About Us
Grad Studies
Theme Topic
Dynamic Optimization

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, with a goal toward the development of an optimization-based decision support tool for on-line application.

  • Dynamic Optimization of Integrated Process Units Under Partial Shutdown Conditions
    Shutdowns in chemical processing plants are detrimental both to plant economics and critical product characteristics. These situations can be due to routine maintenance, or due to the more extreme case of equipment failure. In a recent study, we developed a formulation and computational strategy for determining optimal operating policies in the face of shutdowns in multi-unit operations, with application to a Kraft pulp mill. Extensions have included the optimal design of additional buffer capacities in accordance with probability distributions of failure type and duration; and consideration of model uncertainty via multi-period optimization. Current work extends the approach to include discrete decisions, and incorporation of feedback to mitigate effects of disturbances and model uncertainty.

We are also continuing development of a modeling language for dynamic optimization that accepts as input a dynamic model in a syntax that closely resembles the mathematical description, and generates code in a number of modeling environments which permits different solution strategies and different optimization solvers to be used without having to reformulate the problem. We are also investigating approaches for dynamic optimization that are particularly well suited for large-scale problems, such as those arising in integrated plant and control system design of multi-product air separation plants. One of the avenues bring investigated is a parallel computing implementation of a multiple shooting approach for large-scale, multi-period dynamic optimization problems.

Dr. Chris L. E. Swartz
Professor and Director, MACC
Anthony Quarshie
M.A.Sc. Candidate
Rohil Jaydeep
M.A.Sc. recipient
Tokiso Thatho
MaSC recipient
Ian Washington
Ph.D. recipient
Dynamic real-time optimization with closed-loop prediction
AIChE J (2017)  -  [ Publisher Version ]
Practical optimization for cost reduction of a liquefier in an industrial air separation plant
Cao, Y., Flores-Cerrillo, J, Swartz, C. L. E.
Computers & Chemical Engineering, 99 13-20 (2017)  -  [ Publisher Version ]
A parallel structure exploiting nonlinear programming algorithm for multiperiod dynamic optimization
Computers & Chemical Engineering, 103 151-164 (2017)  -  [ Publisher Version ]
Approximation of closed-loop prediction for dynamic real-time optimization calculations
Computers & Chemical Engineering, 103 23-38 (2017)  -  [ Publisher Version ]
Optimization-based Online Decision Support Tool for Electric Arc Furnace Operation.
IFAC-PapersOnLine , 50 (1) 1078410789 (2017)  -  [ Publisher Version ]
Optimal response under partial plant shutdown with discontinuous dynamic models
Computers & Chemical Engineering, 86 120-135 (2016)  -  [ Publisher Version ]
Optimal Dynamic Operation of a High-Purity Air Separation Plant under Varying Market Conditions
Cao, Y.Swartz, C. L. E., Flores-Cerrillo, J
Ind Eng Chem Res, 55 (37) 9956-9970 (2016)  -  [ Publisher Version ]
Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty
Processes, 3 (3) 541-567 (2015)  -  [ Publisher Version | Open Access Version (free) ]
Design under uncertainty using parallel multi-period dynamic optimization
AIChE Journal (2014)  -  [ Publisher Version ]
Optimal operation of process plants under partial shutdown conditions
AIChE Journal, 59 (11) 4151-4168 (2013)  -  [ Publisher Version ]