Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning (Tech. Rep. No. CMU-CS-94-163). Pittsburgh, PA: Carnegie Mellon University.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....product of n univariate and independent probability distributions, that is p l (x) i=1 p l (x i ) we obtain the Univariate Marginal Distribution Algorithm (UMDA) 34] In this work, UMDA is used. 3. 3 Population Based Incremental Learning Algorithm Population Based Incremental Learning (PBIL) [1] is another paradigm that carries out a population based, stochastic search. Its objective is to obtain the optimum of a function de ned in the binary space = f0; 1g (the next explanations can be easily extended to non binary search spaces) In each generation, the population of individuals ....

S. Baluja, `Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning', Technical Report CMU-CS-94-163, Carnegie Mel-

.... the n dimensional joint probability distribution is decomposed as a product of n univariate independent probability distributions, i.e. p l (x i ) 2) Examples of this type of EDA are Univariate Marginal Distribution Algorithm (UMDA) 18] and Population Based Incremental Learning (PBIL) [1]. In the case of UMDA, p l (x i ) is estimated as the relative frequencies of x i in the data set D l 1 . In contrast, PBIL obtains p l (x i ) updating p l 1 (x i ) by means of a Hebbian inspired rule which requires an extra parameter 2 (0; 1] Bivariate EDA approaches use second order ....

S. Baluja, Population Based Incremental Learning: A method for Integrating Genetic Search Based Function Optimization and Competitive Learning, Technical Report CMU-CS-94-163, Carnegie Mellon University, 1994.

....Although GP with recombina2 tive guidance performs well on some problems, the definition of substree value is problem dependent. Probabilistic Incremental Program Evolution (PIPE) PIPE [22] combines probability vector coding of program instructions, Population Based Incremental Learning [4], and tree coded programs. PIPE iteratively generates successive populations of functional programs according to an adaptive probability distribution, represented as a Probabilistic Prototype Tree (PPT) over all possible programs. Each iteration uses the best program to refine the distribution. ....

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Pittsburgh, PA, 1994.

.... the area of genetic algorithms (GA) Instead of simulating an entire population of n individuals according to selection, crossover and mutation, several authors have highlighted new mod els of Evolutionary Computation (EC) where a distribution of gene probabilities is used to generate individuals [1, 2, 3, 13]. Moreover, this distribution can be computed in such a way that its behavior simulates and encompasses the behavior of a standard binary GA. This distribution is used to generate individuals which can be evaluated. These generated individuals are possibly used with their fitness values to update ....

....f, f : R . We will denote by s one maximum of f. The i th bit value of string s will be denoted by s(i) Considering this very standard problem in evolutionary computation and in optimization, we define now the common notations for the three algorithms and PSM: V: Pl, Pt) with Pi c [0, 1], which denotes the vector of probabilities that will be used to generate points in S. We assume here that Pi represents the probability to generate a 1 , P = 81, n) with si C , which denotes the n binary strings that will be generated at each cycle. The general PSM algorithm can be ....

[Article contains additional citation context not shown here]

Baluja S. (1994). "Population-based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning". Tech. Rep. CMU-CS-94-163, Carnegie Mellon University.

.... tasks [28] Many algorithms have been developed over the years to tackle the challenging task of global optimization [13, 14, 22] In the absence of prior knowledge about the search landscape, stochastic approaches, such as simulated annealing [17] and populationbased incremental learning [2, 3], have been proved to be effective. They attempt to locate the optimal solution by generating sampling points probabilistically. Methods inspired by nature that are equally successful include evolutionary algorithms [1, 11, 12, 26] bacterial chemotaxis [23] differential evolution [27] particle ....

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning,. Technical Report CMU-CS-94-163, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1994.

....Once the cost function, c expected , can be evaluated for any set of threshold weight values, t 1 # t 2 #####t n , a set of threshold weight values which provide a low cost may be found. It was decided to use an optimisation technique known as Population Based Incremental Learning (PBIL) [2] to select such a set of threshold weights. After setting up a random number generator with an initially uniform PDF over the space of the function to be optimised, PBIL repeatedly spawns generations of populations of candidate solutions, adjusting the PDF slightly in each generation so as to ....

