Performance of Evolutionary Algorithms on NK Landscapes with Nearest Neighbor Interactions and Tunable Overlap
|
|
- Lindsay Andrews
- 5 years ago
- Views:
Transcription
1 Performance of Evolutionary Algorithms on NK Landscapes with Nearest Neighbor Interactions and Tunable Overlap Martin Pelikan, Kumara Sastry, David E. Goldberg, Martin V. Butz, and Mark Hauschild Missouri Estimation of Distribution Algorithms Laboratory (MEDAL) University of Missouri, St. Louis, MO Download MEDAL Report No
2 Motivation Testing evolutionary algorithms Adversarial problems on the boundary of design envelope. Random instances of important classes of problems. Real-world problems. This work bridges and extends two prior studies on random problems Random additively decomposable problems (radps) (Pelikan et al., 2006). NK landscapes (superset of radps) (Pelikan et al., 2007). This study Propose the class of polynomially solvable NK landscapes with nearest neighbor interactions and tunable overlap. Generate large number of instances of proposed problem class. Test evolutionary algorithms on the generated instances. Analyze the results.
3 Outline 1. Additively decomposable problems NK landscapes. Random additively decomposable problems (radps). 2. NK with nearest neighbors and tunable overlap. 3. Experiments. 4. Conclusions and future work.
4 Additively Decomposable Problems (ADPs) Additively decomposable problem (ADP) Fitness defined as m f(x 1, X 2,..., X n ) = f i (S i ), i=1 n is the number of bits (variables), m is the number of subproblems, S i is the subset of variables in ith subproblem. ADPs play crucial role in design and analysis of GAs & EDAs. All problems in this work are ADPs. Two prior studies on ADPs serve as starting points Unrestricted NK landscapes. Restricted random ADPs (radps).
5 NK Landscape NK landscape Proposed by Kauffman (1989). Model of rugged landscape and popular test function. An NK landscape is defined by Number of bits, n. Number of neighbors per bit, k. Set of k neighbors Π(X i ) for i-th bit, X i. Subfunction f i defining contribution of X i and Π(X i ). The objective function f nk to maximize is then defined as n 1 f nk (X 0, X 1,..., X n 1 ) = f i (X i, Π(X i )). i=0
6 NK Landscape Exmaple for n = 9 and k = 2:
7 Restricted Random ADPs (radps) of Bounded Order Order-k radps with and without overlap Each subproblem contains k bits. Separable problems contain non-overlapping subproblems: Tight linkage: Shuffled: There may be overlap in o bits between neighboring subproblems (may also be shuffled): Tight linkage: Shuffled:
8 Properties of NK Landscapes and radps Common properties Additive decomposability. Subproblems are complex (look-up tables). High multimodality, complex structure. Overlap further increases problem difficulty. Challenge for most genetic algorithms and local search. NK landscapes NP-completeness (can t solve worst case in polynomial time). radps Using prior knowledge of problem structure, we can exactly solve radps in polynomial time (dynamic programming) in O(2 k n) evaluations. Multivariate EDAs can solve shuffled EDAs polynomially fast.
9 NK Landscapes with Nearest Neighbors & Tunable Overlap NK Landscapes with Nearest Neighbors and Tunable Overlap Neighbors of each bit are restricted to the following k bits. For simplicity, the neighborhoods don t wrap around. Some subproblems may be excluded to provide a mechanism for tuning the size of overlap. Use parameter step {1, 2,..., k + 1}. Only subproblems at positions i, i mod step = 0 contribute. Bit positions shuffled randomly to eliminate tight linkage.
10 NK Landscapes with Nearest Neighbors & Tunable Overlap High overlap (k = 2, step = 1): Sequential Shuffled Note step = 1 maximizes the amount of overlap between subproblems.
11 NK Landscapes with Nearest Neighbors & Tunable Overlap Low overlap (k = 2, step = 2): Sequential Shuffled Note step parameter allows tuning of the size of overlap.
12 NK Landscapes with Nearest Neighbors & Tunable Overlap No overlap (k = 2, step = 3): Sequential Shuffled Note step = k + 1 implies separability (subproblems are independent).
13 NK Landscapes with Nearest Neighbors & Tunable Overlap Why? Nearest neighbors enable polynomial solvability Deshuffle the string. Use dynamic programming. Parameter step enables tunining the overlap between subproblems: For standard NK landscapes, step = 1. With larger values of step, the amount of overlap between consequent subproblems is reduced. For step = k + 1, the problem becomes separable (the subproblems are fully independent).
14 Problem Instances Parameters n = 20 to 120. k = 2 to 5. step = 1 to k + 1 for each k. Variety of instances For each (n, k, step), generate 10,000 random instances. Overall 1,800,000 unique problem instances.
15 Compared Algorithms Basic algorithms Hierarchical Bayesian optimization algorithm (hboa). Genetic algorithm with uniform crossover (GAU). Genetic algorithm with twopoint crossover (G2P). Local search Single-bit-flip hill climbing (DHC) on each solution. Improves performance of all methods. Niching Restricted tournament replacement (niching).
