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, November 4, 2010 XVII International Conference on Information Technology Systems Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Outline 1 Real-Coded Quantum-Inspired Evolutionary Algorithm 1 2 Meta-optimization technique 3 Results 1 da 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 L´ � od´ z, November 4, 2010 1 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Classical Real-Coded Gene g Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 2 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Classical Real-Coded Gene g 1.2 1.0 Probability of Sampling 0.8 g =1 . 5 0.6 0.4 0.2 0.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 University of Discourse Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 2 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum Real-Coded Gene g = ( ρ, σ ) 0.5 g =(1 . 5 , 2) 0.4 Probability of Sampling 0.3 σ =2 0.2 0.1 ρ =1 . 5 0.0 1.5 0.5 0.0 0.5 1.0 2.0 2.5 3.0 3.5 University of Discourse Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 2 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum Population G Quantum Genes Quantum Gene Quantum Individual Quantum Population of N individuals Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 3 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum Individuals Interference Process Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 4 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Probability Distribution Functions 0.06 0.06 0.06 Probability 0.04 0.04 0.04 0.02 0.02 0.02 0.00 0.00 0.00 10 10 10 10 10 10 Variable 1 Variable 2 Variable 3 Probability of Sampling The Search Space Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 5 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum-Inspired Evolutionary Algorithm G Quantum Genes Quantum Gene Quantum Individual Quantum Population of N individuals Interference Probability Distribution Functions Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 6 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum-Inspired Evolutionary Algorithm G Quantum Genes Quantum Gene Quantum Individual Quantum Population of N individuals Interference Probability Distribution Functions Sampling Classical Individual -1.476 -3.272 2.562 0.151 -3.180 -0.724 Classical Population 2.828 5.659 0.265 of K Individuals -4.521 -3.459 10.000 Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 6 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum-Inspired Evolutionary Algorithm G Quantum Genes Quantum Gene Quantum Individual Quantum Population of N individuals Interference Probability Distribution Functions Sampling Classical Individual -1.476 -3.272 2.562 0.151 -3.180 -0.724 Classical Population 2.828 5.659 0.265 of K Individuals -4.521 -3.459 10.000 Crossover Classical Genetic Evaluation Operators Selection Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 6 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Quantum-Inspired Evolutionary Algorithm G Quantum Genes Quantum Gene update Quantum Individual Quantum Population of N individuals Interference Probability Distribution Functions Sampling Classical Individual -1.476 -3.272 2.562 0.151 -3.180 -0.724 Classical Population 2.828 5.659 0.265 of K Individuals -4.521 -3.459 10.000 Crossover Classical Genetic Evaluation Operators Selection Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 6 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Test Functions 30 � x 2 f 1 ( x ) = x j ∈ [ − 30 , 30] j j =1 30 30 � � f 2 ( x ) = | x j | + | x j | x j ∈ [ − 10 , 10] j =1 j =1 � x j 30 30 1 � � x 2 � f 3 ( x ) = j − cos √ j + 1 x j ∈ [ − 600 , 600] 4000 j =1 j =1 � 30 30 � � 1 1 � � � − exp x 2 f 4 ( x ) = − 20 exp − 0 . 2 cos(2 π x j ) j 30 30 j =1 j =1 + 20 + e x j ∈ [ − 32 , 32] Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 7 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm RC QIEA algorithm Two-Dimensional Versions of The Functions f 1 ) f 2 ) f 3 ) f 4 ) Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 8 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization Meta-optimization Idea 1 Quantum-Inspired Evolutionary Algorithm Parameters: T est function 1 T est function 2 T est function 3 ... 1 The 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 L´ � od´ z, November 4, 2010 9 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization Meta-optimization Idea 1 Meta-Optimizer: Local Unimodal Sampling Quantum-Inspired Evolutionary Algorithm Parameters: T est function 1 T est function 2 T est function 3 ... 1 The 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 L´ � od´ z, November 4, 2010 9 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization Approximation of Meta-fitness Landscape Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 10 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization Approximation of Meta-fitness Landscape Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 10 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Meta-optimization Meta-optimization in ( ξ, δ ) Search Space Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 11 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results Performance Comparison for Function f 1 10000 Original RCQiEA algorithm Tuned RCQiEA( ξ,δ ) 8000 Objective function value 6000 4000 2000 0 0 500 1000 1500 2000 Objective function evaluation count Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 12 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results Performance Comparison for Function f 2 Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 12 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results Performance Comparison for Function f 3 500 Original RCQiEA algorithm Tuned RCQiEA( ξ,δ ) 400 Objective function value 300 200 100 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Objective function evaluation count Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 12 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results Performance Comparison for Function f 3 500 Original RCQiEA algorithm Tuned RCQiEA( ξ,δ ) 400 Objective function value 300 200 100 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Objective function evaluation count Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 12 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Results Performance Comparison for Function f 4 16 Original RCQiEA algorithm Tuned RCQiEA( ξ,δ ) 14 12 Objective function value 10 8 6 4 2 0 0 500 1000 1500 2000 2500 3000 3500 4000 Objective function evaluation count Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010 12 / 12
Meta-optimization of Quantum-Inspired Evolutionary Algorithm Thank you for your attention Robert Nowotniak, Jacek Kucharski L´ � od´ z, November 4, 2010
Recommend
More recommend