....repeatedly spawns generations of populations of candidate solutions, adjusting the PDF slightly in each generation so as to favour the best candidate of the population. This is explained in greater detail below. PBIL has been shown to be a simple yet widely effective function optimisation strategy [2]. Furthermore, the PBIL algorithm can restrict the solution vector to consist of integers, which is useful since the threshold weights on the packing line can in practice only be set as integer weight values in grams [33] As the cost function is a summation of integrals, it may be expected to be ....

[Article contains additional citation context not shown here]

Shumeet Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical report, Carnegie Mellon University, June 1994.

....obtain good results. So it is very interesting to look for algorithms which are comparable in the results but which have much less parameters. Then it is more comfortable to model the optimization process mathematically, which also gives advantages in the practical use of such algorithms. Baluja [Bal94] proposed the PBIL algorithm: population based incremental learning (PBIL) a method of combining the mechanisms of a generational genetic algorithm with simple competitive learning. The combination of these two methods reveals a tool which is far simpler than a GA, and which out performs a GA ....

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-193, School of Computer Science, Carnegie Mellon University, Pittsburgh, 1994.

....models they use; 1) no interactions, 2) pairwise interactions, and (3) multivari ate interactions. In models with no interactions, variables are treated independently. Algorithms in this class work well on problems which have no interactions among variables. These algorithms include the PBIL [Baluja 94] cGA [Harik 98] and UMDA [Mhlenbein 96] algorithms. In pairwise interactions, some pairwise interactions among variables are considered. These algorithms include the MIMIC algorithm [De Bonet 97] and the algorithm using dependency trees [Baluja 97] In models with multivariate interactions, ....

Baluja, S.: Population-based incremental learning: A method for interacting genetic search based function optimization and coemptive learning, Tech. Rep. No. CMU-CS-94-163, Carnegie Mellon Univer- sity (1994).

....exist to some degree. Nevertheless, this approximation can lead to a good enough behavior in EDAs in some problems. Several approaches that correspond to this category can be found in the literature, such as Bit Based Simulated Crossover (BSC) 25] Population Based Incremental Learning (PBIL) [26], the compact Genetic Algorithm [27] and the Univariate Marginal Distribution Algorithm (UMDA) 28] Section 4.2.1 explains this algorithm in more detail. 3.4.2 Pairwise dependencies In an attempt to express the simplest possible interdependencies between variables, all the papers in this ....

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical report, Carnegie Mellon Report, CMU-CS-94-163, 1994. 27

....the PGA, but its principles are not necessarily new. We show that the algorithm can be successfully applied to the problem of symmetry detection, and outperform the standard GA. For a comprehensive, interesting discussion on related extensions to Genetic Algorithms the reader is referred to [2]. A detailed description of the PGA follows. 3.1 The Probabilistic Genetic Algorithm As in the standard genetic algorithm, in the PGA each search parameter is encoded as a binary string. The strings are tied together to form a larger string, of total length K, referred to as a chromosome, that ....

S. Baluja, Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning, Technical Report CMU-CS-94-163, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania.

.... fitness of Perform tournament selection Build MPM model using MDL Create Np Pc chromosomes by crossover Transfer Np (1 Pc) best individuals to next generation End Has population converged No Yes Figure 1: ECGA procedure on a partition of the genes and are similar to those of CGA[10] and PBIL[11]. Unlike the models used in CGA and PBIL, MPMs can represent probability distributions for more than one gene at a time. MPMs also facilitate a direct linkage map with each partition separating tightly linked genes. Hence, in the current study each gene partition would refer to a BB. A owchart of ....

S. Baluja, \Population-Based Incremental Learning: A Method of Integrating Genetic Search Based Function Optimization and Competitive Learning," Tech. Rep. CMU-CS-94-163, Carnegie Mellon University, 1994.

....the same) The increased diversity would require additional mixing (crossover) of alleles to produce a distribution more similar to a binomial. The problem is aggravated as longer strings and higher migration rates are used. The predictions should be much more accurate for algorithms such as PBIL (Baluja, 1994), UMDA (M uhlenbein and Paa , 1996) or the compact GA (Harik et al. 1998) which treat each bit independently and do not su er from the inadequate mixing problem described here. However, the predictions are adequate for the purposes of this paper, and therefore the e ect of increased diversity ....

