modeling notation using algebraic equations, which provides great flexibility in modeling. This flexibility has enabled the application of algebraic modeling systems in many different areas, namely agricultural economics, engineering, finance, management science and operations research, contract theory, economic development, power systems, energy economics, and energy markets, among others. In Chemical Engineering they have also been applied in many application areas, for example process optimization, process synthesis, planning and scheduling of plant operations, and supply chain design and operation. Chemical Engineers have a long tradition on building equation models based on first principles for the simulation and optimization of chemical processes, which has contributed to the development of computational tools for the systematic simulation and optimization of chemical processes design and operation. Examples of these computational tools include process simulators, either sequential based modular or equation-oriented, software that targets specific processing applications, modeling systems, and spreadsheets. Specific examples of these computational tools are described in other chapters of this book. However, modeling systems include gPROMS [1], ASCEND [3], and the object-oriented modeling language Modelica [4]. This chapter focuses on a specific class of modeling systems that are mainly applied for optimization applications. It therefore, gives an integrated overview of algebraic modeling systems, and basic notions about the mathematical formulation of optimization problems. In algebraic modeling systems, as with other computational tools for simulation or optimization,