Advances in Optimization and its Applications in Process Industries
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Advances in Optimization and its Applications in Process Industries. Lorenz T Biegler Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213 July , 2012 . Chemical Engineering Department. Pittsburgh, PA. Carnegie Mellon Campus.

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Advances in Optimization and its Applications in Process Industries

Lorenz T Biegler

Department of Chemical Engineering

Carnegie Mellon University

Pittsburgh, PA 15213

July , 2012

Chemical Engineering Department

Pittsburgh, PA

Carnegie Mellon Campus

Center for Advanced Process Decision-making

(CAPD) Faculty and Researchers

Jeff Siirola

Erik Ydstie

Ignacio Grossmann

Nick Sahinidis

Larry Biegler

PhD Students:28 MS Students: 11

Post Docs:7Visitors:10

Long term goal: from molecular to enterprise level

CAPD Goals

  • Provide intellectual leadership on complex modeling, design and operational problems faced by process industries

  • Promote and Enhance PSE Science Base: optimization, control, computer science, systems engineering, business

Basic methodologies

Process modeling

Mathematical programming

Systems Engineering

Process control

Advanced computing

Areas of application

Process and product synthesis

Energy Systems

Supply chain optimization

Molecular Design

Systems Biology

L. T. Biegler

Nonlinear Programming and Parameter Estimation

Optimization of Differential Algebraic Systems

Nonlinear Optimization-based Control

I. E. Grossmann

Mixed Integer Nonlinear Programming for Process Synthesis

Planning and Scheduling of Batch and Continuous Processes

Design under Uncertainty

N. Sahinidis

Global Optimization Algorithms, and Software

Modeling of metabolic and signaling pathways

Design of environmentally benign chemicals

J. J. Siirola

Process Synthesis of Advanced Energy Systems

Synthesis of Nonideal Separation Systems

Product and Process Design

B. E. Ydstie

Adaptive and Robust Control Strategies

Thermodynamic Approaches to Process Control

Discrete Events and Scheduling

 Solar Cell Modeling

CAPD Principal Investigators

Optimal Design of Responsive Process Supply Chains

Ignacio Grossmann

Max: Net present value

Max: Responsiveness

(Expected Lead Time)

Supply chain: an integrated network of business units for the supply, production, distribution and consumption of the products.

Supply Chain Case Study

  • Problem Size MINLP:

    • # of Discrete Variables: 215

    • # of Continuous Variables: 8126

    • # of Constraints: 14617

  • Solution Time:

    • Solver: GAMS/BARON

    • Direct Solution: > 2 weeks

    • Proposed Algorithm: ~ 4 hours


Number and capacity of TLP/FPSO facilities

Installation schedule for facilities

Number of sub-sea/TLP wells to drill

Oil production profile over time

Optimal Development Planning under Uncertainty

  • Offshore oilfield having several reservoirs under uncertainty

  • Maximize the expected net present value (ENPV) of the project

Tarhan, Grossmann (2009)







  • Initial productivity per well

  • Size of reservoirs

  • Water breakthrough time for reservoirs

Distribution of Net Present Value Oilfield Planning

Deterministic Mean Value = $4.38 x 109

Multistage Stoch Progr = $4.92 x 109

=> 12% higher, more robust

Computation: Algorithm 1: 120 hrs; Algorithm 2: 5.2 hrs

Nonconvex MINLP: 1400 discrete vars, 970 cont vars, 8090 Constraints

Simulation-based Optimization

Nick Sahinidis

  • Goals:

    • Efficient optimization of complex chemical processes

    • Accurate solutions using function evaluations from high fidelity simulators

  • Challenges and solutions:

    • Lack of an algebraic model → Build surrogate models

    • Computationally costly simulations → Selectively choose a minimal data set

    • Often noisy function evaluations → Use regression surrogate models

    • Scarcity of fully robust simulations → Disaggregate the process

Process simulation

Optimization model

Function evaluation

Automated Learning of Algebraic Models for Optimization

Process Simulation

Disaggregation and modeling


Block 1

Model 1

Block 2

Model 2

Surrogate model generation using ALAMO

Algebraic optimization

Block 3

Model 3

True vs. Empirical


Ideal Model



Build simple and accurate models with a functional form tailored for an optimization framework




