H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm. I: Continuous parameter optimization," Evol. Comput., vol. 1, no. 1, pp. 25--49, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....x, x i , x j . This rule will allow n or less closely grouped individuals to stay in the population, and expel those more than n. The discrete recombination is most often used in ESs [20, 21] The discrete recombination has also produced good results with real coded GAs (such as Breeder GA) [22]. The implementation is that each new individual s objective variable is randomly decided from one of the two pre selected parents. If parent 1 is (x 1 , x n ) and parent 2 is (y 1 , y n ) We generate o#spring (z 1 , z n ) where z i = x or y , #i # 1, n , x i or ....

....If parent 1 is (x 1 , x n ) and parent 2 is (y 1 , y n ) We generate o#spring (z 1 , z n ) where z i = x or y , #i # 1, n , x i or y i are chosen with probability 0.5. Parts of the mutation operator have been inspired by the breeder genetic algorithm (BGA) [22]. For each objective variable, the probability to perform a mutation is pm . We use pm = 1 n. The Gaussian mutation is implemented as follows. z i = x i 0.1 (x x i ) N(0, 1) i and x i are the upper and lower boundaries of variable x i , respectively, and i # 1, n . N(0, 1) ....

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H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm I. continuous parameter optimization," Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

....results in Sections 3 and 4 respectively. Conclusions are drawn in Section 5. 2 Methods A variation of the Self adaptive Pareto frontier Di#erential Evolution (SPDE) algorithm [1] is used. We present this variation here followed by a similar algorithm using a Breeder Genetic Algorithm (BGA) [9, 10] selection strategy for single objective evolutionary optimization. 2.1 The multiobjective algorithm: The SPDE Algorithm SPDE is a variation of PDE [2, 3] where both crossover and mutation rates self adapt. In the current paper, we do not allow for mutation. The crossover rate is inherited from ....

H. Muhlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithms: continuous parameter optimization. Evolutionary Computation, 1(1):25--49, 1993.

....[9] On the other hand, directly using a real coded representation seems to be naturally suitable when dealing with problems using variables in a continuous domain. In this case, an individual is a vector of floating point numbers. These types of real coded GAs have proven to be very successful [10,11,12]. In this research we aim to tackle the above issues of diversity and representation by extending a cellular GA in two ways. Firstly a selection method making use of the dynamics generated by predator prey interactions is introduced to the GA population. We use prey individuals to represent ....

Muhlenbein, H. & Schlierkamp-Voosen, D. (1993). Predictive Models for the Breeder Genetic Algorithm I: Continuous Parameter Optimization. Evolutionary Computation 1, p.25-49.

....to different channels during the connection time (GAS) The GAS uses all the channels of the cellular environment to reallocate the calls in course and to assign channels to the new calls requests. The proposed GA models are characterized by adaptive parameters [8] truncation selection scheme [9], three point crossover strategy [10] random immigrant mechanism [7] and elitist policy [11] differing from the canonical GA. The performance of each genetic model was evaluated by means of extensive simulations in an environment formed by 49 cells with 70 channels each. Uniform and nonuniform ....

....proposed models seek for a policy, that is, a set of states of all the cells optimising the system use. The proposed GA models use the standard genetic operators (selection, crossover, and mutation) together with random immigrant mechanism [7] adaptive parameters [8] truncation selection scheme [9], greedy policy [11] and three point crossover strategy [10] The number of control parameters in a GA, including population size, mutation, crossover, and selection rates, must be determined. The most important parameter is the amount of variability in the individual chromosomes in the ....

H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive Models for the Breeder Genetic Algorithm Continuous Parameter Optimization", Evolutionary Computation, The MIT Press, vol. 1, no. 1, spring 1993.

....algorithms (when the function to optimize is differentiable) 11] Optimizing continuous (non discrete) parameter functions with EAs requires real parameter genetic coding and highly sophisticated algorithms. Some EAs attempt to solve these problems by working directly on continuous data ( 1] 8] [9]) The use of EAs has shown to be efficient for boolean neural network learning ( 7] 13] Sometimes in certain neural learning problems the only way to find In the framework of function approximation using neural networks 2 a good network is to use EAs. When the parameters of the network belong ....

