CZECH TECHNICAL UNIVERSITY IN PRAGUE Faculty of Electrical Engineering Department of Cybernetics 5. Epistasis. Linkage identification. Optimization by model fitting. Petr Poˇ s´ ık Dept. of Cybernetics ˇ CVUT FEL P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 1 / 22
Contents ■ Epistasis, short example ■ Perturbation techniques for linkage identification Introduction to ■ Optimization by model fitting Epistasis ■ Learnable evolution model Perturbation Techniques of Linkage Identification Optimization by Model Fitting Summary P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 2 / 22
Introduction to Epistasis P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 3 / 22
Black-box Optimization and Genetic Algorithms In BBO, we need to specify: ■ the representation of candidate solution Introduction to ■ the objective function (gives the quality of a candidate solution) Epistasis • Black-box ■ can have almost any form (non-differentiable, discontinuous, multimodal, noisy, Optimization and . . . ) Genetic Algorithms • GA works well... • GA fails... • GA works again... How to solve BBO problems? • Epistasis ■ Algorithm applicable in the BBO scenario can only provide a candidate solution and • Discussion on semestral projects have the objective function to evaluate it. • Linkage Identification ■ It cannot require (assume, take advantage of) any other knowledge about the Techniques objective function. (It can estimate the needed knowledge. . . ) Perturbation ■ Hill-climbing, simulated annealing, taboo, GAs, . . . Techniques of Linkage Identification Optimization by GAs are popular: Model Fitting Summary ■ they are easy to use, ■ applicable without prior knowledge, and ■ easy to parallelize. GAs are great, but not perfect!!! P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 4 / 22
GA works well... Problem f 1 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 1 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 1 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... • GA works again... • Epistasis • Discussion on semestral projects • Linkage Identification Techniques Perturbation Techniques of Linkage Identification Optimization by Model Fitting Summary P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 5 / 22
GA works well... Problem f 1 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 1 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 1 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... Popsize160 Popsize160 • GA works again... 45 1 • Epistasis 40 0.9 • Discussion on semestral projects 0.8 35 • Linkage 0.7 Identification 30 f40x1bitOneMax Techniques 0.6 25 xmean Perturbation 0.5 Techniques of Linkage 20 0.4 Identification 15 Optimization by 0.3 Model Fitting 10 0.2 Summary 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 5 / 22
GA works well... Problem f 1 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 1 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 1 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... Popsize160 Popsize160 • GA works again... 45 1 • Epistasis 40 0.9 • Discussion on semestral projects 0.8 35 • Linkage 0.7 Identification 30 f40x1bitOneMax Techniques 0.6 25 xmean Perturbation 0.5 Techniques of Linkage 20 0.4 Identification 15 Optimization by 0.3 Model Fitting 10 0.2 Summary 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation The f 1 problem contains no epistatic interactions among design variables. P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 5 / 22
GA fails... Problem f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... • GA works again... • Epistasis • Discussion on semestral projects • Linkage Identification Techniques Perturbation Techniques of Linkage Identification Optimization by Model Fitting Summary P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 6 / 22
GA fails... Problem f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... Popsize160 Popsize160 • GA works again... 45 1 • Epistasis 40 0.9 • Discussion on semestral projects 0.8 35 • Linkage 0.7 Identification 30 Techniques 0.6 f8x5bitTrap 25 xmean Perturbation 0.5 Techniques of Linkage 20 0.4 Identification 15 Optimization by 0.3 Model Fitting 10 0.2 Summary 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 6 / 22
GA fails... Problem f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... Popsize160 Popsize160 • GA works again... 45 1 • Epistasis 40 0.9 • Discussion on semestral projects 0.8 35 • Linkage 0.7 Identification 30 Techniques 0.6 f8x5bitTrap 25 xmean Perturbation 0.5 Techniques of Linkage 20 0.4 Identification 15 Optimization by 0.3 Model Fitting 10 0.2 Summary 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation The f 2 problem contains some interactions among variables, GA is not aware of them and works with the individual bits as if they were truly independent of each other. P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 6 / 22
GA fails... Problem f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... • GA fails... Popsize160 Popsize160 • GA works again... 45 1 • Epistasis 40 0.9 • Discussion on semestral projects 0.8 35 • Linkage 0.7 Identification 30 Techniques 0.6 f8x5bitTrap 25 xmean Perturbation 0.5 Techniques of Linkage 20 0.4 Identification 15 Optimization by 0.3 Model Fitting 10 0.2 Summary 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation The f 2 problem contains some interactions among variables, GA is not aware of them and works with the individual bits as if they were truly independent of each other. None of the above mentioned problem characteristics is important to judge if the GA will work well!!! P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 6 / 22
GA works again... Still solving f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... Instead of the uniform crossover, • GA fails... • GA works again... ■ let us allow the crossover only after each 5th bit. • Epistasis • Discussion on semestral projects • Linkage Identification Techniques Perturbation Techniques of Linkage Identification Optimization by Model Fitting Summary P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 7 / 22
GA works again... Still solving f 2 : ■ defined over 40-bit strings Introduction to ■ the quality of the worst solution: f 2 ( x worst ) = 0. Epistasis ■ the quality of the best solution: f 2 ( x opt ) = 40. • Black-box Optimization and ■ the best solution: x opt = ( 1111 . . . 1 ) . Genetic Algorithms • GA works well... Instead of the uniform crossover, • GA fails... • GA works again... ■ let us allow the crossover only after each 5th bit. • Epistasis • Discussion on semestral projects Popsize160 Popsize160 • Linkage 45 1 Identification Techniques 40 0.9 0.8 Perturbation 35 Techniques of Linkage 0.7 30 Identification 0.6 f8x5bitTrap Optimization by 25 xmean Model Fitting 0.5 20 Summary 0.4 15 0.3 10 0.2 5 best 0.1 average 0 0 0 5 10 15 20 0 5 10 15 20 generation generation P. Poˇ s´ ık c � 2014 A0M33EOA: Evolutionary Optimization Algorithms – 7 / 22
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