The simulated annealing algorithm

We may assume without loss of generality [4] that the objective is to locate the minimum of a function X = (x, Xj.—xJ. (Capital letters designate vectors, lowercase letters with 

The parameter p controls the performance of the algorithm it may depend on the value of the objective functions (KXJ and/or the number of executed iterations, k, as discussed below. 

Because analogies other than physical annealing may be used to motivate the simulated annealing optimization [S] one m conjecture that the probability of accepting or rejecting a step in (f) could be determined from distributions other than Boltzman s. However, exploratory calculations carried out with normal and rational polynomial distributions (v th the required properties) showed that none were as effective as the Boltzman distribution. 

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Note The segmentation operation yields a near-optimal estimate x that may be used as initialization point for an optimization algoritlim that has to find out the global minimum of the criterion /(.). Because of its nonlinear nature, we prefer to minimize it by using a stochastic optimization algorithm (a version of the Simulated Annealing algorithm [3]). 

The simulated annealing algorithm (37) for the partitional clustering as we required in this work was designed based on the following problem formation. 

Let us consider an isotropic porous medium under the reconstruction described by a pore phase function fgk r) in the /cth iteration step of the simulated annealing algorithm and let the actual statistical characteristics of this phase function, i.e., the two-point correlation function, be Rgk u). The distance of from the target morphological characteristics Rgtarset(u) of the... 

The simulated annealing algorithm typically starts from the random phase function ff r) having the required porosity s = In the Arth iteration step,... 

This computational approach of finding the optimal alignment for the Kalman filter resolution of the overlapped shifted spectra by the simulated annealing algorithm has been tested on simulated overlapped spectra obtained by linear combination of Gaussian-Lorentzian curves, synthetically generated using the mathematical model described by Eqn. (9)... 

Partitioning is most appropriate when one is only interested in the subsets or clusters, while hierarchical decomposition is most applicable when one seeks to show similarity relationships between clusters. Section 2.1 formalizes the combinatorics of the partitional strategy and Section 2.2 does the same for hierarchical methods. The formulations we derive here provide the basis for the application of the simulated annealing algorithm to the underl5dng optimization problem as we show in Section 3. 

The simulated annealing algorithm requires a generation mechanism to create a Boltzmann distribution at a given temperature T... 

Corana, A. Marches , M. Martini, C. Ridella, S. Minimizing multimodal functions with the simulated annealing algorithm. ACM Trans. Math. Software 1987,13, 262-281. 

Corana A., Marches M., Martini C., Ridella S., Minimizing Multimodal Functions of Continuous Variables with the Simulated Annealing Algorithm. ACM Transactions on Mathematical Software, 1987, 13(3), Pages 262-280. 

We now define the simulated annealing algorithm. Let s be the current state and N s) be a neighbourhood of 5 that includes alternative states. By selecting one state s e N(s) and computing the difference between the current state cost and the selected state energy as D =f f) /( ), s is chosen as the current state based... 

The IBA DataFurnace utilizes the simulated annealing algorithm to analyze RBS, ERD, and... 

In this case, the operations optimization over a time horizon of some one hundred decision time intervals took approximately one minute by using a low-end PC and Matlab environment and the simulated annealing algorithm (Otter and van Ginneken, 1987). 

M. Kundu, S.S. Bandyopadhyay, Modelling vapour— Uquid equilibrium of CO2 in aqueous N-methyldiethanolamine through the simulate annealing algorithm. Can. J. Chem. Eng. 83(2), 344-353 (2005)... 

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