H. Muhlenbein and Dirk Schlierkamp-Voosen. Predictive Models for the Breeder Genetic Algorithm: Continuous Parameter Optimization. Evolutionary Computation, 1(1), 1993.

....2 [ Gamma100; 100] i = 1; 2. 3.1 Experimental conditions The configuration of the genetic algorithm handling each subpopulation is the following one: Linear ranking selection. Elitism. Stochastic Universal Sampling (SUS) 13] Real coding. Extended intermediate recombination [14]. Let P 1 and P 2 be the two parents; the two offspring C 1 and C 2 are generated in the following way: ae C 1 = P 1 ff(P 2 Gamma P 1 ) C 2 = P 2 ff(P 1 Gamma P 2 ) 4) where ff is an uniform random number in [ Gamma0:25; 1:25] The crossover rate is 0.9. BGA Mutation [14] ae x 0 ....

....[14] Let P 1 and P 2 be the two parents; the two offspring C 1 and C 2 are generated in the following way: ae C 1 = P 1 ff(P 2 Gamma P 1 ) C 2 = P 2 ff(P 1 Gamma P 2 ) 4) where ff is an uniform random number in [ Gamma0:25; 1:25] The crossover rate is 0.9. BGA Mutation [14] ae x 0 = x Sigma 0:2(x max Gamma xmin )ffi ffi = P k Gamma1 i=0 ff i 2 Gammai (5) with k = 16 and ff i = 1 with probability equal to 1=k, otherwise ff i = 0; the mutation rate is 0:9. Periodicity of diversification = 5 (one diversification generation after 4 intensification ....

Muhleinben, H., Schlierkamp-Voosen, D.: "Predictive Models for the Breeder Genetic Algorithms: I. Continuous Parameter Optimization", Evolutionary Computation, 1 (1) 25--49 (1993).

....versus population size for the massively multi modal function. using a mutation based GA. In fact, a bit wise mutation operator is found to be detrimental in our study. To solve such problems reliably, an adequate population size and a schemapreserving crossover operator are necessary. Although Muhlenbein and Schlierkamp Voosen (1993) have shown that a breeder GA (BGA) can solve this function in 49n log n (where n is the number of variables) function evaluations, BGA is a real coded implementation and uses a line search which cannot be implemented for binary strings. Moreover, their crossover operator explicitly exploits the ....

Muhlenbein, H., Schlierkamp-Voosen, D. (1993). Predictive models for breeder genetic algorithm: Continuous parameter optimization. Journal of Evolutionary Computation, 1 (1). 25--49.

....a Markovian base model. Thierens and Goldberg [4] Back [5] as well as Blickle and Thiele [6, 7] determined the selection intensity of selection methods, a notion adopted from quantitative genetics [8] and introduced in the field of evolutionary computation by Muhlenbein and Schlierkamp Voosen [9]. This quantity may be used to derive the takeover time if the initial population s distribution differs from the original definition given above. This approach also neglects extinction by chance. In case of spatially structured populations Sarma and De Jong [10, 11] postulated that the growth of ....

H. Muhlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm I: Continuous parameter optimization. Evolutionary Computation, 1(1):25--49, 1993.

....inspired dynamical systems should exploit the results developed in theoretical biology. The problem, however, is that the theoretical questions raised in evolutionary computation usually differ from those raised in theoretical genetics. An exception was detected by Muhlenbein Schlierkamp Voosen [31], who presented a specific evolutionary algorithm that can be analyzed via a theory originally developed for quantitative genetics [32,33] Although this approach is limited to additively separable fitness functions and infinitely large populations, it contributes a piece to the mosaic of ....

H. Muhlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm I: Continuous parameter optimization. Evolutionary Computation, 1(1):25--49, 1993.