16 Results: Flips Until Optimum; hboa; k = 2 and k = 5 Numb Problem size 10 4 k=4, step=1 k=2, step=1 k=4, step=2 k=2, step=2 k=4, step=3 k=2, step=3 k=4, step=4 k=4, step= Number of flips (hboa) Number of flips (hboa) Problem size k=5, step= k=5, step=2 k=5, step=3 k=5, step=4 k=5, step=5 k=5, step= Number of flips (hboa) k=3, step=1 k=3, step=2 k=3, step=3 k=3, step= Problem size Problem size umber of flips (hboa) k=4, step=1 k=4, step=2 k=4, step=3 k=4, step=4 k=4, step= Problem size Problem size umber of flips (hboa) k=5, step=1 k=5, step=2 k=5, step=3 k=5, step=4 k=5, step=5 k=5, step=6 Growth appears to be polynomial w.r.t. problem size, n Performance Figure 1: Average best with number no overlap. of flips for hboa. Besides n, performance depends on both k and step. the effects 10 3 of k on performance of all compared algorithms, figure 6 sh mber of DHC flips with k for hboa and GA on problems of size n = 10 A are not included, because UMDA was incapable of 3 M. Pelikan, K. Sastry, D.E. Goldberg, M.V. Butz, M. Hauschild NK Landscapes with Nearest Neighbors solving and Tunable many Overlap inst
17 Results: Comparison w.r.t. Flips DHC steps (flips) until optimum n k step hboa GA (uniform) GA (twopoint) , , , , , , , , , , , , , , , ,607 35,101 47,576
18 Results: Comparison w.r.t. Evaluations Number of evaluations until optimum n k step hboa GA (uniform) GA (twopoint) ,414 16,519 34, ,011 25,032 56, ,988 30,285 72, ,606 24,016 51, ,307 13,749 26, ,328 6,004 10,949
19 Number o Numb 0.75 Results: Flips Until Optimum; hboa vs. GA; k = Problem size Problem size k=4, step=1 k=4, step=2 k=4, step=3 k=4, step=4 k=4, step=5 Number of flips (GA, uniform) / Number of flips (hboa) k=5, step=1 k=5, step=2 k=5, step=3 k=5, step=4 k=5, step=5 k=5, step= Problem size Problem size Problem size Ratio GA with of the Differences uniform number crossover grow of flips faster for andthan GA hboa. with polynomially twopoint with crossover n. and hboa. Besides n, differences depend on both k and step. DHC flips until optimum GA 5, and (uniform) step GA {1,6}; (twopoint) since UMDA was not capable of solving many o in141,108 practical time, the 220,318 results for UMDA are not included. The figure sho fm. DHC Pelikan, K. flips Sastry, D.E. until Goldberg, optimum M.V. Butz, M. for Hauschild different NK Landscapes percentages with Nearest Neighbors of instances and Tunable Overlap with sm Number Num Number of flips (GA, twopoint) / Number of flips (hboa) 0.75 hboa outperforms both versions of GA k=5, step=1 k=5, step=2 k=5, step=3 k=5, step=4 k=5, step=5 k=5, step= Problem size
20 Results: Correlations Between Algorithms step = 1 (high overlap): step = 6 (separable): I I GA versions more similar than hboa with GA. Correlations stronger for problems with more overlap/less structure. M. Pelikan, K. Sastry, D.E. Goldberg, M.V. Butz, M. Hauschild NK Landscapes with Nearest Neighbors and Tunable Overlap
21 Problem Difficulty: Signal-to-Noise and Signal Variance Signal and noise Signal: The difference between fitness of the best and the 2 nd best solutions to a subproblem. Noise: Models contributions of other subproblems. Signal-to-noise ratio Decision making done by GA is stochastic. The larger the signal-to-noise ratio, the easier the decision making. Signal variance Sequential vs. parallel convergence. How much do contributions of different subproblems differ? One way to model this is to look at the variance of the signal.
22 hboa (a) hboa (b) GA (uniform) (b) GA (uniform) (c) GA (twopoint) (c) GA ( Results: Flips Until Optimum; hboa vs. GA; k = 5 e 13: Figure Influence 13: of Influence overlapof foroverlap n = 120 forandn = k 120 = 5 and (step k = varies 5 (step withvaries overlap). with o step = 1 (high overlap) step = 6 (separable) (divided by mean) Average number of flips (divided by mean) GA (twpoint) GA (uniform) hboa GA (twpoint) GA (uniform) hboa Signal to noise percentile Signal to noise (% smallest) percentile (% smallest) (a) step = 1(a) step = 1 Average number of flips (divided by mean) GA (tw GA (u hboa Signal to noise percentile Signal to noise (% smallest) percentile (% s (b) step = 6(b) step = 6 For problems with overlap, noise appears insignificant. Figure Influence 14: of Influence signal-to-noise of signal-to-noise ratio on the ratio number on theofnumber flips forof n flips = 120 forandn = k 120 = Average number of flips (divided by mean) For separable problems, noise clearly matters. GA (twpoint) GA (uniform) hboa nowledgments
23 Results: Flips Until Optimum; hboa vs. GA; k = 5 (divided by mean) Average number of flips (divided by mean) step = 1 (high overlap) GA (twopoint) GA (twopoint) GA (uniform) GA (uniform) hboa hboa Average number of flips (divided by mean) step = 6 (separable) Average number of flips (divided by mean) GA (twopoint) GA (twopoi GA (uniform) GA (uniform hboa hboa Signal variance Signal percentile variance (% smallest) percentile (% smallest) Signal variance Signal percentile variance (% percentile smallest) (% small (a) step = (a) 1 step = 1 (b) step = (b) 6 step = 6 For problems with overlap, signal variance appears 15: Figure Influence 15: insignificant. Influence of signal of variance signal variance on the number on the of number flips for of n flips = 120 for n and = 120 k = and 5. ferences s For separable problems, signal variance clearly matters.
