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ELEC-E3150 Mathematical Methods
Optimization
A concise hands-on tutorial for Excel Solver and MATLAB optimization
Jorma Selin, Micro and Quantum Systems Group (MQS), Aalto University
Outline
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What is optimization?
Problem types
Excel Solver
MATLAB Optimization Toolbox
MATLAB Global Optimization Toolbox
Homework
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What is optimization?
• Optimization = Finding the best way of doing something
• The overall problem usually consists of a multitude of
decisions that are made simultaneously (decision variables)
• The “goodness” of a certain set of decisions is measured by
a numerical value called the objective function
• The range of suitable solutions is often limited by a set of
constraints
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What is optimization?
• Optimization algorithms can be applied in various
situations
• Finance and investment
• Manufacturing
• Scheduling and project management
• …
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Problem types
The mathematical relationships between the objective function, constraints
and the decision variables determine what type of an optimization problem
one is dealing with, i.e.
• how hard it is to solve
• the solution methods or algorithms that can be used for optimization
• the confidence you can have that the solution is truly optimal
   Difficulty   
Linear / Quadratic / Smooth Nonlinear / Integer / Nonsmooth problems
   Certitude   
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Excel Solver
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Optimization Tutorial:
http://www.solver.com/optimization-tutorial
• The Solver is opened from the “Analysis” section of the “DATA” tab
in Excel
• Three optimization algorithms:
1. Simplex LP for linear (integer) problems
2. GRG Nonlinear for smooth (integer) nonlinear problems
3. Evolutionary for nonsmooth (nonconvex) problems
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MATLAB Optimization Toolbox
Mathematical Modeling with Optimization, Parts 1 and 2:
1. https://se.mathworks.com/videos/mathematical-modeling-withoptimization-part-1-101559.html
2. https://se.mathworks.com/videos/mathematical-modeling-withoptimization-part-2-68974.html
You can also search the MATLAB documentation for “Set Up a Linear
Program”.
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MATLAB Optimization Toolbox
Solving an optimization problem with MATLAB:
1. Separating bounds, linear equalities, linear inequalities, nonlinear equalities, and
nonlinear inequalities
2. Choosing a solver (see Optimization Decision Table)
3. Combining variables into one vector (x)
4. Bound constraints (lb, ub)
5. Inequality constraints (A, b)
6. Equality constraints (Aeq, beq)
7. Nonlinear constraints
8. Write the objective
9. Call the solver
10. Examine the solution
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MATLAB Global Optimization Toolbox
• Includes methods that search for global solutions to
problems that contain multiple maxima or minima, such as
• Genetic algorithm (ga)
•
For a detailed explanation, search the documentation for “How the Genetic
Algorithm Works”.
• GlobalSearch algorithm
•
Peculiar MATLAB syntax
“gs = GlobalSearch” constructs a global search optimization solver object
“run(gs,problem)” has to be used to find the global minimum
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Homework
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Deadline is Wednesday 21st of Dec. at 22:00
Two separate sets of exercises
• 1st set should be solved using the Excel Solver
• 2nd should be solved using MATLAB
• Document your answers and figures, and return all exercises in one
.pdf file to MyCourses
• In your solutions file, also write the amount of active time you used
for each of the assignments
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Go get ‘em!
!