Data points


New point

Error maximization

Rebuild model

Combine surrogate models along with design specs, heat/mass balances, logical constraints, etc. to formulate an algebraic optimization model

Iterative design of experiments

Model functional form

CO2 Capture Case Study

Outlet gas

Solid feed

Minimize the increased cost of electricity

Maximize %CO2 removal ( )



CO2 rich gas

CO2 rich solid outlet

Surrogate model




vs. Environmental impact

Generate a low-complexity surrogate model of %CO2 removal as a function of reactor bed depth and cooling water flow from Aspen Custom Model runs

2. Surrogate model generation

3. Results: Pareto Analysis

1. Optimize a CO2 fluidized bed reactor

Process Control Research at CMUErik Ydstie

Research topics:

Solar Energy (Production processes and DSSC)

Dynamic modeling and Control of Supply Chains

Modeling and Control of Particulate Systems

Adaptive Control and Adaptive Optimization

Plant wide Simulation and Control

Process Automation and Safety

Fundamental Control Theory

Feed Forward Adaptive Control

Applied to Propane Cracker - DOW Chemicals

  • Control Objectives:

  • Stabilize pressure (CV) in response to frequent disturbances

  • Optimally choose cheapest fuel

CV: Pressure

MV: Low-pressure Flow

DV1: Off-gas

DV2: Residue

DV3: Fuel flow to Propane cracker

  • PI Control (green)

  • PI with adaptive optimization (blue)

B Erik Ydstie, CMU

Plantwide Control Systems? From Sand to Windshields(with Dr Yu Jiao PPG Inc, Glass Technology Research Center)

Silicate Sand


Iron Oxide


8 flat glass plants

10 windshield lines

Accuracy of shape, color, distortion (optical properties) depend on mix, melting conditions in furnace and operation of the tin bath.

Results from Trial at Wichita Falls TX

Conditioner temperature (KPI)

  • Yield improved by 3-5%

  • Excellent operator acceptance

  • Maintainable and expandable

  • Implemented on all PPG plants

  • $30-40M per year saving

Defects Measured

Large Scale Nonlinear Programming Algorithms: process optimization for design, control and operations

Evolution of NLP Solvers:

Process OptimizationL. T. Biegler






’80s: Flowsheet optimization

over 100 variables and constraints

’90s: Static Real-time optimization (RTO)

over 100 000 variables and constraints

’00s: Simultaneous dynamic optimization

over 1 000 000 variables and constraints

Object Oriented Codes to tailor structure, architecture to problems

Grade Transitions - Polymer Processes

Large-Scale Optimization (L. T. Biegler)

  • Periodic Adsorption Process Optimization

Simulated Moving Bed - Optimal Operation

CPU Time for optimization: 9.03 min

34098 variables, 34013 equations

Real-time Dynamic Optimization

Dynamic Optimization Problem


t, time

z, differential variables

y, algebraic variables

tf, final time

u, control variables

p, time independent parameters

Collocation on

finite Elements

Nonlinear Programming

Problem (NLP)

Discretized variables


Nonlinear Dynamic

Optimization Problem


Continuous profiles

Nonlinear Programming Problem


Finite elements, hi, can also be variable to determine break points for u(t).

Add hu ≥hi≥ 0, S hi=tf

Can add constraints g(h, z, u) ≤ e for approximation error

Process Optimization with Dynamic Reactor Models

  • Optimal Catalyst Distribution in Graded Fixed Bed Reactors (Y. Nie, Dr. Paul Witt, Dr. AnshulAgarwal)

  • Dynamic Modeling and Recipe Optimization of Polyether Polyol Processes (Y. Nie, Dr. Carlos Villa)

  • Combined Recipe Optimization and Product Scheduling (YisuNie, Dr. John Wassick)

  • Characteristics:

  • Large-scale, nonlinear, (often) exothermic reactive systems

  • Modeled with simultaneous collocation methods

  • Need to capture nonlinear, (often) unstable modes and runaways, enable highly efficient and safe operation