Baluja, S.: 1994, `Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning'. Tech. Rep. No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA.

....variables are not correlated. This resembles the uniform crossover in genetic algorithms where each bit in the two parent strings is exchanged with a certain probability independently of the remaining bits. Even more closely, it resembles the populationbased incremental learning algorithm (PBIL) (Baluja, 1994) and other similar PMBGAs which treat each variable independently of the remaining variables resulting in a very strong recombination. To reduce the disruptive e ects of recombination, methods that were able to learn the structure of the problem and adapt the recombination accordingly were ....

Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning (Tech. Rep. No. CMU-CS-94-163). Pittsburgh, PA: Carnegie Mellon University.

....population representation. The probability distribution used in ECGA is a class of probability models known as marginal product models (MPMs) MPMs are formed as a product of marginal distributions on a partition of the genes and are similar to those of CGA (Harik, Lobo, Goldberg, 1998) and PBIL (Baluja, 1994). Unlike the models used in CGA and PBIL, MPMs can represent probability distributions for more than one gene at a time. MPMs also facilitate a direct linkage map with each partition separating tightly linked genes. Hence, in the current study each gene partition would refer to a BB. 2 The MPM ....

Baluja, S. (1994). Population-based incremental learning: A method of integrating genetic search based function optimization and competitive learning (Technical Report CMU-CS-94-163). Carnegie Mellon University.

....of good solutions is to assume that the variables in a problem are independent. New solutions can be generated by only preserving the proportions of the values of all variables independently of the context. This is the basic principle of the population based incremental learning (PBIL) algorithm (Baluja, 1994), the compact genetic algorithm (cGA) Harik et al. 1998) and the univariate marginal distribution algorithm (UMDA) M uhlenbein, 1997) Since these algorithms take into account only contributions of the values of each variable without considering the contexts where these contributions take ....

Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning (Tech. Rep. No. CMU-CS-94-163). Pittsburgh, PA: Carnegie Mellon University.

....population representation. The probability distribution used in ECGA is a class of probability models known as marginal product models (MPMs) MPMs are formed as a product of marginal distributions on a partition of the genes and are similar to those of CGA (Harik, Lobo, Goldberg, 1998) and PBIL (Baluja, 1994). Unlike the models used in CGA and PBIL, MPMs can represent probability distributions 4 for more than one gene at a time. MPMs also facilitate a direct linkage map with each partition separating tightly linked genes. Hence, in the current study each gene partition would refer to a BB. The MPM ....

Baluja, S. (1994). Population-Based Incremental Learning: A Method of Integrating Genetic Search Based Function Optimization and Competitive Learning (Technical Report CMU-CS94 -163). Carnegie Mellon University.

.... the area of genetic algorithms (GA) Instead of simulating an entire population of n individuals according to selection, crossover and mutation, several authors have highlighted new models of Evolutionary Computation (EC) where a distribution of gene probabilities is used to generate individuals [1, 2, 3, 13]. Moreover, this distribution can be computed in such a way that its behavior simulates and encompasses the behavior of a standard binary GA. This distribution is used to generate individuals which can be evaluated. These generated individuals are possibly used with their fitness values to update ....

.... significant for the field of EC, and that it can be applied efficiently to complex domains which do not need to be binary like for instance in [10] In this paper we will focus on two GA inspired methods: the Bit Simulated Crossover (BSC) 13] and the Population Based Incremental Learning (PBIL) [1, 2, 3]. The second type of optimization techniques considered in this paper are a subpart of ant colonies optimization (ACO) 4] namely the Ant System (AS) 5] In AS, a population of individuals also evolves but with very different principles from GAs. One general AS technique consists in using ....

[Article contains additional citation context not shown here]

Baluja S. (1994). "Population-based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning". Tech. Rep. CMU-CS-94-163, Carnegie Mellon University.

