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Research Themes
Optimization
Optimization is concerned with finding the best among alternatives, and is mathematically formulated through an objective function that is maximized or minimized, and constraints that define the feasible region or space of alternatives. Optimization is ubiquitous in virtually all facets of process systems engineering, where the objective typically relates to economic, operational or environmental performance.

Optimization plays a significant role in MACC research projects. This includes formulation of a wide variety of optimization problem types such as linear programming, nonlinear programming, mixed-integer programming, dynamic optimization and global optimization, and solution through the application of state-of-the-art algorithms and software. Many of the problems exhibit features that make them challenging to solve, such as strong nonlinearity, high dimension, discrete decisions, dynamic models, model discontinuity and uncertainty. Problems are formulated in different modeling environments depending on the application, and include GAMS, AMPL, gPROMS, and Matlab. We also develop novel formulations and solution approaches. Applications include nonlinear predictive control, real-time optimization, supply chain optimization, planning and scheduling, integrated plant and control system design, abnormal situation response, and batch process operation and control.

Dynamic optimization is a key thread that runs through much of our work. It involves solution of an optimization problem that includes a differential or differential-algebraic equation system as constraints. Applications that we consider include optimization of batch process operation and optimal response under plant failure conditions, examples of which are given below.

  • Modeling and Optimization of Electric Arc Furnace Operation
    Electric arc furnaces (EAFs) are widely used in the steel industry for melting scrap. The highly energy intensive nature of these operations, coupled with their complexity, make them prime candidates for optimization. A first-principles based dynamic model of the EAF was developed and calibrated to an industrial operation by estimating model parameters using plant data. Optimization of input trajectories for a number of constraint and objective function scenarios demonstrated significant potential savings. Further research is under way,...

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Dr. Chris L. E. Swartz
Professor and Director, MACC
Rohil Jaydeep
MaSC Candidate
Anthony Quarshie
MaSC Candidate
Smriti Shyamal
Ph.D. Candidate
Tokiso Thatho
MaSC Candidate
Ian Washington
Research Engineer


The design of a plant can have a significant impact on its ability to be satisfactorily controlled. A plant design which is optimal on the basis of steady-state considerations, but which has poor dynamic characteristics, may not be able to achieve the expected economic performance in practice. Moreover, the unfavorable dynamic characteristics could seriously affect the plant's ability to handle safety and environmental constraints effectively. Our research group has been involved in the development of optimization-based computational strategies, both for assessing plant operability and for incorporating operability requirements into optimal design calculations. A key contribution is the rigorous inclusion of actuator saturation effects through a complementarity constraint formulation which achieves significantly superior computational performance over an alternative mixed-integer programming formulation. This led to the development of an effective methodology for including the... [read more]

Dr. Chris L. E. Swartz
Professor and Director, MACC
Xiaoqiang Wang
Visiting PhD Student
Ian Washington
Research Engineer


In order to excel in the present environment of increased market competition and rising costs, industries need to extract the maximum attainable economic performance from their operations subject to product quality, safety, environmental and other prevailing constraints. Real-time optimization (RTO) is a mechanism toward achieving this goal through continual adjustment of the plant operating point to coincide with the economic optimum. The process systems group at McMaster University has been at the forefront of research in RTO systems. (Marlin and Hrymak, 1997; Yip and Marlin, 2004). While significant advances have been made in this area, several challenges remain:

  • Most RTO systems operate in conjunction with model predictive control. However, the interaction between these two control levels has not been fully explored. In particular, industrial MPC systems are generally implemented in conjunction with a linear programming (LP) or quadratic programming (QP) steady-state...

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Dr. Chris L. E. Swartz
Professor and Director, MACC
Dr. Thomas E. Marlin
Professor Emeritus
Mahdi Eskandari
MaSC Candidate
Hao Li
MaSC Candidate
Alexander Nguyen
MaSC Candidate


Black-box optimization problems commonly arise in process systems engineering due to the heavy use of process simulators. Although many simulators use equation-based models derived from theory, the solution of these equations often involves techniques such as sequential modular flowsheeting, table look-ups, the solution of sub-problems (such as minimization of Gibbs free energy), or calls to third-party software for which the underlying equations are hidden from the end user. As a result, most process simulations are effectively black-box.

Optimization of black box problems has been an ongoing area for research, resulting in the development of methods such as moving simplex, particle swarm optimization, differential evolution, genetic algorithms, and the like. Most of these black box solvers are inspired by biology but do not take advantage of the many gains made in white-box optimization theory (mathematical programming, MINLP, etc). Therefore, the focus of this research...

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Dr. Thomas A. Adams II
Associate Professor


Data-driven models provide a useful alternative for the control of complex systems where computation time and numerical solution robustness pose challenges to the use of detailed first-principles models. In this research, we are exploring and analyzing different types of data-driven models for the optimization and control of complex industrial processes such as electric arc furnace operation in the steel industry. [read more]

Dr. Chris L. E. Swartz
Professor and Director, MACC
Dr. Prashant Mhaskar
Professor and Canada Research Chair (Tier II)
Abhinav Garg
Ph.D. Candidate
Mudassir Rashid
Ph.D. Candidate