Abstract
A novel learning algorithm for solving global numerical optimization problems is proposed. The proposed learning algorithm is intense stochastic search method which is based on evaluation and optimization of a hypercube and is called the hypercube optimization (HO) algorithm. The HO algorithm comprises the initialization and evaluation process, displacement-shrink process, and searching space process. The initialization and evaluation process initializes initial solution and evaluates the solutions in given hypercube. The displacement-shrink process determines displacement and evaluates objective functions using new points, and the search area process determines next hypercube using certain rules and evaluates the new solutions. The algorithms for these processes have been designed and presented in the paper. The designed HO algorithm is tested on specific benchmark functions. The simulations of HO algorithm have been performed for optimization of functions of 1000-, 5000-, or even 10000 dimensions. The comparative simulation results with other approaches demonstrate that the proposed algorithm is a potential candidate for optimization of both low and high dimensional functions.
Highlights
One of the basic problems of numerical optimization techniques is the computing globally optimal solutions of highdimensional functions
The algorithms based on derivatives of the cost functions are called derivative based learning algorithms, and the algorithms that do not use the derivatives of the cost functions are called derivative free learning
This paper proposes the hypercube optimization algorithm to solve multivariate systems for global optimization
Summary
One of the basic problems of numerical optimization techniques is the computing globally optimal solutions of highdimensional functions. Number of researches has been done on global optimization, but there are still not many powerful techniques for optimization of dense high-dimensional problems. Some learning algorithms have been designed for global optimization of high-dimensional functions. As shown the designed algorithms are basically modification, improvement, and adaptation of existing evolutionary algorithms in DE, PSO, and GA Using these methods the researchers try to obtain reasonable results for optimization functions. The novel method that solves high-dimensional global optimization problems having sizes of 1000, 5000, and 10000 is proposed. The HO algorithm is based on designing hypercube, selecting the best elements and applied them to multivariate systems for optimization of the objective function This algorithm approaches optimal points using the best elements determined during learning.
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