....(EA) have been applied to many optimization problems successfully in recent years. Genetic algorithms (GA) 1] evolution strategies (ES) 2] and evolutionary programming (EP) 3] are three major fields in EA. One of the essential applications of EA is global optimization on numerical problems [4, 5, 6, 7]. A common feature of EA on solving numerical functions is the usage of the step size concept. EP and ES both use self adaptation to adjust the step size and improve the search progress. The self adaptation schemes normally have the trend of tuning the objective variables with smaller step sizes ....

H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm I. Continuous parameter optimization," Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

....criteria decision making) 1] Although being designed for the BAe problem, the techniques used are generic and could be easily integrated with other conceptual design problems. 2 Genetic algorithms and the optimisation module The genetic algorithm used is based on the Breeder Genetic Algorithm [7]. It also utilises genetic operators suitable for real valued chromosome: arithmetic crossover, exponential mutation etc. As genetic algorithms in general are scalar function optimisers, we have adapted it to use techniques for multi objective optimisation [4] Techniques that we have used ....

Muhlenbein, H. and Schlierkamp-Voosen, D., "Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization", Evolutionary Computations, 1(1)1993, pp. 25--49.

.... but it also plays an important role in constructing high performance application systems (Carbonell, 1990) Recently, Koza introduced a new learning paradigm, called genetic programming (Koza, 1992a) which extends conventional evolutionary algorithms (Back and Schwefel, 1993; Goldberg, 1989; Muhlenbein, 1993) in that the structures undergoing adaptation are hierarchical computer programs instead of bitstrings. Genetic programming has been successfully applied to learn computer programs for solving many interesting problems in artificial intelligence and artificial life (Koza, 1992a; Koza, 1994; ....

....the optimal complexity will also differ from one problem to another. However, the overall analysis suggests that small networks should be preferred to larger ones if no information is available about the configuration space, confirming the principle of Occam s Razor (Blumer et al. 1987; Zhang and Muhlenbein, 1993a) 4 Fitness Functions for Evolving Parsimonious Programs The Bayesian framework offers one approach to the bias variance problem by formalizing the intuitive idea behind Occam s Razor. As described in Section 2, the goal of genetic programming is to find a model A whose evaluation f A (x) ....

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Muhlenbein, H. and Schlierkamp-Voosen, D. (1993). Predictive models for the breeder genetic algorithm I: Continuous parameter optimization. Evolutionary Computation, 1(1):25--49.

....comparison of the Multivalued Evolutionary Algorithm with modal mutations with recently published results concerning the performance of Bayesian Sampling and Very Fast Simulated Reannealing techniques for global optimization is given. I. Introduction For the Breeder Genetic Algorithm (BGA) [5] a discrete mutation scheme is used which tests much more often in the neighborhhod of a given point. In the first section we formulate a generalization of this mutation scheme and analyze its robustness for two test functions from [5, 12] This analysis leads to the notion of continuous modal ....

....I. Introduction For the Breeder Genetic Algorithm (BGA) 5] a discrete mutation scheme is used which tests much more often in the neighborhhod of a given point. In the first section we formulate a generalization of this mutation scheme and analyze its robustness for two test functions from [5, 12]. This analysis leads to the notion of continuous modal mutations. These mutations are shown to be more robust then discrete ones. In the second section we introduce a new simple scaling rule for multiple mutations. Comparisons with a new step size control for Evolution Strategies are given. The ....

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H. Muhlenbein and D. Schlierkamp--Vosen "Predictive Models for the Breeder Genetic Algorithm, I. Continuous Parameter Optimization " Evolutionary Computation 1 (1):25--49, 1993

....in a tree by means of multiple binary weights. Evolving Optimal Neural Networks 7 3 Genetic breeding of neural networks 3. 1 Breeder genetic programming (BGP) For the evolution of optimal neural networks we use the concepts based on the breeder genetic algorithm, BGA, of Muhlenbein et al. [25]. While the usual genetic algorithms model a natural evolution, the BGA models a rational selection performed by human breeders. The BGA can be considered as a recombination between evolution strategies (ES) 27, 30] and genetic algorithms (GA) 8, 5] The BGA uses truncation selection as ....

