Dr. Christopher Swartz

Overview

Research Interests

Current trends of competition in an increasingly global market place, rising costs, and tightening environmental constraints make it increasingly important for process plants to be operated efficiently and in an environmentally responsible manner in order to remain competitive. This includes operation of individual process units, process plants, as well as the supply chains of which they are part. Mathematical optimization provides a tool for addressing this – as the basis of both decision-support and model-based control systems, and for optimal process design.  

My research focus is on applied optimization and automation of process systems, with the goal of developing mathematical formulations and solutions to improve the economics of operations, subject to prevailing operational, safety and environmental constraints.  Key research thrusts are described below.

Design for Dynamic Performance

The design of a plant can have a significant impact on its ability to be satisfactorily controlled.  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 current application seeks to identify design limitations to transition speed in air separation plants, where rapid response to demand and electricity price changes is highly beneficial.

Dynamic Optimization of Process Operations

We consider optimization of transient processes described by differential-algebraic equation (DAE) systems in several contexts, with a focus toward industrial applications.  (i) Electric arc furnaces (EAFs) are widely used in the steel industry for melting scrap, and are large consumers of electrical energy.  Our group has been involved in the development of modeling and computational strategies for dynamic optimization of industrial EAF systems.  (ii) Shutdowns in chemical processing plants are detrimental both to plant economics and critical product characteristics. We have developed formulation and computational strategies for determining optimal operating policies in the face of shutdowns in multi-unit operations, with application to a Kraft pulp mill. Current work extends the approach to include model discontinuities, handling of uncertainty through feedback, and optimal relaxation of specifications under abnormal operating conditions.  (iii) A further area of study within our group is the interaction between model predictive control (MPC) and a higher-level optimization layer. This includes analysis of the performance of LP-MPC cascade control systems – a common configuration in commercial MPC implementations, and the analysis and development of dynamic real-time optimization (D-RTO) systems that utilize a dynamic model at the supervisory optimization level.

Computational Strategies for Large-Scale Dynamic Optimization

We are exploring the use of parallel computing approaches for the solution of large-scale dynamic optimization problems under uncertainty.  A multiple-shooting approach is utilized for solving the dynamic optimization problem, with the uncertain parameter space discretized into a finite number of scenarios. The independent integration tasks are distributed among multiple processors for parallel solution.

Optimal Scheduling and Planning

Our research in this field is driven primarily by industrial needs, and our studies typically involve close collaboration with industrial partners. Recent and current studies include optimal raw material purchasing and plant operation under uncertainty in steel manufacturing, the development of optimal scheduling and planning formulations for an industrial food processing application, and optimal scheduling of converter aisle operations in a nickel smelting plant.  In addition, we are exploring strategies for reactive scheduling, and systematic integration of planning and scheduling.

Supply Chain Optimization

Key drivers in the process industry toward an increased focus on supply chain technologies are increasing pressure to reduce costs and inventories due to market competition, a shift from commodity products toward low-volume, demand-driven specialty products, globalization of operations, and more rapidly fluctuating demands. Within our group, we consider strategies for optimal supply chain operation and design, as well as the development of computational tools for supply chain performance analysis.

Work in this area includes (i) a novel robust model predictive control formulation for application to process supply chain systems, (ii) a supply chain formulation that includes time-limited transportation contracts within an optimal supply chain design, and (iii) development of a systematic framework for supply chain operability analysis, motivated by Canadian forest products industry transformation from commodity production to integrated biorefineries producing biofuels and specialty chemicals, where flexibility and responsiveness to accommodate market variation, feedstock variability and fluctuating customer demands is a key consideration.