  • Fast solution of optimization problems

Optimization of Runaway Reactors

Optimization of Runaway Reactors

Optimal Catalyst DistributionMultizone Optimization Problem

Dynamic Optimization Solution Strategy

Dynamic Optimization Results

Catalyst Distribution Profiles

Recipe Optimization

Semi-Batch Polyether Polyol Process (Yisu Nie)

Semi-batch polyether polyol process

Process Recipe Optimization

Polyol Dynamic Process Calibration

Polyol Dynamic Optimization Results

Special industrial interest group:

Enterprise-wide Optimization for Process Industries

Multidisciplinary team:

Chemical engineers, Operations Research, Industrial Engineering


Carnegie Mellon: Ignacio Grossmann (ChE)

Larry Biegler (ChE)

John Hooker (OR)

Nicola Secomandi (OR)

Lehigh University: Katya Scheinberg (Ind. Eng)

Univ. Pittsburgh: Andrew Schaeffer (Ind. Eng.)

Overall Goal:

  • Novel planning and scheduling models, including consideration of uncertainty

  • Effective integration of Production Planning, Scheduling and Real–time Optimization

  • Optimization of Entire Supply Chains

Hierarchy of Enterprise Wide Optimization

  • Supply Chain, Planning and Scheduling

    • Large LP and MILP models

    • Many Discrete Decisions

    • Few Nonlinearities

    • Essential link needed to process models

    • Decisions need to be feasible at lower levels

Process Operations Applications

  • Real-time Optimization and Control

    • Large, Complex Process Models

    • Few Discrete Decisions

    • Nonlinearities and Dynamics

    • Essential to Link with Logistics and Planning

    • “Time-limited” on-line optimization

    • Optimal performance needs to be passed to higher levels

Multiscale temporal and

spatial integration

Multi-site Production Planning

Polymer plants (25 grades)

Objective: Production Planning and Distribution

Model for Batch Polymerization Reactors

Production Site:

Raw material availability and Raw material costs

Storage tanks with associated capacity

Transportation costs to each customer


Materials it can produce

batch sizes (lbs) for each material it can produce

operating costs ($/hr) for each material

Sequence dependent clean out times (hrs per transition for each material pair)

Time the reactor is available during a given month (hrs)


Reaction 1







Reaction 2




Reaction 3



Production Planning and Scheduling

  • Customers:

  • Monthly forecasted demands for desired products

  • Price paid for each product

  • Materials:

  • Raw materials, Intermediates, Finished products

  • Unit ratios (lbs of needed material per lb of material produced)

Production Scheduling Coupled with Recipe Optimization

Scheduling: State Equipment Network (SEN) Model

Mixed-Logic Dynamic Optimization (MLDO)

SEN/DAE Case Study

Case Results (40% Profit Increase)

Real-time Optimization for ASUs

  • Air Separation Unit, key unit in IGCC-based Power Plants

  • Need for high purity O2

  • Respond quickly to changes in process demand

  • Large, highly nonlinear dynamic separation (MESH) models

  • Related work:

  • Methanol distillation (Diehl, Bock et al., 2005)

    • 40 trays, 210 DAEs, 19746 discretized equations

  • Argon Recovery Column

    • 50 trays, 260 DAEs, 21306 discretized equations

  • Double Column ASU Case Study

    • 80 trays, 1520 DAEs, 116,900 discretized equations

  • w

    Real-time Optimization: Components






    c(x, u, p) = 0


    c(x, u, p) = 0


    • Data reconciliation – identify gross errors and inconsistency in data

    • Periodic update of process model identification

    • Usually requires APC loops (MPC, DMC, etc.)

    • RTO/APC interactions: Assume decomposition of time scales

      • APC to handle disturbances and fast dynamics

      • RTO to handle static operations

    • Typical cycle: 1-2 hours, closed loop

    • What if steady state and dynamic models are inconsistent?



    Dynamic Real-time Optimization (RTO)





    Real-time Optimization

    Dynamic Models

    State Estimation

    Model Updates


    • Goal: Integrate On-line Optimization with Advanced Process Control

    • Requires time-critical calculations

    • Current optimization makes this available in practice

    • Links to Decision-making at other scales/levels

    • Several applications in Chemical Industry

    • Essential for:

      • Inherently Dynamic Energy Systems

      • Handling Uncertainties in prices, supplies and demands

      • Optimal disturbance rejection

    NMPC Estimation and Control

    On-line Optimization: Nonlinear Model Predictive Control (NMPC)

    • Why NMPC?

