Research On Optimal Mechanism Of Light Ray Optimization Algorithm

In order to solve the actual problems, mathematicians and engineering experts usually turn the practical problems into mathematical models, and many engineering application problems can be transformed into global optimization problems. The characteristics of these problems are high dimension, a large amount of calculation and time-consuming. Analytic methods and traditional numerical algorithms can not satisfy people’s need, because they have a lot of derivative operations and other complex operations. In recent years, many new optimization algorithms which are based on the physical phenomena in nature have appeared.The characteristics of these optimization algorithms are of strong robustness and suitable for parallel processing. Therefore, the development of new intelligent optimization algorithm has become the main research direction of experts and scholars.Light Ray Optimization Algorithm is an intelligent optimization algorithm based on Fermat’s principle, which was proposed by Proffessor Jihong Shen from Harbin Engineering University, and the algorithm searches the optimal solution by simulating light ray in nature.In this paper, the two main jobs are as follows:Firstly, many existing literatures have analyzed the optimization mechanism of Light Ray Optimization Algorithm, and they have theoretically proved the fact that the refraction occurs in two directions, both horizontal and vertical, which is helpful to searching the local optimal solution. In this paper, we prove that during the iterative process of the algorithm, the reflection will inevitably occur if refraction makes the increase of objective function value keep going on. And the function of reflection in Light Ray Optimization Algorithm is to change the searching direction, which is helpful to searching the global optimal solution.Secondly, based on amount of numerical experiments,we propose a conjecture about the relation between process of light propagation and solving optimization problems, which can be expressed as that the light ray must pass through the optimal point of objective function no matter how we choose the initial point and the initial direction. In this paper, we will prove the above conjecture under the condition of sphere function. Specifically, we derive the Euler-Lagrange differential equation of true light by means of the variational method based on Fermat’s principle. Then from the above equation, we get the special relationship between the tilt angle of the light ray’s tangent and the light ray’s position coordinates under the condition of sphere function. From this perspective, we will prove that for the sphere function,the light ray must pass through the global optimal point no matter how we choose the initial point and the initial direction.