Adaptive Light Ray Optimization Algorithm Based On Householder Transform

The optimization problem has been widely used in a variety of fields,ranging from modern engineering,economic management,control science to design planning,while the optimization method,the solution to the optimization problem,is a branch of mathmatics which has rapidly developed over the past few years.With the development and application of computer science and artificial intelligence,the optimization theory and the optimization method both have been popularized and developed,becoming the necessary know-how for scientific researchers and managerial staff.Due to the fact that optimization problems have been consistently growing complicated,traditional optimization methods can only find the local minima of optimization problems,and the results depend on the initial conditions,so they are no longer suitable for solving some high-dimensional,multi-parameter and large data volume problems.Therefore,some intelligent optimization algorithms based on natural phenomena and physical phenomena have been proposed.Proposed by Professor Shen Jihong of Harbin Engineering University in 2007,Light Ray Algorithm,LRO for short,is a intelligent optimization algorithm employing the propagation law of light to find the optimal solution,where the theory basis is Fermat's Principle,Refraction Law and Reflection Law in Geometric Optics.Hence,this paper aims to accomplish the following three tasks:Firstly,the updating rules of searching position and direction in LRO were analyzed,and the problem of wasting refraction iteration steps in the process of achieving total reflection condition was put forward in this paper,based on which Householder Transform was thus introduced.The definition of Householder transformation in N-dimensional Euclidean space was given by analyzing the Householder transformation of any vector on the orthogonal and non-orthogonal axes.Therefore,the Householder matrix and the calculation formula for updating the search direction were deduced when light rays reach to the horizontal and vertical planes according to the Householder transform.Secondly,the existence of Householder matrix was proved,aiming to ensure the feasibility of Householder transform in adaptive algorithm for ray optimization.The adaptive conditions of Householder transform and the algorithm flow of ray optimization adaptive algorithm were given.Thirdly,it was concluded that the improved adaptive algorithm shortened the search time,saved iteration steps and improved the search efficiency under the condition of effective optimization,as a result of the greater effectiveness of the adaptive algorithm based on Householder transform verified by numerical experiments and the comparison to the LRO before it was improved.