Abstract
Global optimization problem still becomes an interest due to the challenge of locating the global optimum of nonlinear objective function with multiple local minima. Two challenges on solving global optimization problem are; firstly how to reach the better minimizer from the current minimizer, and secondly how to decide that the obtained minimizer is the desired global minimizer. One of the recent considered deterministic easy applied methods, which concerned in the mentioned problems, is the filled function method. The basic concept of filled function method is to build such an auxiliary function to locate a point with lower function value than the current minimizer. One of the keys to the successfully filled function method is how to decide the search direction to reach and locate a better local minimizer. In this paper, a three-dimensional filled function method and its search direction are introduced. The algorithm is presented and implemented to some benchmark test function. The numerical performance of the method on solving three-dimensional global optimization problems is presented.
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