441-final-presenation
TRANSCRIPT
GA DUALSTAGE MULTIPURPOSE OPTIMIZATION ALGORITHM
441 – Engineering Optimization for Product Design and Manufacturing
Andreas Schneider & Muyang Deng
2 441 – Final Project Presentation
• Purpose of the project
• Working Principle of Dualstage Optimization Algorithms
• Genetic Algorithm
• Downhill Simplex
• Demonstration
• Conclusion
Agenda
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• Easy to use optimization
algorithm
• Global Optimum
• Exact Solution
• Excel Interface
• Adjustable Parameters
Purpose of the project
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• Measures of a Good algorithm Robustness Generality Accuracy Ease of use Efficiency
• Combination of different methods
Working Principle of Dualstage Optimization Algorithms
GA Downhill simplex
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Working Principle of Dualstage Optimization Algorithms
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Working Principle of Dualstage Optimization Algorithms
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• Stochastic Method • Natural Selection • Main components
Selection Crossover Mutation
Genetic Algorithm
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• Optimization Algortihm for Nonlinear Problems
• No gradient information necessary
• Commonly used for curve fitting operations
Downhill Simplex
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Downhill Simplex
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Demonstration
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• a. In most case, Genetic Algorithm can converge to the global optimal solution.
• b. The dual-stage excel solver shows a better convergence to the global optimal result compare to simple GA.
• c. The population and the bounds are the two most important parameters for the dual-stage solve.
Conclusion
441 – Final Project Presentation
Thank you for you time
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Population for different iterations
0 200 400 600 800 1000 1200 1400 16005.3
5.35
5.4
5.45
5.5
5.55
5.6
The GA shows a really good convergence for each iterations
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Function history of GA
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 960
5000
10000
15000
20000
25000
30000
Run 1 Run 2 Run 3 Run 4
No matter how many runs, the GA can converge to the optimal result in an robust and effective way
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Function history of Downhill
13000
3050
3100
3150
3200
3250
3300
3350
3400
Run 1 Run 2 Run 3 Run 4
The Downhill simplex can converge to the optimal result really fast and got more specific result
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Mutation rate VS Function history
10
10000000000
20000000000
30000000000
40000000000
50000000000
60000000000
8421Series1
Higher mutation rate lead to mis-order and more fluctuations for the
function history
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Different Population VS Function history
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 960
2000000000
4000000000
6000000000
8000000000
10000000000
12000000000
14000000000
16000000000
18000000000
20000000000
1020304050
The population and converge rate doesn’t have a linear relationship.
Overall the higher the population is the faster the algorithm converge.