....artificial intelligence [4, 18, 31] The discrete valued weights may be extended to more general real valued weights. In this extension, it will be necessary to modify or replace the discrete hillclimbing search by a continuous parameter optimization method which may be again genetic algorithms [25, 30] or conventional gradient based search methods [29] Notice that this adaptation does not change the top level structure of the breeder genetic programming method described in Figure 4. As opposed to conventional learning algorithms for neural networks, the genetic programming method makes ....

H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive Models for the Breeder Genetic Algorithm I: Continuous Parameter Optimization," Evolutionary Computation, 1 (1993) 25--49.

....L. This represents the fifth consideration in the modeling process, the approximation or optimization process O (this includes the initialization of the free parameters) There are a range of methods that may be used for this optimization process, including simulated annealing, genetic algorithms [13] and neural networks. Neural networks normally represent methods employing harmonic or hyperbolic basis functions (a sigmoid is a hyperbolic construct) and generally Sigma combinations. The parameters to optimize are the weights , or f i g above. The learning procedure is the method used to ....

H. Muhlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm: Continuous parameter optimization. Evolutionary Computation, 1, 1993.

....a technique should, if possible, be easily parallelisable, so as to take advantage of the nowadays widely available parallel computers, with the aim to further reduce the search time. In the last years Muhlenbein and Schlierkamp Voosen proposed an approach called Breeder Genetic Algorithms (BGAs) [9, 10, 11] which can be seen as a recombination between Evolution Strategies (ESs) 12] and GAs. In fact BGAs use truncation selection which is very similar to the ( strategy in ESs and the search process is mainly driven by recombination making BGAs very similar to GAs. It has been proved that BGAs ....

....truncation selection which is very similar to the ( strategy in ESs and the search process is mainly driven by recombination making BGAs very similar to GAs. It has been proved that BGAs can solve problems more efficiently than GAs due to the theoretical faster convergence to the optimum [10] and they can, like GAs, be easily written in a parallel form, so we wish to test them on the inverse design. The paper is organised as follows. Section 2 describes the BGAs. In section 3 the problem faced is described in detail and in section 4 the Parallel BGA (PBGA) is depicted. Section 5 ....

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H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive Models for the breeder Genetic Algorithm I. Continuous Parameter Optimization," Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

....results in a conservative estimate of the convergence quality. We compare this estimate with the prediction from the gambler s ruin model in the experimental section of this paper. Muhlenbein derived an expression for the expected quality of convergence for the counting bits (or one max) problem [8]. Calibrating their theoretical results with empirical experimentation resulted in a very accurate model for the particular problem they studied. C. Decomposing the problem Despite their operational simplicity, GAs are complex algorithms. To have any hope of understanding and designing GAs we ....

....of good individuals in the population. However, selection methods differ in how they allocate copies of good individuals. More formally, the selection intensity can be viewed as the expected average fitness after selection of a population whose fitness distribution is normally distributed [8]. The selection pressure of tournament selection varies with the size of the tournament size s. As the tournament 0 20 40 60 80 100 Pop size 0.6 0.7 0.8 0.9 1 Proportion BBs Fig. 6. Results comparing theory and experimental results for a 100bit one max function varying the selection intensity. ....

H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm: I. Continuous parameter optimization, " Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

....III. Evolving Sigma Pi Nets In order to evolve problem specific sigma pi networks we use the breeder genetic programming (BGP) 36] Similar to GPs, BGP uses tree representation for individuals. BGP uses, however, ranking based truncation selection as in the breeder genetic algorithm (BGA) [26] instead of fitnessproportionate selection or tournament selection [2] Another feature of BGP is its fitness function which uses the Occam s razor principle. The truncation selection combined with Occam s razor has been proved useful to balance the accuracy and parsimony of multilayer ....

