Partitioned Fitness Distributions Predict GA Performance
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On Partitioned Fitness Distributions of Genetic Operators for Predicting GA Performance.
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Partitioned Fitness Distributions Predict GA Performance
- 1. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 1 of 25 On Partitioned Fitness-Distributions of Genetic Operators for Predicting GA Performance WSC6 6th Online World Conference on Soft Computing in Industrial Applications Departamento de Lenguajes y Ciencias de la Computación Universidad de Málaga Rafael Nogueras, Carlos Cotta September 10-24, 2001
- 2. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 2 of 25 Outline of the Presentation 1. Introduction 2. Virtual Genetic Algorithms 3. Enhancing the Model 4. Experimental Results 5. Conclusions Outline of the Presentation
- 3. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 3 of 25 • The computational cost of running a GA can be overwhelming. • Maximizing GA effectiveness minimizing the number of fitness calculations needed to achieve a certain solution. • A careful instantiation of the basic template is required (popsize, pX, pm, …). • Tools for predicting GA performance are necessary: ▪ Information-based ▪ Fitness-based Introduction Introduction
- 4. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 4 of 25 Virtual Genetic Algorithms • Virtual Genetic Algorithms (VGAs) constitute a statistical approach aimed at GA-performance prediction. • VGAs vs GAs: individuals do not carry genetic information; they are used as place- holders for fitness information. • Fitness is transmitted from parents to offspring, using a statistical model to simulate the effects of genetic operators. • This statistical model is utilized to predict the fitness of a new individual in terms of the fitnesses of its parents. Virtual Genetic Algorithms
- 5. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 5 of 25 Sketch of a VGA Initialize population Termination condition? Select parents Apply virtual operators Insert in population NO YES Statistical model fo = fo(fp,P) Parameters of the model Inferred off-line Virtual Genetic Algorithms Sketch of a VGA
- 6. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 6 of 25 • Based on a linear regression approach for each genetic operator. • Input: a dataset comprising N pairs (fp, fo). – fp = (mean) fitness of random (pair of) solution(s). – fo = fitness of the solution obtained by applying an genetic operator to the solution(s) above. • Output: a tuple (a, b, sa, sb). – a, b = Least-squares fit of fo = a+ bfp to the dataset. – sa, sb = Least-squares fit of so = sa + sb fp, where so and fp are the standard deviation of fo and the average of fp when grouped in bins of K pairs. The Basic VGA Virtual Genetic Algorithms The Basic VGA
- 7. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 7 of 25 The Basic VGA • The VGA predicts the descendant fitness using a Gaussian distribution: fo=N(a+bfp, sa+ sbfp) . • This approach just provides discrete results. OneMax Brachystochrone • Two major reasons: acquisition of the dataset and asymmetry of the distribution. Virtual Genetic Algorithms The Basic VGA
- 8. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 8 of 25 Problems of the Basic VGA Acquisition of the dataset: Random sampling provides significant information in simple functions, but not in general. OneMax Brachystochrone Virtual Genetic Algorithms Problems of the Basic VGA
- 9. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 9 of 25 Problems of the Basic VGA Asymmetry of the distribution: The Gaussian distribution is symmetric, but the fitness distribution can be asymmetric. Brachystochrone Rastrigin Function Virtual Genetic Algorithms Problems of the Basic VGA
- 10. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 10 of 25 The L-VGA1 • An enhanced version of the VGA was obtained. • Acquisition of the dataset: use a dataset obtained by means of a pilot run of a GA. – Computational cost similar to random sampling. – The dataset covers a larger region of the fitness space. • Asymmetry: find the parameters of the linear fit fo=a+bfp, and split the dataset in two datasets: – U = { (fp,fo) | fo > a + bfp } – L = { (fp,fo) | fo a + bfp } Virtual Genetic Algorithms Enhancing the Model
- 11. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 11 of 25 The L-VGA1 • Input: a dataset comprising N pairs (fp, fo). • Output: a tuple • COMPUTE-MODEL: – a, b = Least-squares fit of fo = a+ bfp to the dataset. – = Least-squares fit of so = sa + sb fp, where so and fp are the standard deviation of fo and the average of fp when grouped in bins of K pairs For U or L. – = Least-squares fit of mo = la + lb fp, where mo and fp are the minimum of fo and the average of fp when grouped in bins of K pairs for U or L. – p = relative weight of U vs. L. ) , , , , , , , , p b a L b L a U b U a L b L a U b U a l l l l s s s s ( ) , | | L U b L U a s (s ) , | | L U b L U a l (l Virtual Genetic Algorithms Enhancing the Model
