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A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization

Ignacio Segovia-Domínguez, S. Ivvan Valdez, Arturo Hernández-Aguirre
2014 Proceedings of the International Conference on Evolutionary Computation Theory and Applications  
A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization.  ...  This paper introduces an approach for continuous optimization using an Estimation of Distribution Algorithm (EDA), based on the Boltzmann distribution.  ...  This is a general framework for Boltzmann distribution based estimation of distribution algorithms, where practical EDAs have been derived from.  ... 
doi:10.5220/0005079902510258 dblp:conf/ijcci/DominguezVA14 fatcat:3jhhvoo2qrebpbstz6polzanz4

Probabilistic modeling for continuous EDA with Boltzmann selection and Kullback-Leibeler divergence

Cai Yunpeng, Sun Xiaomin, Jia Peifa
2006 Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06  
The difficulty of estimating the exact Boltzmann distribution in continuous state space is circumvented by adopting the multivariate Gaussian model, which is popular in continuous EDA, to approximate only  ...  This paper extends the Boltzmann Selection, a method in EDA with theoretical importance, from discrete domain to the continuous one.  ...  To make use of the Boltzmann distribution, Mühlenbein et.al. proposed the Boltzmann Selection and the Boltzmann Estimation of Distribution Algorithm(BEDA) [18] for combinatory optimization.  ... 
doi:10.1145/1143997.1144070 dblp:conf/gecco/YunpengXJ06 fatcat:4gak5wgoqrebrner3aoi754jbi

Symmetric-approximation Energy-based Estimation of Distribution (SEED): a continuous optimization algorithm

Juan de Anda-Suarez, Martin Carpio, Hector J. Puga, Valentin Calzada-Ledesma, Alfonso Rojas-Dominguez, Solai Jeyakumar, Andres Espinal
2019 IEEE Access  
Estimation of Distribution Algorithms (EDAs) maintain and iteratively update a probabilistic model to tackle optimization problems.  ...  INDEX TERMS Boltzmann selection, estimation of distribution algorithms, Kullback-Leibler divergence, J-divergence.  ...  Some examples of this type of EDAs are: Boltzmann-EDA (BEDA) [44] , Boltzmann-Gaussian Univariate Marginal Distribution Algorithm (BG-UMDA) [45] , Estimation of Multivariate Normal Algorithm with Boltzmann  ... 
doi:10.1109/access.2019.2948199 fatcat:kztqipe6tbcn7h6v3yr3kolaja

Experience in Using Stochastic Optimization Methods for Determining Numerical Parameters of Models in Materials Structurization Management Systems

Korneev Andrey Mastislavovich, Buzina Olga Petrovna, Sukhanov Andrey Vladimirovich, Shipulin Ilya Andreevich
2018 International Journal of Engineering & Technology  
The program implements ten modifications of the simulation algorithm for annealing, allowing for a finite number of steps to make an estimate of the optimal value of the input elements of the function  ...  In particular, modification of A, B and B algorithm schemes using the Boltzmann and Cauchy distribution functions, as well as the superfast annealing algorithm and the Xin Yao algorithm are implemented  ...  In the random search algorithm for simulated annealing of optimal parameters Ξ by the Boltzmann scheme, it was customary to modify the Gibbs distribution function.  ... 
doi:10.14419/ijet.v7i3.5.15196 fatcat:awh4w6dytbgp3h3z7zmnzmspcq

A Boltzmann based estimation of distribution algorithm

S. Ivvan Valdez, Arturo Hernández, Salvador Botello
2013 Information Sciences  
The Elitist Convergent Estimation of Distribution Algorithm (ECEDA), is a definition of a class of EDA which guarantees convergence to the optimum.  ...  This paper introduces the conceptual ECEDA and a practical approach derived from it, called the Boltzmann Univariate Marginal Distribution Algorithm (BUMDA).  ...  Introduction The Estimation of Distribution Algorithms (EDAs) were first introduced for global optimization in discrete spaces [12] [1] , then several approaches were extended to continuous domains  ... 
doi:10.1016/j.ins.2013.02.040 fatcat:ijegtm375jcpra72fkf7hb3vkm

Deep Boltzmann Machines in Estimation of Distribution Algorithms for Combinatorial Optimization [article]

Malte Probst, Franz Rothlauf
2016 arXiv   pre-print
Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled.  ...  We integrate a DBM into an EDA and evaluate the performance of this system in solving combinatorial optimization problems with a single objective.  ...  Introduction Estimation of Distribution Algorithms (EDAs) [12, 8] are metaheuristics for combinatorial and continuous non-linear optimization.  ... 
arXiv:1509.06535v2 fatcat:2r3jlxutfvcxzcl4avnjvhz5gi

Efficient Estimation of Distribution Algorithms by Using the Empirical Selection Distribution [chapter]

