Research on Optimial Method Based on Optical Theory
|School||Harbin Engineering University|
|Keywords||Light Ray Optimization Fermat’s Principle Snell’s Law Law ofreflection convergent analysis random benchmark Particle Swarm Optimization|
The optimization problems in real life and engineering have the complex features, such as high dimensions, huge calculations, multi optima and so on. It makes the traditional optimization methods can not meet the practical requirements. So, researching a new optimization method to tackle the complex problem has a significant practical meaning.The optimized development pattern of nature provides a new solution to deal with the complex characters in the engineering optimization problems. The beauty of the nature comes from its depicting of all creations with simple rules. In this process, the nature shows out the economic with certain pattern of the optimal development.This paper will propose a new optimization method, in which there is no empirical parameter and no random elements. As one of the commonest phenomena in nature, the light ray propagating in uneven medium shows out the saving of energy. Inspired from this phenomenon, a new optimization method--Light Ray Optimization, according to the Fermat’s Principle is proposed after analyzing the refraction and the reflection of light ray. Light Ray Optimization (LRO for short) is an iterative optimization method which searches the optimization by simulating the light ray propagating in uneven transparent medium. The LRO divides the feasible region with mesh to get grids. Each grid has its medium density. Because of the different fitness value which leads different speed of light ray, the light ray will refract or reflect when propagating between the different grids, and update the searching position and searching direction. Finally, the LRO will convergent to the optimization of the problem automatically. This paper illustrates the importance of the grid chosen, and analyzes the updating process of searching direction. Based on the LRO in the2-dimensional space, the possibility of the LRO searching in n-dimensional space(n>2) is analyzed. The updating of searching direction and the definition of the angle in n-dimensional space is discussed. And the LRO is expended into the n-dimensional space.The convergence of LRO is analyzed. The theorems proof that the searching direction of light ray will lean to the steepest descent direction in horizontal and vertical direction. With the shift between the horizontal and vertical searching direction updating, LRO will convergent to the local optimization.In the numerical experiment, the LRO is applied on several benchmarks with different characters. After analyzing the searching results of the benchmarks in different dimensional spaces via LRO, the features and feasibility of LRO to different optimization problems are given. Because of the shortage of classical benchmarks, the random benchmark is introduced into the paper to test the searching ability of LRO. And the features and feasibility of LRO are further discussed.From analyzing the searching results of traditional benchmarks in numerical experiment, the paper furtherly discussed how to reduce the searching time of LRO and how to search the optimization problem with negative value. The paper discussed the practical meaning of LRO searching in2-dimensional space, and based on the2-dimensional LRO, the improvement of the grid is given. The hexagonal grid with good property is introduced to improve the searching efficiency. To LRO in N-dimensional space, the initialized big size grid is given. And with the iterative searching going on, the grid size shrinks with different patterns to reduce the searching time and improve the searching precision. This paper applied several transforms to the objective function with negative value. The modified objective function meets the requirement of LRO. The feasibility of LRO is extended.This paper compares the LRO and the PSO, which is a class of swarm intelligence. Both the advantage and the disadvantage are illustrated by analyzing the searching mechanism and searching process. The results are testified by the numerical experiment. Based on the works above, the future work of LRO is proposed, such as the initialized parameters of LRO, the searching direction updating pattern, and multi-start searching and so on.