Computational Science and Techniques

This paper is focused on the Bayes approach to multiextremal optimization problems, based on modelling the objective function by Gaussian random field (GRF) and using the Euclidean distance matrices with fractional degrees for presenting GRF covariances. A recursive optimization algorithm has been developed aimed at maximizing the expected improvement of the objective function at each step, using the results of the optimization steps already performed. Conditional mean and conditional variance expressions, derived by modelling GRF with covariances expressed by fractional Euclidean distance matrices, are used to calculate the expected improvement in the objective function. The efficiency of the developed algorithm was investigated by computer modelling, solving the test tasks, and comparing the developed algorithm with the known heuristic multi-extremal optimization algorithms.

A method for the calculation of the one-particle generalized coefficients of fractional parentage for an arbitrary number of j-orbits with isospin and an arbitrary number of oscillator quanta (generalized CFPs or GCFPs) is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, an efficient algorithm for the calculation of the CFPs for a single j-orbit with isospin, and a general procedure for the computation of the angular momentum (isospin) coupling coefficients describing the transformation between different momentum-coupling schemes. The method provides fast calculation of GCFPs for a given particle number and produces results possessing small numerical uncertainties. The introduced GCFPs make it feasible calculation of expectation values of one-particle nuclear shell-model operators within the isospin formalism.

When doing a searching process, Binary Search is one of the classic algorithm used in sorted data. The characteristic of this algorithm is to make a comparison of the keywords you want to find with the start, middle, and end values of a data series. Keyword search is done by reducing the range of start and end points to finally find the keyword you want to search. The time complexity of the binary search algorithm is O(log2n) while the memory capacity needed is O(1) for iterative implementation and O(log2n) for recursive implementation. This research will develop a level of comparison in binary search in order to get optimal performance in accordance with the amount of data available.