Diversity Loss in General Estimation of Distribution Algorithms
نویسنده
چکیده
A very general class of EDAs is defined, on which universal results on the rate of diversity loss can be derived. This EDA class, denoted SML-EDA, requires two restrictions: 1) in each generation, the new probability model is build using only data sampled from the current probability model; and 2) maximum likelihood is used to set model parameters. This class is very general; it includes simple forms of many well-known EDAs, e.g. BOA, MIMIC, FDA, UMDA, etc. To study the diversity loss in SML-EDAs, the trace of the empirical covariance matrix is the proposed statistic. Two simple results are derived. Let N be the number of data vectors evaluated in each generation. It is shown that on a flat landscape, the expected value of the statistic decreases by a factor 1−1/N in each generation. This result is used to show that for the Needle problem, the algorithm will with a high probability never find the optimum unless the population size grows exponentially in the number of search variables.
منابع مشابه
E-Bayesian Approach in A Shrinkage Estimation of Parameter of Inverse Rayleigh Distribution under General Entropy Loss Function
Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first the $ E $-Bayesian estimation of the parameter of inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter i...
متن کاملEstimation for the Type-II Extreme Value Distribution Based on Progressive Type-II Censoring
In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes ...
متن کاملBayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions
In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using variou...
متن کاملBayesian Estimation for the Pareto Income Distribution under Asymmetric LINEX Loss Function
The use of the Pareto distribution as a model for various socio-economic phenomena dates back to the late nineteenth century. In this paper, after some necessary preliminary results we deal with Bayes estimation of some of the parameters of interest under an asymmetric LINEX loss function, using suitable choice of priors when the scale parameter is known and unknown. Results of a Monte C...
متن کاملOptimal Reconfiguration of Distribution Network for Power Loss Reduction and Reliability Improvement Using Bat Algorithm
In power systems, reconfiguration is one of the simplest and most low-cost methods to reach many goals such as self-healing, reliability improvement, and power loss reduction, without including any additional components. Regarding the expansion of distribution networks, communications become more complicate and the number of parameters increases, which makes the reconfiguration problem infeasib...
متن کامل