    • Track a profile – evolve from linear dynamic models (MPC)

    • Severe nonlinear dynamics (e.g, sign changes in gains)

    • Operate process over wide range (e.g., startup and shutdown)

    z : differential states

    y : algebraic states


    d : disturbances

    u : manipulated


    NMPC Controller

    ysp : set points

    Model Updater

    NMPC Subproblem

    What about Fast NMPC?

    • Fast NMPC is not just NMPC with a fast solver (Engell, 2007)

    • Computational delay – between receipt of process measurement and injection of control, determined by cost of dynamic optimization

    • Leads to loss of performance and stability(see Findeisen and Allgöwer, 2004; Santos et al., 2001)

    As larger NLPs are considered for NMPC, can computational delay be overcome?

    Can we avoid on-line optimization?

    • Divide Dynamic Optimization Problem:

      • preparation, feedback response and transition stages

      • solve complete NLP in background (‘between’ sampling times)

        as part of preparation and transition stages

      • solve perturbed problem on-line based on NLP sensitivity

      • > two orders of magnitude reduction in on-line computation

    • Based on NLP sensitivity of z0 for dynamic systems

      • Extended to Collocation approach – Zavala et al. (2008, 2009)

      • Similar approach for Moving Horizon Estimation – Zavala et al. (2008)

    • Stability Properties (Zavala et al., 2009)

      • Nominal stability – no disturbances nor model mismatch

        • Lyapunov-based analysis for NMPC

      • Robust stability – some degree of mismatch

        • Input to State Stability (ISS) from Magni et al. (2005)

      • Extension to economic objective functions

    Advanced Step Nonlinear MPC (Zavala, B., 2008)

    Solve NLP in background (between steps, not on-line)

    Update using sensitivity on-line




    tk tk+1 tk+2


    Solve NLP(k) in background (between tk and tk+1)

    Advanced Step Nonlinear MPC (Zavala, B., 2008)

    Solve NLP in background (between steps, not on-line)

    Update using sensitivity on-line






    tk tk+1 tk+2


    Solve NLP(k) in background (between tk and tk+1)

    Sensitivity to update problem on-line to get (u(k+1))

    Advanced Step Nonlinear MPC (Zavala, B., 2008)

    Solve NLP in background (between steps, not on-line)

    Update using sensitivity on-line






    tk tk+1 tk+2


    Solve NLP(k) in background (between tk and tk+1)

    Sensitivity to update problem on-line to get (u(k+1))

    Solve NLP(k+1) in background (between tk+1 and tk+2)

    Nonlinear Model Predictive Control

    Air Separation Unit (Huang, B., 2011)

    Objective: minimize operating cost subject to demand specifications

    4manipulated variables.

    4 output variables.

    Horizon: 100minutes in 20

    finite elements.

    Sampling time: 5 minutes.

    First Principle Index 1 Model:

    1520 DAEs

    OCFE Discretization:

    Variables: 117,140

    Constraints: 116,900

    NMPC Ramping for Air Separation Unit

    (Huang, Zavala, B., 2009)

    At t = 30-60 min, product rates are ramped down by 40%.

    At t =1000-1030 min, they are ramped back. 5% disturbance is added to Mi.

    N = 20, K = 3

    320 ODEs, 1200 AEs.

    Variables: 117,140

    Constraints: 116,900

    400 NLPs solved

    Background: 200 CPUs, 6 iters.

    Online: 1 CPUs

    Computational Feedback Delay Reduced from 200 1 CPUs

    Blue dashed lines are ideal NMPC profile

    Red lines are AS-NMPC profile.

    In contrast, linearized controller is unstable

    Market Operations and Electricity Price Bidding

    D-RTO to Minimize Electricity Cost

    Min SiPriceix (MA+EA)i + Regi

    S.t. ASU model

    time horizon 2hrs

    sampling time 6 min

    D-RTO with day ahead costs

    Dynamic Optimization for Day Ahead Strategy

    Air Separation Unit

    ASU Compressor feeds follow trend of electricity price. Output profiles satisfied for demand specifications.