- 12. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 12 of 25 Some Results Brachystochrone Some Results Virtual Genetic Algorithms
- 13. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 13 of 25 Some Results Rastrigin Function Some Results Virtual Genetic Algorithms
- 14. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 14 of 25 Some Results Flowshop Scheduling Some Results Virtual Genetic Algorithms
- 15. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 15 of 25 Partitioning the Dataset Problem of the L-VGA1: • The underlying linear model is somewhat inflexible. • Different behavior of the GA in different regions of fitness space. • The chances for obtaining a descendant better than the parent are higher when the latter has a lower quality, for example, during some initial stages of the GA run. Partitioning the Dataset
- 16. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 16 of 25 Partitioning the Dataset Solutions: • Use a higher-degree polynomial model, but it does not offer a conclusive improvement for a low-degree polynomial. • Partition of the dataset into several prediction intervals, and extract a model for each of them. Flowshop Scheduling Brachystochrone Partitioning the Dataset
- 17. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 17 of 25 The L-VGAM Input: a dataset comprising N pairs (fp, fo). Output: M tuples • Sort the dataset according to fp, and partition it into M subsets Si. • Si = [Li, Ri), Li = Ri-1, L1 = min(fp), RM = max(fp)+1, i.e., Si = { ( fp,fo ) | Li fp < Ri } • Mi = COMPUTE MODEL for Si, i=1..M, where: Mi = • OUTPUT the complete model M = {M1,…, MM} ) , , , , , , , , p b a L b L a U b U a L b L a U b U a l l l l s s s s ( ) , , , , , , , , p b a L b L a U b U a L b L a U b U a l l l l s s s s ( The Enhanced VGA Partitioning the Dataset
- 18. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 18 of 25 Experimental Results • Experiments have been done with an elitist generational GA/VGA (popsize = 100, pX = .9, pm=.01, maxevals=10000) and PGA/PVGA (popsize = 300/400, pX = .9, pm = .01, maxevals = = 20000) using ranking selection. • All results correspond to series of 50 runs. • Three problems have been considered: the Rastrigin function, the Fletcher-Powell function, and flowshop scheduling. • Issues tackled: – Goodness of quantitative estimation – Goodness of qualitative estimation – Computational speed-up Experimental Results
- 19. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 19 of 25 Quantitative Estimations Fletcher-Powell Function Experimental Results Quantitative Estimations
- 20. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 20 of 25 Quantitative Estimations Flowshop Scheduling Experimental Results Quantitative Estimations
- 21. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 21 of 25 Qualitative Estimations Three different GA configurations are compared on the Rastrigin Function: A = {popsize=100, pX=.9, pm=.01} B = {popsize=50, pX=.5, pm=.10} C = {popsize=80, pX=.7, pm=.05} Real GA Virtual GA Relative properties are preserved. Experimental Results Qualitative Estimations
- 22. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 22 of 25 Qualitative Estimations Four different Parallel GA (PGA) configurations are compared on a flowshop scheduling problem: A = {GAs=1}, C = {GAs=4} B = {GAs=2}, D = {GAs=8} Real PGA Virtual PGA Relative properties are preserved. Experimental Results Qualitative Estimations (ring topology)
- 23. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 23 of 25 Qualitative Estimations Three different PGA configurations are compared on a flowshop scheduling problem: A = {GAs = 2, migfreq = 1000, migrate-best} B = {GAs = 2, migfreq = 300, migrate-random} C = {GAs = 4, migfreq = 500, migrate-random} Real PGA Virtual PGA Relative properties are preserved. Experimental Results Qualitative Estimations
- 24. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 24 of 25 Speed-Up The larger the problem instance, the higher the speed-up of the VGA vs. GA. Experimental Results Speed-Up
- 25. On Partitioned Fitness- Distributions of Genetic Operators for Predicting GA Performance Outline of the Presentation Introduction Virtual Genetic Algorithms Experimental Results Conclusions Sketch of a VGA The Basic VGA Problems of the Basic VGA Enhancing the Model Quantitative Estimations Qualitative Estimations Speed-Up Some Results Partitioning the Dataset The Enhanced VGA 9/26/2021 25 of 25 Conclusions • VGAs can be a useful tool for predicting GA performance. • An enhanced VGA model has been proposed to grasp some properties of the fitness distribution such as asymmetry, statistical anisotropy, or the different behaviour of GA. • The obtained results show: ✓ a much more accurate performance estimation ✓ high computational speed-ups • Future work: study other schemes for partitioning the dataset and other non-linear statistical models Conclusions