The main research objective of this paper is the development, analysis, implementation and determination of the efficiency of hybrid optimization methods applied to a variety of mathematical concepts describing real-life problems which involve a large number of variables. The optimization is carried out by a hybrid serialized cascading procedure which combines several different sub-procedures with dissimilar characteristics, sharing the same objective function. During the efficiency-determination phase, several effectiveness tests were conducted, comparing the hybrid method with other optimization techniques.
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In this article we investigate the maxima of two unilaterally approximately continuous and approximately regulated functions. In particular we prove that if / is the maximum of two unilaterally approximately continuous and approximately regulated functions then for each x is an element of Dunap(f) = {x : f is not unilaterally approximately continuous at x} the inequality f(x) < max(fap(x+),fap(x-)) holds. Moreover, we show some condition ensuring that an approximately regulated function f such that Dap(f) is countable and for each x is an element of Dunap(f) the inequality f(x) < max(fap(x+),fap(x-)) holds, is the maximum of two unilaterally approximately continuous and approximately regulated functions.
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