Meta-optimization of Quantum-Inspired Evolutionary Algorithm Robert - - PowerPoint PPT Presentation

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Robert - - PowerPoint PPT Presentation

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization of Quantum-Inspired Evolutionary Algorithm Robert Nowotniak, Jacek Kucharski Computer Engineering Department Technical University of Lodz L od z,

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm

Meta-optimization of Quantum-Inspired Evolutionary Algorithm

Robert Nowotniak, Jacek Kucharski

Computer Engineering Department Technical University of Lodz

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z, November 4, 2010 XVII International Conference on Information Technology Systems

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm

Outline

1 Real-Coded Quantum-Inspired Evolutionary Algorithm1 2 Meta-optimization technique 3 Results

1da Cruz, A., Vellasco, M., Pacheco, M.: Quantum-Inspired Evolutionary

Algorithm for Numerical Optimization, Quantum Inspired Intelligent Systems,

  • pp. 115-132, Springer, 2008

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 1 / 12

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SLIDE 3

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Classical Real-Coded Gene g

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 2 / 12

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SLIDE 4

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Classical Real-Coded Gene g

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 University of Discourse 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Probability of Sampling

g =1.5

Robert Nowotniak, Jacek Kucharski

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SLIDE 5

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum Real-Coded Gene g = (ρ, σ)

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 University of Discourse 0.0 0.1 0.2 0.3 0.4 0.5 Probability of Sampling

ρ =1.5 σ =2

g =(1.5 , 2)

Robert Nowotniak, Jacek Kucharski

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum Population

Quantum Gene Quantum Individual Quantum Population

  • f N individuals

G Quantum Genes

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 3 / 12

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SLIDE 7

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum Individuals Interference Process

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 4 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Probability Distribution Functions

10 10 Variable 1 0.00 0.02 0.04 0.06 Probability 10 10 Variable 2 0.00 0.02 0.04 0.06 10 10 Variable 3 0.00 0.02 0.04 0.06

Probability of Sampling The Search Space

Robert Nowotniak, Jacek Kucharski

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SLIDE 9

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum-Inspired Evolutionary Algorithm

Quantum Gene Quantum Individual Quantum Population

  • f N individuals

Probability Distribution Functions G Quantum Genes Interference

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 6 / 12

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SLIDE 10

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum-Inspired Evolutionary Algorithm

Quantum Gene Quantum Individual Quantum Population

  • f N individuals

Probability Distribution Functions G Quantum Genes Interference Classical Population

  • f K Individuals
  • 1.476
  • 3.272

2.562 0.151

  • 3.180
  • 0.724

2.828 5.659 0.265

  • 4.521
  • 3.459

10.000

Sampling Classical Individual

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 6 / 12

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SLIDE 11

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum-Inspired Evolutionary Algorithm

Quantum Gene Quantum Individual Quantum Population

  • f N individuals

Probability Distribution Functions G Quantum Genes Interference Classical Population

  • f K Individuals
  • 1.476
  • 3.272

2.562 0.151

  • 3.180
  • 0.724

2.828 5.659 0.265

  • 4.521
  • 3.459

10.000

Sampling Classical Individual Crossover Evaluation Selection Classical Genetic Operators

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 6 / 12

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SLIDE 12

Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Quantum-Inspired Evolutionary Algorithm

Quantum Gene Quantum Individual Quantum Population

  • f N individuals

Probability Distribution Functions G Quantum Genes Interference Classical Population

  • f K Individuals
  • 1.476
  • 3.272

2.562 0.151

  • 3.180
  • 0.724

2.828 5.659 0.265

  • 4.521
  • 3.459

10.000

Sampling Classical Individual Crossover Evaluation Selection Classical Genetic Operators

update

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 6 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Test Functions

f1(x) =

30

  • j=1

x2

j

xj ∈ [−30, 30] f2(x) =

30

  • j=1

|xj| +

30

  • j=1

|xj| xj ∈ [−10, 10] f3(x) = 1 4000

30

  • j=1

x2

j − 30

  • j=1

cos xj √j

  • + 1

xj ∈ [−600, 600] f4(x) = −20 exp  −0.2

  • 1

30

30

  • j=1

x2

j

  − exp   1 30

30

  • j=1

cos(2πxj)   + 20 + e xj ∈ [−32, 32]

Robert Nowotniak, Jacek Kucharski

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm

Two-Dimensional Versions of The Functions

f1) f2) f3) f4)

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 8 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization

Meta-optimization Idea1

Quantum-Inspired Evolutionary Algorithm T est function 1 T est function 2 ... T est function 3 Parameters:

1The idea is based on Pedersen’s tuning technique:

Pedersen, M.E.H. Tuning & Simplifying Heuristical Optimization (PhD thesis). 2010. University of Southampton, School of Engineering Sciences

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 9 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization

Meta-optimization Idea1

Meta-Optimizer: Local Unimodal Sampling Quantum-Inspired Evolutionary Algorithm T est function 1 T est function 2 ... T est function 3 Parameters:

1The idea is based on Pedersen’s tuning technique:

Pedersen, M.E.H. Tuning & Simplifying Heuristical Optimization (PhD thesis). 2010. University of Southampton, School of Engineering Sciences

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 9 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization

Approximation of Meta-fitness Landscape

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 10 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization

Approximation of Meta-fitness Landscape

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 10 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization

Meta-optimization in (ξ, δ) Search Space

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 11 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results

Performance Comparison for Function f1

500 1000 1500 2000 Objective function evaluation count 2000 4000 6000 8000 10000 Objective function value

Original RCQiEA algorithm Tuned RCQiEA(ξ,δ)

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 12 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results

Performance Comparison for Function f2

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 12 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results

Performance Comparison for Function f3

1000 2000 3000 4000 5000 6000 7000 8000 Objective function evaluation count 100 200 300 400 500 Objective function value

Original RCQiEA algorithm Tuned RCQiEA(ξ,δ)

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 12 / 12

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SLIDE 23

Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results

Performance Comparison for Function f3

1000 2000 3000 4000 5000 6000 7000 8000 Objective function evaluation count 100 200 300 400 500 Objective function value

Original RCQiEA algorithm Tuned RCQiEA(ξ,δ)

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 12 / 12

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SLIDE 24

Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results

Performance Comparison for Function f4

500 1000 1500 2000 2500 3000 3500 4000 Objective function evaluation count 2 4 6 8 10 12 14 16 Objective function value

Original RCQiEA algorithm Tuned RCQiEA(ξ,δ)

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010 12 / 12

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Meta-optimization of Quantum-Inspired Evolutionary Algorithm

Thank you for your attention

Robert Nowotniak, Jacek Kucharski

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z, November 4, 2010