24 Conclusions and Future Work Summary and conclusions Considered subset of NK landscapes as class of random test problems with tunable subproblem size and overlap. All proposed instances solvable in polynomial time. Generated a broad range of problem instances. Analyzed results using hybrids of GEAs. Future work Use generated problems to test other algorithms. Relate performance to other measures of problem difficulty. Develop/test new tools for understanding of problem difficulty. Wrap subproblems around. Use other distributions for generating look-up tables.
25 Acknowledgments Acknowledgments NSF; NSF CAREER grant ECS U.S. Air Force, AFOSR; FA University of Missouri; High Performance Computing Collaboratory sponsored by Information Technology Services; Research Award; Research Board.
Analysis of Epistasis Correlation on NK Landscapes. Landscapes with Nearest Neighbor Interactions
Analysis of Epistasis Correlation on NK Landscapes with Nearest Neighbor Interactions Missouri Estimation of Distribution Algorithms Laboratory (MEDAL University of Missouri, St. Louis, MO http://medal.cs.umsl.edu/
More informationFinding Ground States of SK Spin Glasses with hboa and GAs
Finding Ground States of Sherrington-Kirkpatrick Spin Glasses with hboa and GAs Martin Pelikan, Helmut G. Katzgraber, & Sigismund Kobe Missouri Estimation of Distribution Algorithms Laboratory (MEDAL)
More informationAnalysis of Epistasis Correlation on NK Landscapes with Nearest-Neighbor Interactions
Analysis of Epistasis Correlation on NK Landscapes with Nearest-Neighbor Interactions Martin Pelikan MEDAL Report No. 20102 February 2011 Abstract Epistasis correlation is a measure that estimates the
More informationInitial-Population Bias in the Univariate Estimation of Distribution Algorithm
Initial-Population Bias in the Univariate Estimation of Distribution Algorithm Martin Pelikan and Kumara Sastry MEDAL Report No. 9 January 9 Abstract This paper analyzes the effects of an initial-population
More informationSpurious Dependencies and EDA Scalability
Spurious Dependencies and EDA Scalability Elizabeth Radetic, Martin Pelikan MEDAL Report No. 2010002 January 2010 Abstract Numerous studies have shown that advanced estimation of distribution algorithms
More informationAnalyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses
Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses Mark Hauschild, Martin Pelikan, Claudio F. Lima, and Kumara Sastry IlliGAL Report No. 2007008 January 2007 Illinois Genetic
More informationFinding Ground States of Sherrington-Kirkpatrick Spin Glasses with Hierarchical BOA and Genetic Algorithms
Finding Ground States of Sherrington-Kirkpatrick Spin Glasses with Hierarchical BOA and Genetic Algorithms Martin Pelikan, Helmut G. Katzgraber and Sigismund Kobe MEDAL Report No. 284 January 28 Abstract
More informationAnalyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses
Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses Mark Hauschild Missouri Estimation of Distribution Algorithms Laboratory (MEDAL) Dept. of Math and Computer Science, 320 CCB
More informationHierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses
Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses Martin Pelikan 1, Alexander K. Hartmann 2, and Kumara Sastry 1 Dept. of Math and Computer Science, 320 CCB University of Missouri at
More informationHierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses
Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses Martin Pelikan and Alexander K. Hartmann MEDAL Report No. 2006002 March 2006 Abstract This paper analyzes the hierarchical Bayesian
More informationEstimation-of-Distribution Algorithms. Discrete Domain.
Estimation-of-Distribution Algorithms. Discrete Domain. Petr Pošík Introduction to EDAs 2 Genetic Algorithms and Epistasis.....................................................................................
