INTRODUCTION TO OPTIMIZATION

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INTRODUCTION TO OPTIMIZATION
We have lots of excellent choices for an elective
course. Why take optimization? - What is it? -
How does it fit into engineering? - What
advantage for me?
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INTRODUCTION TO OPTIMIZATION
Why take 4G03?
I want to build process systems engineering
skills that can be applied to a wide range of
challenges in science, engineering, business and
public policy.
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INTRODUCTION TO OPTIMIZATION
Overview of the Class Topics Very brief overview
of optimization - History and scope - Who does
Optimization - The market for products and
services Optimization in Chemical Engineering -
Quick introduction to optimization problem -
Model-based optimization - Typical
applications Course learning goals
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INTRODUCTION TO OPTIMIZATION

• Key developments in optimization
• (pre-digital computer)
• Fermat (1646)
• and Newton (1670)
• Euler (1755)
• (pronounced oiler)
• Lagrange (1797)

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INTRODUCTION TO OPTIMIZATION

• Key developments from the 2nd half of 20th
  century
• Dantzig (1947) Linear programming
• (inequality constraints)
• Kuhn Tucker (1951)
• Conditions for NL optimization
• Many contributors (1960-80s) Algorithms for NL
  optimization
• Khachain and Karmarkar (1980) Renewed interior
  point methods
• Continued developments in diverse problems
  (integer, stochastic, global, etc.) - Its still
  a developing area!

http//www-gap.dcs.st-and.ac.uk/history/PictDispl
ay/Dantzig_George.html
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INTRODUCTION TO OPTIMIZATION
This is the optimization tree, which shows some
major categories. Wow, there is a lot to learn!
http//www.ece.northwestern.edu/OTC/
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INTRODUCTION TO OPTIMIZATION
Who does optimization?

• Mathematical Programming
• not computer programming
• Operations research
• Includes statistics, modelling, etc.
• Applied optimization
• All engineering disciplines
• Logistics and planning
• Business planning for resources, inventory, etc.
  Now called Supply chain management, which is a
  hot topic.

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INTRODUCTION TO OPTIMIZATION
The market
Worldwide shipments of Process Simulation and
Optimization (PSO) software and services, which
exceeded 338 million in 2002, will reach 500
million by the end of 2007 according to the
Process Simulation and Optimization Worldwide
Outlook study from ARC Advisory Group.
That is rapid growth. Must be some opportunities
there!
http//www.arcweb.com/research/ent/pso.asp.
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INTRODUCTION TO OPTIMIZATION
In Chemical Engineering 4G03, we will be using
mathematical models for finding very good -
optimum - designs, operating conditions,
business decisions, and so forth. The course will
build on our understanding of fundamental
principles and mathematical models. In previous
courses, we solved for a solution, but we could
not find the best. We will learn how to formulate
and solve optimization problems that give use the
best decisions. In this preliminary discussion,
we will relate optimization to other aspects of
chemical engineering.
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INTRODUCTION TO OPTIMIZATION
OPTIMIZATION USING MODELS
We will use mathematical models extensively in
optimization. Lets think about how we have used
models in previous courses. How did we use
models in each of these tasks?

• Design
• Operations
• Process Monitoring
• Process Control

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INTRODUCTION TO OPTIMIZATION
Lets consider the optimization of a distillation
tower. We would like to understand the new
modeling concepts.
Variables to be decided
Objective to be optimized
What is the value of the degrees of freedom?
What is the objective to be optimized?
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INTRODUCTION TO OPTIMIZATION
We want to change some variables to improve
(optimize) an objective. Is that always possible?

• What must we achieve with every process system?
• Safety
• Equipment protection
• Product quality
• Production rate
• All of above for a range of conditions
• Can we optimize ? How do we know?

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INTRODUCTION TO OPTIMIZATION
What is the key characteristic of optimization
problems?
Product cost (-value)
Energy costs
(high) Product purities (low)
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INTRODUCTION TO OPTIMIZATION
What is the key characteristic of optimization
problems?
Key characteristic A tradeoff exists between one
or more variables and the objective. We must
identify these key tradeoffs before building
mathematical models! We must understand the
problem qualitatively, before we solve it
quantitatively.
Product cost (-value)
Energy costs
(high) Product purities (low)
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INTRODUCTION TO OPTIMIZATION
HOW DO WE OPTIMIZE Two options exist
Opportunity for optimization exists
Chem. Eng. 4G03
Chem. Eng. 4C03
Model-based optimization
Empirical optimization
Lots of applications of both!

