An Analysis of a Model-based Evolutionary Algorithm: Learnable Evolution Model

AN ANALYSIS OF A MODEL-BASED EVOLUTIONARY ALGORITHM: LEARNABLE EVOLUTION MODEL Mark Coletti, PhD George Mason University, 2014 Dissertation Director: Dr. Kenneth De Jong An evolutionary algorithm (EA) is a biologically inspired metaheuristic that uses mutation, crossover, reproduction, and selection operators to evolve solutions for a given problem. Learnable Evolution Model (LEM) is an EA that has an evolutionary algorithm component that works in tandem with a machine learner to collaboratively create populations of individuals. The machine learner infers rules from best and least t individuals, and then this knowledge is exploited to improve the quality of o spring. Unfortunately, most of the extant work on LEM has been ad hoc, and so there does not exist a deep understanding of how LEM works. And this lack of understanding, in turn, means that there is no set of best practices for implementing LEM. For example, most LEM implementations use rules that describe value ranges corresponding to areas of higher tness in which o spring should be created. However, we do not know the e cacy of di erent approaches for sampling those intervals. Also, we do not have su cient guidance for assembling training sets of positive and negative examples from populations from which the ML component can learn. This research addresses those open issues by exploring three di erent rule interval sampling approaches as well as three di erent training set con gurations on a number of test problems that are representative of the types of problems that practitioners may encounter. Using the machine learner to create o spring induces a unique emergent selection pressure separate from the selection pressure that manifests from parent and survivor selection; an outcome of this research is a partially ordered set of the impact that these rule interval sampling approaches and training set con gurations have on this selection pressure that practitioners can use for implementation guidance. That is, a practitioner can modulate selection pressure by traversing a set of design con gurations within a Hasse graph de ned by partially ordered selection pressure. Chapter 1: Introduction In this chapter I rst brie y describe evolutionary algorithms and Model-based Evolutionary Algorithms (MBEAs). I then discuss my motivation for focusing on a speci c MBEA, Learnable Evolution Model (LEM), and the approach I used to addressing its open issues. Finally, I relate the contributions I made towards our understanding of this algorithm. 1.1 Evolutionary Algorithms Evolutionary algorithms (EAs) are a biologically inspired approach to problem solving, and their very nature makes it straightforward to construct an EA to solve a given problem. That is, posed solutions to real-world solutions can be recast as individuals in an arti cial ecosystem where their respective quality serves as a measure of tness. Then parent selection, survival-of-thettest, and reproduction processes similar to their biological analogs can, over time, \breed" better solutions. EAs have been successfully applied in this way to a variety of problems that include real-value function optimization, job-shop scheduling, planning, design, and so on [De Jong, 2006]. Generally, an evolutionary algorithm consists of a set of individuals that each represents a proposed solution to a problem of interest. Associated with each individual is a tness value that indicates the quality of that solution. Each individual is comprised of a set of genes that re ect some aspect of the problem to be solved. E.g., one set of genes may represent design parameters for an engine simulation, for a di erent problem the genes may represent a tour for a Traveling Salesman problem, and a still di erent set of genes may by comprised of an S-expression corresponding to a simple equation to solve a given problem. New individuals are created by selecting individuals to be parents and then using some form of reproduction to create o spring from those selected parents. Reproduction typically 1

[1]  Kumara Sastry,et al.  Linkage Learning via Probabilistic Modeling in the Extended Compact Genetic Algorithm (ECGA) , 2006, Scalable Optimization via Probabilistic Modeling.

[2]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[3]  Kenneth A. Kaufman,et al.  Inductive Learning System AQ15c: The Method and User's Guide , 1995 .

[4]  Nir Friedman,et al.  Building Classifiers Using Bayesian Networks , 1996, AAAI/IAAI, Vol. 2.

[5]  D. Wolpert,et al.  No Free Lunch Theorems for Search , 1995 .

[6]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[7]  Ian H. Witten,et al.  The WEKA data mining software: an update , 2009, SKDD.

[8]  Ryszard S. Michalski,et al.  Experimental validations of the learnable evolution model , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[9]  Colin R. Reeves,et al.  Evolutionary computation: a unified approach , 2007, Genetic Programming and Evolvable Machines.

[10]  Swarm, Evolutionary, and Memetic Computing , 2011, Lecture Notes in Computer Science.