More informationProbabilistic Model-Building Genetic Algorithms
Probabilistic Model-Building Genetic Algorithms Martin Pelikan Dept. of Math. and Computer Science University of Missouri at St. Louis St. Louis, Missouri pelikan@cs.umsl.edu Foreword! Motivation Genetic
More informationFrom Mating Pool Distributions to Model Overfitting
From Mating Pool Distributions to Model Overfitting Claudio F. Lima DEEI-FCT University of Algarve Campus de Gambelas 85-39, Faro, Portugal clima.research@gmail.com Fernando G. Lobo DEEI-FCT University
More informationFrom Mating Pool Distributions to Model Overfitting
From Mating Pool Distributions to Model Overfitting Claudio F. Lima 1 Fernando G. Lobo 1 Martin Pelikan 2 1 Department of Electronics and Computer Science Engineering University of Algarve, Portugal 2
More informationHierarchical BOA Solves Ising Spin Glasses and MAXSAT
Hierarchical BOA Solves Ising Spin Glasses and MAXSAT Martin Pelikan 1,2 and David E. Goldberg 2 1 Computational Laboratory (Colab) Swiss Federal Institute of Technology (ETH) Hirschengraben 84 8092 Zürich,
More informationUpper Bounds on the Time and Space Complexity of Optimizing Additively Separable Functions
Upper Bounds on the Time and Space Complexity of Optimizing Additively Separable Functions Matthew J. Streeter Computer Science Department and Center for the Neural Basis of Cognition Carnegie Mellon University
More informationScalability of Selectorecombinative Genetic Algorithms for Problems with Tight Linkage
Scalability of Selectorecombinative Genetic Algorithms for Problems with Tight Linkage Kumara Sastry 1,2 and David E. Goldberg 1,3 1 Illinois Genetic Algorithms Laboratory (IlliGAL) 2 Department of Material
More informationLinkage Identification Based on Epistasis Measures to Realize Efficient Genetic Algorithms
Linkage Identification Based on Epistasis Measures to Realize Efficient Genetic Algorithms Masaharu Munetomo Center for Information and Multimedia Studies, Hokkaido University, North 11, West 5, Sapporo
More informationFitness Inheritance in Multi-Objective Optimization
Fitness Inheritance in Multi-Objective Optimization Jian-Hung Chen David E. Goldberg Shinn-Ying Ho Kumara Sastry IlliGAL Report No. 2002017 June, 2002 Illinois Genetic Algorithms Laboratory (IlliGAL) Department
More informationCentric Selection: a Way to Tune the Exploration/Exploitation Trade-off
: a Way to Tune the Exploration/Exploitation Trade-off David Simoncini, Sébastien Verel, Philippe Collard, Manuel Clergue Laboratory I3S University of Nice-Sophia Antipolis / CNRS France Montreal, July
More informationProbabilistic Model-Building Genetic Algorithms
Probabilistic Model-Building Genetic Algorithms a.k.a. Estimation of Distribution Algorithms a.k.a. Iterated Density Estimation Algorithms Martin Pelikan Foreword Motivation Genetic and evolutionary computation
More informationState of the art in genetic algorithms' research
State of the art in genetic algorithms' Genetic Algorithms research Prabhas Chongstitvatana Department of computer engineering Chulalongkorn university A class of probabilistic search, inspired by natural
More informationBehaviour of the UMDA c algorithm with truncation selection on monotone functions
Mannheim Business School Dept. of Logistics Technical Report 01/2005 Behaviour of the UMDA c algorithm with truncation selection on monotone functions Jörn Grahl, Stefan Minner, Franz Rothlauf Technical
More informationInteraction-Detection Metric with Differential Mutual Complement for Dependency Structure Matrix Genetic Algorithm
Interaction-Detection Metric with Differential Mutual Complement for Dependency Structure Matrix Genetic Algorithm Kai-Chun Fan Jui-Ting Lee Tian-Li Yu Tsung-Yu Ho TEIL Technical Report No. 2010005 April,
More informationc Copyright by Martin Pelikan, 2002
c Copyright by Martin Pelikan, 2002 BAYESIAN OPTIMIZATION ALGORITHM: FROM SINGLE LEVEL TO HIERARCHY BY MARTIN PELIKAN DIPL., Comenius University, 1998 THESIS Submitted in partial fulfillment of the requirements
More informationProbabilistic Model-Building Genetic Algorithms
Probabilistic Model-Building Genetic Algorithms a.k.a. Estimation of Distribution Algorithms a.k.a. Iterated Density Estimation Algorithms Martin Pelikan Missouri Estimation of Distribution Algorithms
More informationLecture 22. Introduction to Genetic Algorithms
Lecture 22 Introduction to Genetic Algorithms Thursday 14 November 2002 William H. Hsu, KSU http://www.kddresearch.org http://www.cis.ksu.edu/~bhsu Readings: Sections 9.1-9.4, Mitchell Chapter 1, Sections
More informationBounding the Population Size in XCS to Ensure Reproductive Opportunities
Bounding the Population Size in XCS to Ensure Reproductive Opportunities Martin V. Butz and David E. Goldberg Illinois Genetic Algorithms Laboratory (IlliGAL) University of Illinois at Urbana-Champaign
More informationLandscapes and Other Art Forms.