• process must exist!
• experiments could be costly
• no delay for modelling
• possible w/o model
• slow but persistent and accurate

• process can be investigated before it exists!
• experiments are not needed
• model required, which might involve experiments
• fast if model exists
• depends on model accuracy

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INTRODUCTION TO OPTIMIZATION
HOW DO WE OPTIMIZE Empirical optimization
Opportunity for optimization exists

Empirical optimization

• Perform some local experiments
• determine the change of objective
• move in the direction of improved objective
• iterate until change is within noise

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INTRODUCTION TO OPTIMIZATION
HOW DO WE OPTIMIZE Model-Based Optimization
Opportunity for optimization exists
Model-based Optimization

• Determine the direction of improvement using
  model
• take a long move that maximizes the objective
• check the direction at the new conditions
• continue until converged

• can evaluate many systems that do not exist
• ensure conformance to fundamental balances
• can make large changes, one solution to optimum
• very large systems can be optimized

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INTRODUCTION TO OPTIMIZATION
HOW DO WE OPTIMIZE Two options exist
Opportunity for optimization exists
Model-based optimization
Empirical optimization
This is 4G03

• Typical applications - systems for which good
  models exist
• Liquid and gas components in typical chemical and
  petrochemical industries
• Business applications for inventory, shipping
  etc.
• Public policy where experiments are not possible

• Typical applications - fast process development
  with poorly understood basics
• Pharmaceuticals
• Micro-electronics
• Process development in any industry
• Small application in an operating plant

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WHAT ARE EXAMPLES OF OPTIMIZATION? 1. Economics
Plant design
Tower decision capital cost operating
cost increase in NT reduces energy
increases equipment best NF reduces
energy lower P no refrigeration higher Fcw
(?) Exch A smaller exchanger cooler
Tcw XD, XB -- separation cost and downstream
processes --
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WHAT ARE EXAMPLES OF OPTIMIZATION? 2. Economics
Plant operations
Opt. P - must know condenser performance and
limits XD and XB - energy/yield tradeoff Tf -
tradeoff energy in feed/reboil tray
limitations Feed rate - run at peak efficiency
meet sales requirements
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PROCESS DECISIONS DETERMINED USING MODELS
What is similar and what is different in these
two examples of modelling design and operations?
SIMILAR DIFFERENT
How do we combine these factors to determine
best solution for both?
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WHAT ARE EXAMPLES OF OPTIMIZATION? 3. Economics
Company logistics / supply chain management
Which raw material?
Which plant (different yields, etc.)
What routes and modes used for transportation?
How much inventory?
How much inventory?
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WHAT ARE EXAMPLES OF OPTIMIZATION? 4. Process
Control Model Predictive Control
Not a PID algorithm!

• How can we make the CV follow the set point (---)
  as closely as possible?
• Why isnt control perfect?

• The controller calculates the entire transient
  response.
• Is this good control performance?

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WHAT ARE EXAMPLES OF OPTIMIZATION? 5. Technical
Model equilibrium as minimizing Free Energy

Equilibrium at constant T and P is Minimum Free
Energy
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WHAT ARE EXAMPLES OF OPTIMIZATION? 6. Policy
Generate the desired electricity with minimum
pollution

• Define pollution
• What is the cost for the policy?
• What other pollution is produced?

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WHAT ARE EXAMPLES OF OPTIMIZATION? 7. Model
calibration Statistics
Get the right data (experimental design)
Select model structure estimate
parameters using the data
Evaluate the reliability of conclusions
A ? B
k01 1.2e7 ? k02 ...
T ?
F ?
Max (information) Min (uncertainty)

• Min predicted-measured
• sum of squares
• maximum deviation
• sum of absolute values

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WHO USES OPTIMIZATION?

• Business
• - Management Science/Operations Research
• Engineering Operations
• Engineering Design
• Public Policy - Effects of various policies
• Econometrics - Effects of economic policies
• Physical Science
• - Statistics
• - Model optimizing systems (minimize free energy)

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Chemical Engineering 4G03 Learning Goals

• We dont achieve without a good attitude!
• Finding the best (a very good) answer is worth
  the effort.
• The engineer will accept a solution only after
  thorough analysis to eliminate errors - Trouble
  shoot your answers.
• All mathematical problems contain simplifications
  and uncertainties. The engineer understands the
  source and effects of these factors.

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Chemical Engineering 4G03 Learning Goals

• We dont achieve without excellent skills!
• The engineer applies a systematic problem solving
  method to convert an issue into a mathematical
  problem.
• The engineer uses creative methods for
  communicating the results of complex optimization
  problems.
• The engineer applies knowledge from many fields
  to formulate a meaningful objective that
  satisfies technical, economic, safety, and social
  needs.

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Chemical Engineering 4G03 Learning Goals

• We dont achieve without thorough knowledge!
• The engineer can identify opportunities for
  optimization using qualitative methods.
• The engineer can match the model and solution
  method to the problem needs.
• The engineer can perform results analysis to
  provide meaningful interpretations and
  conclusions.
• The engineer can translate the mathematical
  solution into an implementation plan.

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Chemical Engineering 4G03 Course Schematic
Now
Optimization mathematics
Modelling for optimization
P.S. Results Analysis
Many special formulations improve performance
Understanding, not just numbers!
The complete Optimizer
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WHAT IS THE GOAL OF THE COURSE?
You will become an educated user, who can
formulate and solve meaningful problems using
existing software. Whats next depends on you.
Algorithm Guru
Public Policy
Business applications
Computer implementation
Engineering Design
Engineering Operations
Many more