Global optimization method based on the selective averaging coordinate with restrictions

There are described ideas of design of non-differentiable global optimization algorithms, which are based on: separation in time of exploratory and pattern steps, selective averaging of coordinates on the results of test movements, adaptive reconstruction the size of rectangular region of test motions and taking into account the restrictions in the form of inequalities and equalities. Inequality restrictions are less restrictive than equality constraints. If there is only inequality restrictions and a fairly wide feasible region one can (before every working step) relatively simple implement the procedure of placing the sampling points in the admissible region. In other cases, penalties are used. Sampling points with are uniformly placed in a rectangular area centered at the point from which the algorithm performs the pattern step. Most of the sampling points (or all) are out of the admissible area. For these points are formed penalties. They are of two types: 1) the calculation of the normalized core pattern steps built in the form of the product cores for function to be minimized, for functions with violated inequalities and for modules of all functions with equality restrictions, and 2) minimizing the penalty function. In test points the penalty function has several forms built on combinations of operations of maximization and summation. In all global optimization algorithms the transformations of optimized functions and functions of restrictions are performing for dimensionless variables. This increases accuracy and reduces the number of adjustable parameters in the algorithms. Convergence rate of the algorithm is rather high: 5-12 pattern steps in the absence and in the presence of additive noise of high intensity for optimized functions.

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