The Research On Convergence About A Function Of Light Ray Optimization Algorithm

With the rapid development of science, the continuous progress of the society, the problems encountered in scientific research and practical engineering are becoming more and more complicated, optimization problems are often encountered in the practice of production.In the process of solving the optimization problems,there are always some difficulties,such as the high dimension, the large amount of computation, time-consuming and complex process. Hence, traditional optimization algorithms are not available to meet the needs of people. At this time, some intelligent algorithms based on biological intelligence or natural phenomena have emerged. These algorithms are simple, robust and suitable for parallel computing. Therefore, many mathematical scholars and engineering experts turn their attention to the new area of the new intelligent optimization algorithm.Based on Fermat's principle, Professor Shen Jihong in 2007 first proposed Light Ray Optimization. It is a complete simulation of the propagation path of true light in different media. The feasible region is divided into a number of small rectangles. The algorithm assumes that the medium is uniform in the same rectangular grid,which is filled with the same refractive index of the medium each rectangular grid, and the path of finding the optimal solution is conceived as the actual light. In the optimization process, the adjustable parameters are few and the iteration rule is simple.This paper mainly completed the following two work:1. We made the analysis of the results of a large number of numerical experiments in the existing literature. For the spherical function, a conjecture is proved by the theory of the light propagation process and the optimization problem: starting from any initial point, the light emitted in any initial direction is bound to be the optimal point of the target function. On the basis of this paper, the spherical function was extended to a class of functions so that the application of the Light Ray Optimization became simpler. Specifically, divided the function into two parts,we converted it into spherical form by function transformation,then solved it by means of the algorithm, finally, we got the optimal solution by the inverse transformation of implicit function. Meanwhile, the feasibility was verified by some examples.2. In the case of random selection of initial point and initial direction, we made a comparative study of the convergence speed of the objective function transformation by numerical experiments for four functions. The experimental results showed that under the same condition, the convergence of the transformed spherical function was better than that of the target function before transformation, then we explained the reason from the aspect of the complexity of the algorithm.