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Towards billion bit optimization via parallel estimation of distribution algorithm
 Genetic and Evolutionary Computation Conference (GECCO2007
, 2007
"... This paper presents a highly efficient, fully parallelized implementation of the compact genetic algorithm (cGA) to solve very large scale problems with millions to billions of variables. The paper presents principled results demonstrating the scalable solution of a difficult test function on instan ..."
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This paper presents a highly efficient, fully parallelized implementation of the compact genetic algorithm (cGA) to solve very large scale problems with millions to billions of variables. The paper presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of cGA. The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling up to a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The compact GA, on the other hand, is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billionvariable problems across the landscape of search problems.
Substructural Surrogates for Learning Decomposable Classification Problems: Implementation and First Results
, 2007
"... This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model that represents salient interactions between attributes for a given data, (2) a s ..."
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Cited by 3 (0 self)
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This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model that represents salient interactions between attributes for a given data, (2) a surrogate model which provides a functional approximation of the output as a function of attributes, and (3) a classification model which predicts the class for new inputs. The structural model is used to infer the functional form of the surrogate and its coefficients are estimated using linear regression methods. The classification model uses a maximallyaccurate, leastcomplex surrogate to predict the output for given inputs. The structural model that yields an optimal classification model is searched using an iterative greedy search heuristic. Results show that the proposed method successfully detects key variable interactions in hierarchical problems, group them in linkages groups, and build maximally accurate classification models. The initial results on nontrivial hierarchical test problems indicate that the proposed method holds promise and have also shed light on several improvements to enhance the capabilities of the proposed method. 1
Substructrual Surrogates for Learning Decomposable Classification Problems: Implementation and First Results
"... This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model that represents salient interactions between attributes for a given data, (2) a s ..."
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Cited by 1 (1 self)
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This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model that represents salient interactions between attributes for a given data, (2) a surrogate model which provides a functional approximation of the output as a function of attributes, and (3) a classification model which predicts the class for new inputs. The structural model is used to infer the functional form of the surrogate and its coefficients are estimated using linear regression methods. The classification model uses a maximallyaccurate, leastcomplex surrogate to predict the output for given inputs. The structural model that yields an optimal classification model is searched using an iterative greedy search heuristic. Results show that the proposed method successfully detects the interacting variables in hierarchical problems, group them in linkages groups, and build maximally accurate classification models. The initial results on nontrivial hierarchical test problems indicate that the proposed method holds promise and have also shed light on several improvements to enhance the capabilities of the proposed method.
Convergence Theorems of Estimation of Distribution Algorithms
"... Estimation of Distribution Algorithms (EDAs) have been proposed as an extension of genetic algorithms. We assume that the function to be optimized is additively decomposed (ADF). The interaction graph of the ADF is used to create exact or approximate factorizations of the Boltzmann distribution. Con ..."
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Estimation of Distribution Algorithms (EDAs) have been proposed as an extension of genetic algorithms. We assume that the function to be optimized is additively decomposed (ADF). The interaction graph of the ADF is used to create exact or approximate factorizations of the Boltzmann distribution. Convergence of the algorithm MNGIBBS is proven. MNGIBBS uses a Markov network easily derived from the ADF and Gibbs sampling. The Factorized Distribution Algorithm (FDA) uses a less general representation, a Bayesian network and probabilistic logic sampling (PLS). We shortly describe the algorithm LFDA which learns a Bayesian network from data. The relation between the network computed by LFDA and the optimal network used by FDA is investigated. Convergence of FDA to the optima is shown for finite samples if the factorization fulfills the running intersection property. The sample size is bounded by O(nm ln nm) where n is the size of the problem and m the number of subfunctions. For the proof results from statistical learning theory and Probably Approximately Correct (PAC) learning are used. Numerical experiments show that even for difficult test functions a sample size which scales linearly with n is often sufficient. We also show that a good approximation of the true distribution is not necessary, it suffices to use a factorization where the global optima have a large enough probability. This explains the success of EDAs in practical applications.
Intelligent Systems Group
"... This paper incorporates Belief Propagation into an instance of Estimation of Distribution Algorithms called Estimation of Bayesian Networks Algorithm. Estimation of Bayesian Networks Algorithm learns a Bayesian network at each step. The objective of the proposed variation is to increase the search c ..."
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This paper incorporates Belief Propagation into an instance of Estimation of Distribution Algorithms called Estimation of Bayesian Networks Algorithm. Estimation of Bayesian Networks Algorithm learns a Bayesian network at each step. The objective of the proposed variation is to increase the search capabilities by extracting information of the, computationally costly to learn, Bayesian network. Belief Propagation applied to graphs with cycles, allows to find (with a low computational cost), in many scenarios, the point with the highest probability of a Bayesian network. We carry out some experiments to show how this modification can increase the potentialities of Estimation of Distribution Algorithms. Due to the computational time implied in the resolution of high dimensional optimization problems, we give a parallel version of the Belief Propagation algorithm for graphs with cycles and introduce it in a parallel framework for Estimation of Distribution Algorithms [13]. In addition we point out many ideas on how to incorporate Belief Propagation algorithms into Estimation Distribution Algorithms. 1
Genetic Algorithms and . . . MODELING: APPLICATIONS IN MATERIALS SCIENCE AND CHEMISTRY AND ADVANCES IN SCALABILITY
, 2007
"... Effective and efficient multiscale modeling is essential to advance both the science and synthesis in a wide array of fields such as physics, chemistry, materials science, biology, biotechnology and pharmacology. This study investigates the efficacy and potential of using genetic algorithms for mult ..."
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Effective and efficient multiscale modeling is essential to advance both the science and synthesis in a wide array of fields such as physics, chemistry, materials science, biology, biotechnology and pharmacology. This study investigates the efficacy and potential of using genetic algorithms for multiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale modeling with the help of two nontrivial case studies in materials science and chemistry. The first case study explores the utility of genetic programming (GP) in multitimescaling alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte Carlo methods to span ordersofmagnitude in simulation time. Specifically, GP is used to regress symbolically an inline barrier function from a limited set of molecular dynamics simulations to enable kinetic Monte Carlo that simulate seconds of real time. Results on a nontrivial example of vacancyassisted migration on a surface of a facecentered cubic (fcc) CopperCobalt (CuxCo1−x) alloy show that GP predicts all barriers with 0.1 % error from calculations for less than 3 % of active
External Examiner:
, 2010
"... The grammar in the grammarbased Genetic Programming (GP) approach of Grammatical Evolution (GE) is explored. The GE algorithm solves problems by using a grammar representation and an automated and parallel trialanderror approach, Evolutionary Computation (EC). The search for solutions in EC is ..."
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The grammar in the grammarbased Genetic Programming (GP) approach of Grammatical Evolution (GE) is explored. The GE algorithm solves problems by using a grammar representation and an automated and parallel trialanderror approach, Evolutionary Computation (EC). The search for solutions in EC is driven by evaluating each solution, selecting the fittest and replacing these into a population of solutions which are modified to further guide the search. Representations have a strong impact on the efficiency of search and by using a generative grammar domain knowledge is encoded into the population of solutions. The grammar in GE biases the search for solutions, and in combination with a linear representation this is what distinguishes GE from other GPsystems. After a review of grammars in EC and a description of GE, several different constructions of grammars and operators for manipulating the grammars and the evolutionary algorithm are studied. The thesis goes on to study a metagrammar GE, which allows a larger grammar with different bias. By adopting a divideandconquer strategy the goal is to investigate how a modular GE approach solves problems of increasing size and in dynam