Abstract
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.
Highlights
Uk Y k ; X k , xk 1 E Uk 1 Y k , yk 1; X k , xk 1 Y k U yk 1 k 1 Y k , yk 1; X k , xk 1 pX k 1,xk yk 1 Y k dyk 1.
U~k X k ,Y k min yk , ck xk 1 opt arg x k 1 min y k 1
Exk 1 min yk 1 min Y k ,0 Y k min z Y k ,0
Summary
Uk Y k ; X k , xk 1 E Uk 1 Y k , yk 1; X k , xk 1 Y k U yk 1 k 1 Y k , yk 1; X k , xk 1 pX k 1,xk yk 1 Y k dyk 1.
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