S. Ivvan, Arturo Hernndez, Salvador Botello
2010 New Achievements in Evolutionary Computation  
Continuous variables For the continuous case, consider a univariate search space with domain in the interval [a,b] , then a set of points i x for i=1,2,...,|X| define partitions.  ...  Introduction Estimation of Distribution Algorithms (EDAs) (Mühlenbein et al., 1996; Mühlenbein & PaaB, 1996) are a promising area of research in evolutionary computation.  ...  from: http://www.intechopen.com/books/newachievements-in-evolutionary-computation/efficient-estimation-of-distribution-algorithms-by-using-theempirical-selection-distribution © 2010 The Author(s).  ... 
doi:10.5772/8056 fatcat:e2f3hj6ambgvboa3ydpnt4vvxe

A Survey of Some Model-Based Methods for Global Optimization [chapter]

Jiaqiao Hu, Yongqiang Wang, Enlu Zhou, Michael C. Fu, Steven I. Marcus
2012 Optimization, Control, and Applications of Stochastic Systems  
Abstract We review some recent developments of a class of random search methods: model-based methods for global optimization problems.  ...  We have developed various frameworks for model-based algorithms to guide the updating of probabilistic models and to facilitate convergence proofs.  ...  (a) In continuous optimization when multivariate normal distributions with mean vector µ and covariance matrix Σ are used as the parameterized family, then it is easy to show that Theorem 1 implies lim  ... 
doi:10.1007/978-0-8176-8337-5_10 fatcat:2ngptgrckvhkdez2bamxssyf4e

Application of continuous restricted Boltzmann machine to identify multivariate geochemical anomaly

Yongliang Chen, Laijun Lu, Xuebin Li
2014 Journal of Geochemical Exploration  
In this research, a continuous restricted Boltzmann machine (CRBM), which is a generative stochastic artificial neural network, was used to recognize the mineral potential area in Korit 1:100000 sheet,  ...  For this purpose, 470 geochemical stream sediment samples were collected from the study area and analyzed for 36 elements.  ...  Also special thanks go to Industry, Mine & Trade Organization of South Khorasan for providing the required data.  ... 
doi:10.1016/j.gexplo.2014.02.013 fatcat:ll7zrqysone3tpn2qhvse4t4wm

Detection of Voltage Anomalies in Spacecraft Storage Batteries Based on a Deep Belief Network

Li, Zhang, Liu
2019 Sensors  
detection algorithm for spacecraft storage batteries based on a deep belief network (DBN) is proposed.  ...  For a spacecraft, its power system is vital to its normal operation and capacity to complete flight missions. The storage battery is an essential component of a power system.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/s19214702 pmid:31671886 pmcid:PMC6864756 fatcat:46elsftf7nfyppwi6fieiruf3a

Mathematical Analysis of Evolutionary Algorithms [chapter]

H. Mühlenbein, Th. Mahnig
2002 Operations Research/Computer Science Interfaces Series  
We present a mathematical theory based on probability distributions.  ...  Today evolutionary algorithms have been successfully used in a number of applications.  ...  to define the (Boltzmann Estimated Distribution Algorithm).  ... 
doi:10.1007/978-1-4615-1507-4_24 fatcat:m5womgzhzzbftjhe3dpmpsy4ii

Generative Adversarial Networks in Estimation of Distribution Algorithms for Combinatorial Optimization [article]

Malte Probst
2016 arXiv   pre-print
Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled.  ...  We integrate a GAN into an EDA and evaluate the performance of this system when solving combinatorial optimization problems with a single objective.  ...  Introduction Estimation of Distribution Algorithms (EDA) [7, 6] are metaheuristics for combinatorial and continuous non-linear optimization.  ... 
arXiv:1509.09235v2 fatcat:yhneqaql7jg2lfuobemcif5uzy

Bayesian Optimization for Adaptive MCMC [article]

Nimalan Mahendran, Ziyu Wang, Firas Hamze, Nando de Freitas
2011 arXiv   pre-print
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization.  ...  We demonstrate the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust  ...  This algorithm is restricted to the adaptation of the multivariate random walk Metropolis algorithm with Gaussian proposals.  ... 
arXiv:1110.6497v1 fatcat:swkhgdjzjzbblkzb7z4poblwzy

Simulated annealing: Practice versus theory

L. Ingber
1993 Mathematical and computer modelling  
Acknowledgements Many of the authors cited here generously responded to my electronic mail requests for (p)reprints on current work in this field; quite a few read earlier drafts and contributed their  ...  Graphs were produced using XVGR (graphics for exploratory data analysis), a public domain software package running under UNIX and X11, developed by Paul Turner at the Oregon Graduate Institute.  ...  These estimates are used to estimate an optimal ensemble size.  ... 
doi:10.1016/0895-7177(93)90204-c fatcat:jpooy3cutbaujmdhpxf5yaybsm

The Nonnegative Boltzmann Machine

Oliver B. Downs, David J. C. MacKay, Daniel D. Lee
1999 Neural Information Processing Systems  
Application of maximum likelihood estimation to this model gives a learning rule that is analogous to the binary Boltzmann machine.  ...  We illustrate learning of the NNBM on a transiationally invariant distribution, as well as on a generative model for images of human faces.  ...  interpretation of the Boltzmann machine.  ... 
dblp:conf/nips/DownsML99 fatcat:ebespnqfnfdlnpzf65eg6bnuma
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