[11]  David W. Corne,et al.  The simplest evolution/learning hybrid: LEM with KNN , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[12]  Kenneth A. Kaufman,et al.  The AQ21 Natural Induction Program for Pattern Discovery: Initial Version and its Novel Features , 2006, 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06).

[13]  Mark Coletti.  Learnable evolution model performance impaired by binary tournament survival selection , 2009, GECCO '09.

[14]  Xavier Llorà,et al.  Wise Breeding GA via Machine Learning Techniques for Function Optimization , 2003, GECCO.

[15]  Conor Ryan,et al.  Evaluation of population partitioning schemes in bayesian classifier EDAs: estimation of distribution algoithms , 2009, GECCO '09.

[16]  James Smith,et al.  A tutorial for competent memetic algorithms: model, taxonomy, and design issues , 2005, IEEE Transactions on Evolutionary Computation.

[17]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[18]  Patrick D. Surry,et al.  Formal Memetic Algorithms , 1994, Evolutionary Computing, AISB Workshop.

[19]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[20]  Ian H. Witten,et al.  Generating Accurate Rule Sets Without Global Optimization , 1998, ICML.

[21]  KalyanmoyDebandSamirAgrawal KanpurGeneticAlgorithmsLaboratory,et al.  A Niched-Penalty Approach for Constraint Handling in Genetic Algorithms , 2002 .

[22]  Laetitia Vermeulen-Jourdan,et al.  Hybridising rule induction and multi-objective evolutionary search for optimising water distribution systems , 2004, Fourth International Conference on Hybrid Intelligent Systems (HIS'04).

[23]  Marcus Gallagher,et al.  On the importance of diversity maintenance in estimation of distribution algorithms , 2005, GECCO '05.

[24]  L. Darrell Whitley,et al.  Building Better Test Functions , 1995, ICGA.

[25]  Kenneth A. Kaufman,et al.  Combining Machine Learning with Evolutionary Computation: Recent Results on LEM , 2000 .

[26]  Lothar Thiele,et al.  A Comparison of Selection Schemes Used in Evolutionary Algorithms , 1996, Evolutionary Computation.

[27]  Michèle Sebag,et al.  Controlling Evolution by Means of Machine Learning , 1996, Evolutionary Programming.

[28]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[29]  Kenneth A. De Jong,et al.  The relationship between evolvability and bloat , 2009, GECCO.

[30]  Michèle Sebag,et al.  An Advanced Evolution Should Not Repeat its Past Errors , 1996, ICML.

[31]  Adrian Grajdeanu,et al.  Characterization of atmospheric contaminant sources using Adaptive Evolutionary Algorithms , 2010 .

[32]  Guido Cervone,et al.  Non-Darwinian evolution for the source detection of atmospheric releases , 2011 .

[33]  Kenneth A. Kaufman,et al.  Learning from Inconsistent and Noisy Data: The AQ18 Approach , 1999, ISMIS.

[34]  N. Garc'ia-Pedrajas,et al.  CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features , 2005, J. Artif. Intell. Res..

[35]  Kenneth A. Kaufman,et al.  Progress Report on the Learnable Evolution Model , 2007 .

[36]  Luca Maria Gambardella,et al.  Results of the first international contest on evolutionary optimisation (1st ICEO) , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[37]  Nada Lavrac,et al.  The Multi-Purpose Incremental Learning System AQ15 and Its Testing Application to Three Medical Domains , 1986, AAAI.

[38]  J.A. Ramirez,et al.  Optimization of Cost Functions Using Evolutionary Algorithms With Local Learning and Local Search , 2006, IEEE Transactions on Magnetics.

[39]  Ryszard S. Michalski,et al.  Comparing Performance of the Learnable Evolution Model and Genetic Algorithms , 1999, GECCO.

[40]  Kenneth A. Kaufman,et al.  Intelligent Optimization via Learnable Evolution Model , 2006, 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06).

[41]  Mark Coletti.  The effects of training set size and keeping rules on the emergent selection pressure of learnable evolution model , 2012, GECCO '12.

[42]  Kenneth A. Kaufman,et al.  Recent Results from the Experimental Evaluation of the Learnable Evolution Model , 2002, GECCO Late Breaking Papers.

[43]  H. Mühlenbein,et al.  Gene Pool Recombination in Genetic Algorithms , 1996 .

[44]  Guido Cervone,et al.  Analysis of Emergent Selection Pressure in Evolutionary Algorithm and Machine Learner Offspring Filtering Hybrids , 2012, SEMCCO.