Landscapes and Other Art Forms. Darrell Whitley Computer Science, Colorado State University Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted
More informationA Tractable Walsh Analysis of SAT and its Implications for Genetic Algorithms
From: AAAI-98 Proceedings. Copyright 998, AAAI (www.aaai.org). All rights reserved. A Tractable Walsh Analysis of SAT and its Implications for Genetic Algorithms Soraya Rana Robert B. Heckendorn Darrell
More informationoptimization problem x opt = argmax f(x). Definition: Let p(x;t) denote the probability of x in the P population at generation t. Then p i (x i ;t) =
Wright's Equation and Evolutionary Computation H. Mühlenbein Th. Mahnig RWCP 1 Theoretical Foundation GMD 2 Laboratory D-53754 Sankt Augustin Germany muehlenbein@gmd.de http://ais.gmd.de/οmuehlen/ Abstract:
More informationOn the Impact of Objective Function Transformations on Evolutionary and Black-Box Algorithms
On the Impact of Objective Function Transformations on Evolutionary and Black-Box Algorithms [Extended Abstract] Tobias Storch Department of Computer Science 2, University of Dortmund, 44221 Dortmund,
More informationEvolutionary computation
Evolutionary computation Andrea Roli andrea.roli@unibo.it DEIS Alma Mater Studiorum Università di Bologna Evolutionary computation p. 1 Evolutionary Computation Evolutionary computation p. 2 Evolutionary
More informationOptimization and Complexity
Optimization and Complexity Decision Systems Group Brigham and Women s Hospital, Harvard Medical School Harvard-MIT Division of Health Sciences and Technology Aim Give you an intuition of what is meant
More informationEvolutionary Computation
Evolutionary Computation - Computational procedures patterned after biological evolution. - Search procedure that probabilistically applies search operators to set of points in the search space. - Lamarck
More informationCS 6901 (Applied Algorithms) Lecture 3
CS 6901 (Applied Algorithms) Lecture 3 Antonina Kolokolova September 16, 2014 1 Representative problems: brief overview In this lecture we will look at several problems which, although look somewhat similar
More informationConvergence Time for Linkage Model Building in Estimation of Distribution Algorithms
Convergence Time for Linkage Model Building in Estimation of Distribution Algorithms Hau-Jiun Yang Tian-Li Yu TEIL Technical Report No. 2009003 January, 2009 Taiwan Evolutionary Intelligence Laboratory
More informationMassive Experiments and Observational Studies: A Linearithmic Algorithm for Blocking/Matching/Clustering
Massive Experiments and Observational Studies: A Linearithmic Algorithm for Blocking/Matching/Clustering Jasjeet S. Sekhon UC Berkeley June 21, 2016 Jasjeet S. Sekhon (UC Berkeley) Methods for Massive
More informationIntroduction. Genetic Algorithm Theory. Overview of tutorial. The Simple Genetic Algorithm. Jonathan E. Rowe
Introduction Genetic Algorithm Theory Jonathan E. Rowe University of Birmingham, UK GECCO 2012 The theory of genetic algorithms is beginning to come together into a coherent framework. However, there are
More informationUnit 1A: Computational Complexity
Unit 1A: Computational Complexity Course contents: Computational complexity NP-completeness Algorithmic Paradigms Readings Chapters 3, 4, and 5 Unit 1A 1 O: Upper Bounding Function Def: f(n)= O(g(n)) if
More informationGeometric Semantic Genetic Programming (GSGP): theory-laden design of semantic mutation operators
Geometric Semantic Genetic Programming (GSGP): theory-laden design of semantic mutation operators Andrea Mambrini 1 University of Birmingham, Birmingham UK 6th June 2013 1 / 33 Andrea Mambrini GSGP: theory-laden
More informationEfficient Discretization Scheduling in Multiple Dimensions. Laura A. Albert and David E. Goldberg. IlliGAL Report No February 2002
Efficient Discretization Scheduling in Multiple Dimensions Laura A. Albert and David E. Goldberg IlliGAL Report No. 2002006 February 2002 Illinois Genetic Algorithms Laboratory University of Illinois at
More informationProbabilistic Methods in Landscape Analysis: phase transitions, interaction structures, and complexity measures
Probabilistic Methods in Landscape Analysis: phase transitions, interaction structures, and complexity measures Yong Gao and Joseph Culberson Department of Computing Science, University of Alberta Edmonton,
More informationResearch Article Effect of Population Structures on Quantum-Inspired Evolutionary Algorithm
Applied Computational Intelligence and So Computing, Article ID 976202, 22 pages http://dx.doi.org/10.1155/2014/976202 Research Article Effect of Population Structures on Quantum-Inspired Evolutionary
More information2-bit Flip Mutation Elementary Fitness Landscapes
RN/10/04 Research 15 September 2010 Note 2-bit Flip Mutation Elementary Fitness Landscapes Presented at Dagstuhl Seminar 10361, Theory of Evolutionary Algorithms, 8 September 2010 Fax: +44 (0)171 387 1397
More informationAnalyzing the Evolutionary Pressures in XCS Martin V. Butz Institute for Psychology III University of Wurzburg Wurzburg, 977, Germany
Analyzing the Evolutionary Pressures in XCS Martin V. Butz and Martin Pelikan IlliGAL Report No. 219 February 21 Illinois Genetic Algorithms Laboratory University of Illinois at Urbana-Champaign 117 Transportation