    Optimal D-RTO: $12,511

    Optimal set-point tracking: $13,042

    4.25% ($100k/yr) decrease over

    Optimal setpoint tracking.

    ARIMA Model to Real Time Price

    ARIMA (2,1,1)

    Online ARIMA model for Price Estimation

    Energy Price

    Update ARIMA price model with moving horizon estimation.

    Predicted price for a 24 hour period

    Dynamic Real-time Optimization for Real Time Pricing

    Same formulation as in day ahead strategy but using predicted price.

    Cost of the proposed method: $5,939

    Cost of set-point tracking: $6,307

    6.19% ($135k/yr) savings over optimal setpoint tracking

    Projects with EWO partners

    ABB: Optimal Design of Supply Chain for Electric Motors

    Contact: Iiro HarjunkoskiIgnacio Grossmann, Analia Rodriguez

    Air Liquide: Optimal Coordination of Production and Distribution of Industrial Gases

    Contact: Jean Andre, Jeffrey ArbogastIgnacio Grossmann, Vijay Gupta, Pablo Marchetti

    Air Products: Design of Resilient Supply Chain Networks for Chemicals and Gases

    Contact: James HuttonLarry Snyder, Katya Scheinberg

    Braskem: Optimal production and scheduling of polymer production

    Contact: Rita Majewski, Wiley BuceyIgnacio Grossmann, Pablo Marchetti

    Cognizant: Optimization of gas pipelines

    Contact: Phani SistuLarry Biegler, Ajit Gopalakrishnan

    Dow: Multisite Planning and Scheduling Multiproduct Batch Processes

    Contact: John WassickIgnacio Grossmann, Bruno Calfa

    Dow: Batch Scheduling and Dynamic Optimization

    Contact: John WassickLarry Biegler, Yisu Nie

    Ecopetrol: Nonlinear programming for refinery optimization

    Contact: Sandra Milena Montagut Larry Biegler, Yi-dong Lang

    ExxonMobil: Global optimization of multiperiod blending networks

    Contact: Shiva Kameswaran, Kevin Furman Ignacio Grossmann, Scott Kolodziej

    ExxonMobil: Design and planning of oil and gasfields with fiscal constraints

    Contact: Bora Tarhan Ignacio Grossmann, Vijay Gupta

    Praxair:Capacity Planning ofPower Intensive Networks with Changing Electricity Prices

    Contact: Jose Pinto Ignacio Grossmann, Sumit Mitra

    UNILEVER: Scheduling of ice cream production

    Contact: Peter BongersIgnacio Grossmann, Martijn van Elzakker

    BP*:Refinery Planning with Process Models

    Contact: Ignasi Palou-RiveraIgnacio Grossmann, Abdul Alattas

    PPG*: Planning and Scheduling for Glass Production

    Contact: Jiao Yu Ignacio Grossmann, Ricardo Lima

    TOTAL*:Scheduling of crude oil operations

    Contact: Pierre PestiauxIgnacio Grossmann, Sylvain Mouret

    Projects and Seminars:

    Collaborative Cyberinfrastructure for (MINLP)

    CMU:Ignacio Grossmann, PietroBelotti, Lorenz Biegler, Pedro Castro, Francois Margot,

    Juan Ruiz, NikolaosSahinidis

    • Objectives

    • Create a library of optimization problems that can be

    • generally formulated as MINLP models.

    • Provide high level descriptions of the problems with one or several model

    • formulations with corresponding input files for one or several instances.

    • MILP, NLP and MINLP models in diverse areas: engineering, physics, biology, finance

    - Formulation of models is emphasized

    which allows comparison and

    evaluation of numerical performance

    of different codes

    - Supports discussion through forum

    • Future:

    • Guidelines for modeling

    • Contribute open problems


    Air Liquide

    Air Products



    Dow Chemical

    Eastman Chemical




    GS Eng. & Constr.


    CAPD Industrial Members

    Mitsubishi Electric Res. Lab.