....the distribution of good solutions assumes the independence between the features 2 of the problem. New candidate solutions are sampled by only regarding the proportions of the values of the variables independently to the remaining ones. Population Based Incremental Learning (PBIL, Baluja [5]) Compact Genetic Algorithm (cGA, Harik et al. 20] Univariate Marginal Distribution Algorithm (UMDA, Muehlenbein [42] and BitBased Simulated Crossover (BSC, Syswerda [57] are four algorithms of this type. They work well in problems with no significant interactions (or relationships) among ....

Baluja, S., Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning, Technical Report CMUCS -94-163, Carnegie Mellon University, Pittsburgh, PA, 1994.

....work was supported by the University of the Basque Country under the grant 9 UPV EHU 00140.22612084 2000. C. Gonzalez is also supported by UPV EHU. variables of the joint probability distribution. In the simplest case it is supposed that all the variables of the problem are independent, 3] [4], 5] PBIL) 1] and [6] In a second step second order relations between the variables are considered, De Bonet et al. 7] A step forward involves factorizing the joint probability distribution in a tree like structure [8] Recently, some works have appeared where the joint probability ....

....two parameters. The remainder of this work is organized as follows. Section 2 describes PBIL. Section 3 is dedicated to show some experimental results. A theoretical analysis is presented in Section 4, leaving Section 5 to draw conclusions. 2 An introduction to PBIL PBIL was introduced by Baluja [4] in 1994. This algorithm is based on the idea of substituting the individuals of the population by a set of statistics of them. In our case we suppose that the function to optimize is defined in the binary space # = 0, 1 l . At each iteration of the algorithm a vector of probabilities p = ....

S. Baluja, "Population Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning", Carnegie Mellon Report, CMU-CS-94163, 1994.

....of the joint probability distribution are made. A review of the di#erent approaches in the combinatorial and numerical fields can be seen in Larranaga et al. 3, 4] and Pelikan et al. 5] The Population Based Incremental Learning algorithm (PBIL) can be considered as an EDA, as proposed by Baluja [6]. PBIL supposes that all the variables are independent. At each step of the algorithm a probability vector is maintained. This vector is sampled # times to obtain # new solutions. The # # best solutions are selected and these are used to modify the probability vector with a neural ....

....and a component of a vector by a normal letter. The random variables will be written in capital letters. We use the letters m and r as component indexes, and the letters i and k as vector indexes, hence y i,m will represent the mth component of the y i individual. PBIL was introduced by Baluja [6] in 1994 and further improved by Baluja and Caruana [22] in 1995. This algorithm is based on the idea of substituting the individuals of a population by a set of their statistics. In our case we suppose that the function to optimize is defined in the binary space # = 0, 1 l with # = 2 ....

S. Baluja, "Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning," Technical Report CMU-CS-94-163, (1994) (Computer Science Department, Carnegie Mellon University).

.... population iterative improvement algorithms are equivalent to the (1 1) ES and (1; ES, respectively [5, 6] assuming independence between variables. Population Based Incremental Learning (PBIL) was proposed as an optimization algorithm which removes the genetics from the genetic algorithm [1, 3], and has created much of the initial interest in probabilistic modelling EAs. PBIL can be re formulated for continuous search spaces [10, 12] by using the update rule p 0 (x) N ( 0 ; oe) 8) Phi : p t 1 (x) N ( i;t 1 ; oe) 9) with i;t 1 = 1 Gamma ff) i;t ffx t (10) for the ....

S. Baluja, "Population-Based Incremental Learning: A method for integrating genetic search based function optimization and competitive learning," Techn. Report CMU-CS-94-163, School of Computer Science, Carnegie Mellon University, 1994.

....exist to some degree. Nevertheless, this approximation can lead to a good enough behaviour in EDAs in some problems. Several approaches that correspond to this category can be found in the literature, such as Bit Based Simulated Crossover (BSC) 64] Population Based Incremental Learning (PBIL) [2], the compact Genetic Algorithm [29] and Univariate Marginal Distribution Algorithm (UMDA) 45] Section 4.2.1 explains this algorithm in more detail. 3.4.2 Pairwise dependencies In an attempt to express the simplest possible interdependencies between variables, all the papers in this category ....

