Research And Improvement Of Light Ray Optimization Algorithm

There exist many optimization problems in various fields of scientific researchengineering application. Complication, scale and other aspects of optimization objects areincreasing. Intelligence algorithms, based on biological intelligence or natural phenomena,characterize in the simple and general usage, sounding robustness and fitting for parallelprocessing. Therefore, they become a powerful tool for solving large-scale complexoptimization problems.Light ray optimization algorithm is a new intelligent optimization algorithm based onFermat’s principle. The algorithm searches the optimal solution by simulating the propagationprocess of light in gradient-index media, and provides a new idea for intelligent computingsolving optimization problems. The algorithm was proposed to solve the problem that globaloptimum is not easy to search. It has the advantages of not involving random factors, fewtuning parameters, simple structure, and being easy to realize. In light ray optimizationalgorithm, the searching area is divided by rectangular grids which are full of media withdifferent refractivities, that is let the propagation velocity of light in each grid be the objectivefunction value of some point in this grid. Then the searching path is assumed to be thepropagation path of light rays. Refraction and reflection merely occur on the boundaries ofgrids, and light rays propagate along straight lines in the same grid. The refraction path ischosen as optimal path when refraction and reflection occur simultaneously. The reflectionpath is chosen as optimal path when only reflection occurs, that is the conditions of totalreflection are satisfied. According to these rules, light rays propagate in these media to searchthe optimal value automatically in the algorithm.Theoretical study of optimization methods is important to perfect algorithm systems,improve algorithm performance and widen its application fields. Therefore, optimizationmechanism, convergence and stability of light ray optimization algorithm were theoreticallyanalyzed based on variational principle. And then the algorithm was used for solving functionoptimization problems. The concrete research contents are as follows:Firstly, optimization mechanism of light ray optimization algorithm was analyzed, andthe following conclusions were proved. Refractions in the algorithm alternatively occur inboth horizontal and vertical directions, that is the setting of rectangular grids is meanful. The decrease of objective function is accelerated and the increase of function is reduced byrefraction in algorithm. Reflection will inevitably occur if the search along the directions thatmake the increase of function value keep going. Feasibility of the algorithm was proved fromthe theoretic aspect.Secondly, according to Fermat’s principle and variational method, realization ofminimization process was derived in light ray optimization algorithm based on refraction, thatis concrete analysis of optimization function of the algorithm was made in layered medium.Light rays have the auto optimization property that will get closer to the direction that makesrefractivity increase, and get further from the one that makes it decrease. From the real lightpath in continuous media and by analyzing the equations that light rays are satisfied, the papergot the conclusion that real light rays also have the optimization function. The relationbetween the searching path determined by light ray optimization algorithm and the onedetermined by light rays equation was analyzed, and auto optimization function of algorithmin partitioned medium was also derived.Thirdly, the relation between Euler method of ray equations and the iterative formula oflight ray optimization was studied. Light ray optimization algorithm was improved by addinga term to the iterative formula of this algorithm, by which the accuracy is increased and orderand the convergence speed is accelerated. This solve the problem that light ray optimizationalgorithm has a slow convergence speed when it is used for computing high dimensionalproblems.Fourthly, light ray optimization algorithm is an intelligent algorithm with the weak localoptimization ability and the difficulty of perfection of convergence theory. To solve theseproblems, greedy light ray optimization algorithm was proposed. Local convergence of theproposed algorithm was proved via theoretical derivation. Comparing with light rayoptimization algorithm, the only difference of greedy light ray optimization algorithm is thatreflection path is chosen as optimal path when function value increases. It doesn’t accept any“bad solution”, and is suitable for solving single extremum optimization problems.Fifthly, theoretical analysis and numerical experiments show that the smaller the grid,the higher accuracy solution is obtained, but with the increasing iterative times and slowerconvergence speed. An improved algorithm named light ray optimization algorithm based onvariable grid was proposed to solve this problem. Large grids are used to determine the approximate position of global optimal point at the early stages of the optimization, and thensmaller grids are used to continue searching. Grid size can be reduced for many timesaccording to concrete precision requirement, which improves the convergence precision andspeed.Sixthly, light ray optimization algorithm was used for solving two dimensional, onedimensional, and more than three dimensional optimization problems, and was comparedexperimentally with genetic algorithm, simulated annealing algorithm and particle swarmoptimization algorithm. Local convergence of light ray optimization algorithm solving onedimensional optimization problems was analyzed by variational method.Seventhly, a new hybrid algorithm named light ray optimization algorithm based onannealing strategy was proposed by introducing the annealing strategy of simulated annealingalgorithm. By introducing grid free thought, light ray optimization based on grid free methodwas proposed. This algorithm doesn’t need grid generation, but determines refraction orreflection interfaces according to certain rules. Study and comparative analysis of numericalexperiments of these two improved algorithms were made respectively.