Orthogonal Optimization Algorithm of Swarm Intelligence Based on the Analysis of Variance Ratio

Abstract

This paper presents an algorithm of population-based orthogonal intelligent optimization against the deficiency such as much calculation amount and slow speed of global convergence in current algorithms of swarm intelligent optimization. In view of the actuality so far that the effect of optimization searching in orthogonal design has not displayed completely because it is limited to be used in initializing the swarm or to be used in optimization searching only once in general application of evolution calculation. We not only break the limitation of only once searching in the orthogonal optimization but also find out the method of confirmation for further searching direction and searching scale of orthogonal optimization which is based on the variance analysis and variance ratio analysis of orthogonal design. Moreover, using the characteristic of orthogonal design which is easy to find the optimal variable composition of the current optimal value and to find the variable interval which includes the optimal solution in one arrayed test or calculation, we put forward an orthogonal optimization algorithm of swarm intelligence optimization based on the analysis of variance ratio, which is able to be circulating in the optimization searching. Based on the further searching direction and searching scale supplied by the variance ratio analysis, the global optimal solution will be approached only by two generations of orthogonal evolution for orthogonal initialized swarm selected randomly and the accurate solution will be obtained within ten generations of orthogonal evolution if the orthogonal intelligent evolution is kept on doing. Through the simulation analysis for the Shubert multi-peaked function, it shows the orthogonal optimization algorithm of swarm intelligence optimization based on the analysis of variance ratio is much better than other current algorithms of intelligent optimization because the former has less calculation amount, shorter searching time, more rapid speed and higher accuracy of optimization searching than the latter and is without deficiency of premature or slow convergence. This new algorithm is not only suitable to solve both the unimodal function and the multi-modal function problems but also is worthy of generalizing into the practical application since the orthogonal array is very easy to be used and popularized.