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Carnegie Mellon Report, CMU-CS-94163, 1994.

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S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Carnegie Mellon University, 1994.

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S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Computer Science, Carnegie Mellon, 1994.

.... to generate new solutions, BSC generates new query points by stochastically assigning each bit s value with the probability of having seen that value in the previous population (the value specified by the weighted count) The ideas incorporated into Population Based Incremental Learning (PBIL) [1] were similar to those used in BSC. While BSC used a population of solutions from which the sampling statistics were entirely rederived after each generation, PBIL incrementally adjusts its sampling statistics after each generation. PBIL is similar to a cooperative system of discrete learning ....

....Basic PBIL Framework PBIL employs a simple probabilistic model to independently track the distributions of the bits in the high evaluation solutions. In each generation, only the samples with the best evaluations contribute to the next generation s population; the remaining members are discarded [1][2] This is akin to truncation selection in genetic algorithms. The algorithm works as follows: candidate solutions are generated by sampling a real valued vector, P. P specifies the probability of generating a 1 in each bit position. A number of solution vectors are generated by stochastically ....

Baluja, S. (1994), "Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning," Technical Report CMUCS -94-163, Carnegie Mellon University, Pittsburgh, PA.

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Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning (Tech. Rep. No. CMU-CS-94-163). Pittsburgh, PA: Carnegie Mellon University.

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Baluja, S., 1994, Population-based incremental learning: A method of integrating genetic search based function optimization and competitive learning, Technical Report CMU-CS-94-163, Carnegie Mellon University.

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Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Comp. Sci. Dep., Carnegie Mellon U.

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S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Comp. Sci. Dep., Carnegie Mellon U., 1994.

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S. Baluja, Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning, Technical Report CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, 1994.

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Baluja, S.: Population based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA (1994).

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Baluja, S. , "Population based incremental learning: A method for integrating genetic search based function optimization and competitive learning", Technical Report No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, Pennsylvania, 1994.

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S. Baluja, Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning, Tech. Report CMU-CS94 -163, Carnegie Mellon University, Pittsburgh, Pennsylvania, 1994.

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Baluja, S. (1994). Population based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report No. CMUCS -94-163, Carnegie Mellon University, Pittsburgh, Pennsylvania.

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Baluja, S. (1994), Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning,, Technical Report CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA.

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Shumeet Baluja, Population Based Incremental Learning -- A Method for Integrating Genetic Search Based Function Optimisation and Competitive Learning, (Tech. Rep. No. CMUCS -94-163). Pittsburgh, PA: Carnegie Mellon University (1994)

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S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competive learning. Technical Report CMUCS -94-163, Computer Science Department, Carnegie Mellon University, 1994.

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S. Baluja. Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical Report No. 163, Carnegie Melon University, Pittsburgh PA, 1994.

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S. Baluja. Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical Report No. 163, Carnegie Melon University, Pittsburgh PA, 1994.

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Baluja S.: Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Technical Report No. 163. Carnegie Melon University, Pittsburgh PA (1994)

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S. Baluja. Population-Based Incremental Learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, School of Computer Science, Carnegie Mellon University, 1994.

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Shumeet Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Pittsburgh, PA, 1994.

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Shumeet Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Carnegie Mellon University, 1994.

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Shumeet Baluja, Population Based Incremental Learning -- A Method for Integrating Genetic Search Based Function Optimisation and Competitive Learning, (Tech. Rep. No. CMU-CS94 -163). Pittsburgh, PA: Carnegie Mellon University (1994)

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Baluja, S.: Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Tech. Rep. No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA (1994)

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S. Baluja, "Population--based incremental learning: A method for integrating genetic search based function optimization and competitive learning," Tech. Rep. CMU-CS-94-163, Carnegie Mellon University, 1994. 23

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S. Baluja. Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Carnegie Mellon University, 1994.

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Baluja S Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Carnegie Mellon University,1994.

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Baluja, S. 1994. Population-based incremental learning : A method for integrating genetic search based function optimization and competitive learning. Tech Rep. CMU-CS-94-164, Dept. Comp . Sci., Carnegie-mellon Uni.

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Baluja S Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Carnegie Mellon University,1994.

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