More informationCSC 4510 Machine Learning
10: Gene(c Algorithms CSC 4510 Machine Learning Dr. Mary Angela Papalaskari Department of CompuBng Sciences Villanova University Course website: www.csc.villanova.edu/~map/4510/ Slides of this presenta(on
More informationRepeated Occurrences of the Baldwin Effect Can Guide Evolution on Rugged Fitness Landscapes
Repeated Occurrences of the Baldwin Effect Can Guide Evolution on Rugged Fitness Landscapes Reiji Suzuki and Takaya Arita Graduate School of Information Science, Nagoya University Furo-cho, Chikusa-ku,
More informationGaussian EDA and Truncation Selection: Setting Limits for Sustainable Progress
Gaussian EDA and Truncation Selection: Setting Limits for Sustainable Progress Petr Pošík Czech Technical University, Faculty of Electrical Engineering, Department of Cybernetics Technická, 66 7 Prague
More informationLecture 9 Evolutionary Computation: Genetic algorithms
Lecture 9 Evolutionary Computation: Genetic algorithms Introduction, or can evolution be intelligent? Simulation of natural evolution Genetic algorithms Case study: maintenance scheduling with genetic
More informationDensity Modeling and Clustering Using Dirichlet Diffusion Trees
p. 1/3 Density Modeling and Clustering Using Dirichlet Diffusion Trees Radford M. Neal Bayesian Statistics 7, 2003, pp. 619-629. Presenter: Ivo D. Shterev p. 2/3 Outline Motivation. Data points generation.
More informationLocal Search and Optimization
Local Search and Optimization Outline Local search techniques and optimization Hill-climbing Gradient methods Simulated annealing Genetic algorithms Issues with local search Local search and optimization
More informationLocal search algorithms. Chapter 4, Sections 3 4 1
Local search algorithms Chapter 4, Sections 3 4 Chapter 4, Sections 3 4 1 Outline Hill-climbing Simulated annealing Genetic algorithms (briefly) Local search in continuous spaces (very briefly) Chapter
More informationFoundations of Artificial Intelligence
Foundations of Artificial Intelligence 32. Propositional Logic: Local Search and Outlook Martin Wehrle Universität Basel April 29, 2016 Propositional Logic: Overview Chapter overview: propositional logic
More informationA.I.: Beyond Classical Search
A.I.: Beyond Classical Search Random Sampling Trivial Algorithms Generate a state randomly Random Walk Randomly pick a neighbor of the current state Both algorithms asymptotically complete. Overview Previously
More informationChapter 8: Introduction to Evolutionary Computation
Computational Intelligence: Second Edition Contents Some Theories about Evolution Evolution is an optimization process: the aim is to improve the ability of an organism to survive in dynamically changing
More informationNew Epistasis Measures for Detecting Independently Optimizable Partitions of Variables
New Epistasis Measures for Detecting Independently Optimizable Partitions of Variables Dong-Il Seo, Sung-Soon Choi, and Byung-Ro Moon School of Computer Science & Engineering, Seoul National University
More informationExperimental Supplements to the Theoretical Analysis of EAs on Problems from Combinatorial Optimization
Experimental Supplements to the Theoretical Analysis of EAs on Problems from Combinatorial Optimization Patrick Briest, Dimo Brockhoff, Bastian Degener, Matthias Englert, Christian Gunia, Oliver Heering,
More informationSimulation of quantum computers with probabilistic models
Simulation of quantum computers with probabilistic models Vlad Gheorghiu Department of Physics Carnegie Mellon University Pittsburgh, PA 15213, U.S.A. April 6, 2010 Vlad Gheorghiu (CMU) Simulation of quantum
More informationTimo Latvala Landscape Families
HELSINKI UNIVERSITY OF TECHNOLOGY Department of Computer Science Laboratory for Theoretical Computer Science T-79.300 Postgraduate Course in Theoretical Computer Science Timo Latvala Landscape Families
More informationREIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531
U N I V E R S I T Y OF D O R T M U N D REIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531 Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence
More informationInteger weight training by differential evolution algorithms
Integer weight training by differential evolution algorithms V.P. Plagianakos, D.G. Sotiropoulos, and M.N. Vrahatis University of Patras, Department of Mathematics, GR-265 00, Patras, Greece. e-mail: vpp
More informationClassification 2: Linear discriminant analysis (continued); logistic regression
Classification 2: Linear discriminant analysis (continued); logistic regression Ryan Tibshirani Data Mining: 36-462/36-662 April 4 2013 Optional reading: ISL 4.4, ESL 4.3; ISL 4.3, ESL 4.4 1 Reminder:
More informationGenetic Algorithm. Outline
Genetic Algorithm 056: 166 Production Systems Shital Shah SPRING 2004 Outline Genetic Algorithm (GA) Applications Search space Step-by-step GA Mechanism Examples GA performance Other GA examples 1 Genetic
More informationImplicit Formae in Genetic Algorithms
Implicit Formae in Genetic Algorithms Márk Jelasity ½ and József Dombi ¾ ¾ ½ Student of József Attila University, Szeged, Hungary jelasity@inf.u-szeged.hu Department of Applied Informatics, József Attila
More informationThe Story So Far... The central problem of this course: Smartness( X ) arg max X. Possibly with some constraints on X.