H. Muhlenbein and D. Schierkamp-Voosen, "Predictive models for the breeder genetic algorithm I: Continuous parameter optimization, " Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

....method for constructing minimal neural networks. Using an Occam s razor in the fitness function, the method prefers a simple network architecture to a complex one. The weights are trained not by backpropagation, but by a next ascent hillclimbing search. The breeder genetic algorithm BGA (Muhlenbein et al. 1993) is used for evolving optimal networks. The paper is organized as follows. In Section 2, the fitness function for the genetic search of minimal complexity solutions is derived. The representation scheme and genetic operators as well as the control algorithm for adapting the architectures and the ....

....But it is easily seen that minimization of the fitness function (4) approximates maximization of p(M) under the assumption (6) 3 GENETIC BREEDING OF MINIMAL NEURAL NETS 3. 1 BREEDER GENETIC ALGORITHM For the evolution of minimal neural networks we use the breeder genetic algorithm BGA of Muhlenbein et al. 1993). In contrast to the usual GA s model of natural evolution, the BGA models rational selection performed by human breeders. The BGA maintains a population P consisting of M individuals of neural networks. Each network of the initial population, P(0) is generated with a random number of layers. The ....

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H. Muhlenbein, and D. Schlierkamp-Voosen (1993). Predictive models for the breeder genetic algorithm I: continuous parameter optimization. Evolutionary Computation, 1(1).

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Muhlenbein,H., & Schlierkamp-Voosen, D. (1993b). Predictive Models for the Breeder Genetic Algorithm: Continuous Parameter Optimization. Evolutionary Computation, 1:25-- 49.

....by competition is demonstrated for multimodal functions. 2 The BGA for Continuous Parameter Optimization Let an unconstrained optimization problem be given on a domain D ae IR n min(F (x) a i x i b i i = 1; n : 1) The breeder genetic algorithm BGA was designed to solve the above problem [6]. The BGA depends on some control parameters which we summarize shortly. The selection is done by truncation selection, also called mass selection by breeders. The T best of the individuals are selected as parents and then mated randomly. Discrete recombination Let x = x 1 ; xn ) and y ....

....operator is able to locate the optimal x i up to a precision of range i Delta 2 Gamma(k Gamma1) Discrete recombination is a breadth search. It uses the information contained in the two parent points. The BGA line recombination tries new points in a direction defined by the parent points. In [6] we have proven that a BGA with popsize N = 1 (1 parent, 1 offspring, the better of the two survives) using only mutation has approximate linear order of convergence for unimodal functions. Theorem 1. Given a point with distance range i Delta 2 Gamma(k Gamma1) r range i to the optimum, then ....

[Article contains additional citation context not shown here]

Heinz Muhlenbein and Dirk Schlierkamp-Voosen. Predictive Models for the Breeder Genetic Algorithm: Continuous Parameter Optimization. Evolutionary Computation, 1(1):25--49, 1993.

....to the great variety of algorithms we also have a great variety of selection operators. This ranges from proportionate selection [5] tournament selection [6, 2] selection [12, 13, 1] Boltzmann selection [9] linear and exponential ranking selection [4, 17] to truncation selection [10, 3, 8]. Perhaps the most widespread used selection schemes in modern Evolutionary Algorithms are tournament selection and truncation or ( selection. With this paper we consider selection from a breeder s perspective. The ultimate selection scheme in livestock breeding is truncation selection. The ....

H. Muhlenbein & D. Schlierkamp--Voosen "Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization". Evolutionary Computation 1:335--360, 1993

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H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm. I: Continuous parameter optimization," Evol. Comput., vol. 1, no. 1, pp. 25--49, 1993.

No context found.

H. Muhlenbein and D. Schlierkamp-Voosen, "Predictive models for the breeder genetic algorithm. I: Continuous parameter optimization", Evolutionary Computation, 1, No. 1, pp. 25-49, 1993.

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H. Muhlenbein and D.S. Voosen, "Predictive models for the breeder genetic algorithm: I continuous parameter optimization," Evolutionary Computation, vol. 1, no. 1, pp. 25--49, 1993.

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