    Neste Engineering Oy

    Paragon Decision



    Procter & Gamble


    Rockwell Automation




    • Industrial Impact of CAPD

    • Large number of graduates in petroleum, chemical, consulting companies

    • Refinery and batch scheduling –ABB

    • NLP optimization of gas separation plants -Air Products

    • Flowsheet optimization with SQP- Air Products, Aspen Technology

    • LSSQP, SPLIT - Aspen Technology

    • Combustion Verification – Alcoa

    • Optimal synthesis of separation of olefins -BP

    • Optimal synthesis of crystallization process –BP

    • Energy optimization in corn-based ethanol plants - Cargill

    • Optimal planning polymer plants –Dow

    • Large-scale supply chain optimization under uncertainty - Dow

    • Gasfield development model under uncertainty – ExxonMobil

    • Control and optimization of polymerization reactors - ExxonMobil


    • IPOPT Large-scale NLP software -IBM

    • Glass Furnace Control – PPG

    • Solar Grade Silicon – REC Silicon

    • Power plant control systems – Emerson Process Management

    • CAPD Academic Impact

    • Largest PSE group in US

    • Graduates in academia

    • Achenie (VPI), Bañares (Oxford), Bullard (UNC), Floudas (Princeton), Govind (Cincinnati), Halemane (Karnataka), Hrymak (Western Ontario), Laird (Texas A&M), Lee (CCNY), Kawajiri (GaTech), Maravelias (Wisconsin), Oliveira (Coimbra), Pekny (Purdue), Pinto (Polytechnic), Pistikopoulos (Imperial), Rico (Celaya), Sahinidis (CMU), Swaney (Wisconsin), Turkay (Koc), Zamora (UAM), You (Northwestern)

    • 3.Textbook: Systematic methods of chemical process design

    • Biegler, Grossmann, Westerberg (Prentice-Hall)

    • 4. Adoption of CMU-research and software

    • MINLP, SQP, collocation, passivity theory, fault trees,ASCEND, BARON, SQP, IPOPT, DICOPT, LOGMIP

  • 5. Assoc. Editors Journals: AIChE J. (Grossmann), I&EC Res. (Biegler),

  • Optimization Methods and Software, Adaptive Control and Signal

  • Processing (Ydstie)

  • PSE [email protected]

    • Strong Scientific Research Base

    • Numerical analysis  Simulation

    • Math. Programming  Process Optimization

    • Systems/Control Theory  Process Control

    • Computer Science  Software/Advanced Computing

    • Operations Research  Business/Operations

    • Strong Industrial Interactions

    • Enterprise Wide Optimization

    • Energy Systems

    • Process and Product Design and Development

    • Control, Dynamics and Real-time Optimization

    • Synergy of Modern Optimization Algorithms and Optimization Models

    • Design and Operation under Uncertainty

    • Planning, Scheduling and Operations

    • Optimization in Real-time

    • For more information: http//

    • http//

    Research Collaborations

    Across Carnegie Mellon

    • Tepper School of Business

    • Institute for Complex Engineered Systems (ICES)

    • Mechanical Engineering

    • Electrical and Computer Engineering

    • Biomedical Engineering

    • Software Engineering Institute

    • Computer Science

    • Mathematical Sciences

    • Material Science and Engineering

    Research Collaborations

    Around the World

    • Imperial College (UK)

    • ETH (Zürich)

    • RWTH-Aachen + IWR-Heidelberg + TUBerlin + MPI Magdeburg (Germany)

    • Abo Akademi + Jyvaskyla (Finland)

    • NTNU (Trondheim)

    • UPC + Alicante + Cantabria (Spain)

    • Coimbra + Porto (Portugal)

    • Maribor (Slovenia)

    • INTEC+INGAR+PLAPIQUI (Argentina)

    • Antofagasta + PUC + USACH (Chile)

    • UIA+Tec Celaya (Mexico)

    • Kyoto (Japan)

    • KAIST (Korea)

    • Tsinghua + Zhejiang+ECUST (China)

    • IIT Bombay (India)

    Process Systems Engineering Research

    Process Systems Engineering is concerned with the systematic analysis and optimization of decision making processes for the discovery, design, manufacture and distribution of chemical products.

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