Heuristic Search The Story So Far... The central problem of this course: arg max X Smartness( X ) Possibly with some constraints on X. (Alternatively: arg min Stupidness(X ) ) X Properties of Smartness(X)
More informationThe Parameterized Complexity of Approximate Inference in Bayesian Networks
The Parameterized Complexity of Approximate Inference in Bayesian Networks Johan Kwisthout j.kwisthout@donders.ru.nl http://www.dcc.ru.nl/johank/ Donders Center for Cognition Department of Artificial Intelligence
More informationUsing Genetic Algorithms for Maximizing Technical Efficiency in Data Envelopment Analysis
Using Genetic Algorithms for Maximizing Technical Efficiency in Data Envelopment Analysis Juan Aparicio 1 Domingo Giménez 2 Martín González 1 José J. López-Espín 1 Jesús T. Pastor 1 1 Miguel Hernández
More informationPengju
Introduction to AI Chapter04 Beyond Classical Search Pengju Ren@IAIR Outline Steepest Descent (Hill-climbing) Simulated Annealing Evolutionary Computation Non-deterministic Actions And-OR search Partial
More information3.4 Relaxations and bounds
3.4 Relaxations and bounds Consider a generic Discrete Optimization problem z = min{c(x) : x X} with an optimal solution x X. In general, the algorithms generate not only a decreasing sequence of upper
More informationEvolutionary Computation. DEIS-Cesena Alma Mater Studiorum Università di Bologna Cesena (Italia)
Evolutionary Computation DEIS-Cesena Alma Mater Studiorum Università di Bologna Cesena (Italia) andrea.roli@unibo.it Evolutionary Computation Inspiring principle: theory of natural selection Species face
More informationBinary Particle Swarm Optimization with Crossover Operation for Discrete Optimization
Binary Particle Swarm Optimization with Crossover Operation for Discrete Optimization Deepak Singh Raipur Institute of Technology Raipur, India Vikas Singh ABV- Indian Institute of Information Technology
More informationUna descrizione della Teoria della Complessità, e più in generale delle classi NP-complete, possono essere trovate in:
AA. 2014/2015 Bibliography Una descrizione della Teoria della Complessità, e più in generale delle classi NP-complete, possono essere trovate in: M. R. Garey and D. S. Johnson, Computers and Intractability:
More informationComputer Vision Group Prof. Daniel Cremers. 2. Regression (cont.)
Prof. Daniel Cremers 2. Regression (cont.) Regression with MLE (Rep.) Assume that y is affected by Gaussian noise : t = f(x, w)+ where Thus, we have p(t x, w, )=N (t; f(x, w), 2 ) 2 Maximum A-Posteriori
More informationStatistical learning. Chapter 20, Sections 1 4 1
Statistical learning Chapter 20, Sections 1 4 Chapter 20, Sections 1 4 1 Outline Bayesian learning Maximum a posteriori and maximum likelihood learning Bayes net learning ML parameter learning with complete
More informationThe Role of Crossover in Genetic Algorithms to Solve Optimization of a Function Problem Falih Hassan
The Role of Crossover in Genetic Algorithms to Solve Optimization of a Function Problem Falih Hassan ABSTRACT The genetic algorithm is an adaptive search method that has the ability for a smart search
More informationFinding Multiple Global Optima Exploiting Differential Evolution s Niching Capability
Finding Multiple Global Optima Exploiting Differential Evolution s Niching Capability Michael G. Epitropakis Computational Intelligence Laboratory, Department of Mathematics, University of Patras, Greece.
More informationhow should the GA proceed?
how should the GA proceed? string fitness 10111 10 01000 5 11010 3 00011 20 which new string would be better than any of the above? (the GA does not know the mapping between strings and fitness values!)
More informationAn Analysis on Recombination in Multi-Objective Evolutionary Optimization
An Analysis on Recombination in Multi-Objective Evolutionary Optimization Chao Qian, Yang Yu, Zhi-Hua Zhou National Key Laboratory for Novel Software Technology Nanjing University, Nanjing 20023, China
More information8 Basics of Hypothesis Testing
8 Basics of Hypothesis Testing 4 Problems Problem : The stochastic signal S is either 0 or E with equal probability, for a known value E > 0. Consider an observation X = x of the stochastic variable X
More informationLocal Search & Optimization
Local Search & Optimization CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2018 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 4 Some
More informationAdiabatic quantum computation a tutorial for computer scientists
Adiabatic quantum computation a tutorial for computer scientists Itay Hen Dept. of Physics, UCSC Advanced Machine Learning class UCSC June 6 th 2012 Outline introduction I: what is a quantum computer?
More informationCOMS W4995 Introduction to Cryptography October 12, Lecture 12: RSA, and a summary of One Way Function Candidates.
