Mathematical Optimization Models
Javad Alikhani Koupaei; Mohammad Javad Ebadi; Majid Iran Pour
Abstract
This study aims to compare the performance of the First Carrier Wave Chaos Optimization (FCW) algorithm with other optimization methods to determine the appropriate shape parameter of radial basis functions (RBF) for solving partial differential equations (PDEs). The selection of the FCW method is based ...
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This study aims to compare the performance of the First Carrier Wave Chaos Optimization (FCW) algorithm with other optimization methods to determine the appropriate shape parameter of radial basis functions (RBF) for solving partial differential equations (PDEs). The selection of the FCW method is based on its simplicity and foundational characteristics among chaotic optimization algorithms. To achieve this goal, a two-stage process will be employed, in which the Kanza method, based on non-grid-based local techniques, is combined with the FCW method. In the first stage, the FCW algorithm is used to obtain the optimal shape parameter for the radial basis function, and then in the second step, the Kanza method is employed to estimate the root mean square (RMS) error for the approximate solutions. The numerical results derived from two partial differential equations, employing the PSO and FCW algorithms, reveal an approximate 95% conformity. This signifies the effectiveness and efficiency of this methodology in estimating appropriate shape parameters. It accentuates the pivotal role of chaos-based optimization algorithms as powerful tools in the effective resolution of partial differential equations.
stochastic/Probabilistic/fuzzy/dynamic modeling
Hossein Jafari; Mohammad Javad Ebadi
Abstract
The Cramer-Rao lower bound is obtained by using integration by parts and the Cauchy-Schwarz inequality. The integration by parts formulas of Malliavin calculus plays a role in this study. The point estimation problem is very crucial and has a wide range of applications. When we deal with some concepts ...
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The Cramer-Rao lower bound is obtained by using integration by parts and the Cauchy-Schwarz inequality. The integration by parts formulas of Malliavin calculus plays a role in this study. The point estimation problem is very crucial and has a wide range of applications. When we deal with some concepts such as random variables, the parameters of interest and estimates may be observed as imprecise. Therefore, the theory of fuzzy sets is important in formulating such situations. Using the fuzzy set theory, we define a fuzzy-valued random variable and fuzzy stochastic process. We use the Malliavin derivative and Skorohod integral to study the asymptotic properties of the statistical model for fuzzy random variables. We show how to use the conditional expectations of certain expressions to derive Cramer-Rao lower bounds for Fuzzy valued Random Variables that they do not require the explicit expression of the likelihood function. As an example, we consider a fuzzy random sample of size n induced by independent standard normally distributed random variables with fuzzy parameter.