COMS W4995 Introduction to Cryptography October 12, 2005 Lecture 12: RSA, and a summary of One Way Function Candidates. Lecturer: Tal Malkin Scribes: Justin Cranshaw and Mike Verbalis 1 Introduction In
More informationImproved TBL algorithm for learning context-free grammar
Proceedings of the International Multiconference on ISSN 1896-7094 Computer Science and Information Technology, pp. 267 274 2007 PIPS Improved TBL algorithm for learning context-free grammar Marcin Jaworski
More informationLocal search algorithms. Chapter 4, Sections 3 4 1
Local search algorithms Chapter 4, Sections 3 4 Chapter 4, Sections 3 4 1 Outline Hill-climbing Simulated annealing Genetic algorithms (briefly) Local search in continuous spaces (very briefly) Chapter
More informationBeta Damping Quantum Behaved Particle Swarm Optimization
Beta Damping Quantum Behaved Particle Swarm Optimization Tarek M. Elbarbary, Hesham A. Hefny, Atef abel Moneim Institute of Statistical Studies and Research, Cairo University, Giza, Egypt tareqbarbary@yahoo.com,
More informationApplication of a GA/Bayesian Filter-Wrapper Feature Selection Method to Classification of Clinical Depression from Speech Data
Application of a GA/Bayesian Filter-Wrapper Feature Selection Method to Classification of Clinical Depression from Speech Data Juan Torres 1, Ashraf Saad 2, Elliot Moore 1 1 School of Electrical and Computer
More informationMachine Learning for OR & FE
Machine Learning for OR & FE Regression II: Regularization and Shrinkage Methods Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com
More information5. Simulated Annealing 5.1 Basic Concepts. Fall 2010 Instructor: Dr. Masoud Yaghini
5. Simulated Annealing 5.1 Basic Concepts Fall 2010 Instructor: Dr. Masoud Yaghini Outline Introduction Real Annealing and Simulated Annealing Metropolis Algorithm Template of SA A Simple Example References
More informationEvolutionary Design I
Evolutionary Design I Jason Noble jasonn@comp.leeds.ac.uk Biosystems group, School of Computing Evolutionary Design I p.1/29 This lecture Harnessing evolution in a computer program How to construct a genetic
More informationParallel Genetic Algorithms
Parallel Genetic Algorithms for the Calibration of Financial Models Riccardo Gismondi June 13, 2008 High Performance Computing in Finance and Insurance Research Institute for Computational Methods Vienna
More informationEvolutionary Algorithms How to Cope With Plateaus of Constant Fitness and When to Reject Strings of The Same Fitness
Evolutionary Algorithms How to Cope With Plateaus of Constant Fitness and When to Reject Strings of The Same Fitness Thomas Jansen and Ingo Wegener FB Informatik, LS 2, Univ. Dortmund, 44221 Dortmund,
More informationLocal Search & Optimization
Local Search & Optimization CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2017 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 4 Outline
More informationLOCAL SEARCH. Today. Reading AIMA Chapter , Goals Local search algorithms. Introduce adversarial search 1/31/14
LOCAL SEARCH Today Reading AIMA Chapter 4.1-4.2, 5.1-5.2 Goals Local search algorithms n hill-climbing search n simulated annealing n local beam search n genetic algorithms n gradient descent and Newton-Rhapson
More informationLimitations of Algorithm Power
Limitations of Algorithm Power Objectives We now move into the third and final major theme for this course. 1. Tools for analyzing algorithms. 2. Design strategies for designing algorithms. 3. Identifying
More informationIntroduction to Optimization
Introduction to Optimization Blackbox Optimization Marc Toussaint U Stuttgart Blackbox Optimization The term is not really well defined I use it to express that only f(x) can be evaluated f(x) or 2 f(x)
More information1. Computação Evolutiva
1. Computação Evolutiva Renato Tinós Departamento de Computação e Matemática Fac. de Filosofia, Ciência e Letras de Ribeirão Preto Programa de Pós-Graduação Em Computação Aplicada 1.6. Aspectos Teóricos*
More informationChapter 1 - Lecture 3 Measures of Location
Chapter 1 - Lecture 3 of Location August 31st, 2009 Chapter 1 - Lecture 3 of Location General Types of measures Median Skewness Chapter 1 - Lecture 3 of Location Outline General Types of measures What
More informationEvolving Presentations of Genetic Information: Motivation, Methods, and Analysis
Evolving Presentations of Genetic Information: Motivation, Methods, and Analysis Peter Lee Stanford University PO Box 14832 Stanford, CA 94309-4832 (650)497-6826 peterwlee@stanford.edu June 5, 2002 Abstract
More informationA Genetic Algorithm Approach for Doing Misuse Detection in Audit Trail Files
A Genetic Algorithm Approach for Doing Misuse Detection in Audit Trail Files Pedro A. Diaz-Gomez and Dean F. Hougen Robotics, Evolution, Adaptation, and Learning Laboratory (REAL Lab) School of Computer
More information