Orthogonal direction algorithm for global function optimization

A global optimization algorithm for function optimization named orthogonal direction algorithm was raised. This algorithm uses 3 times of large ranged orthogonal design to find the approximate location of the global optimization solution and then uses several times of small ranged orthogonal design to make precise approach. In each times of orthogonal design, the experimental points which detect the design space are generated according to the orthogonal table around a central point and the range of the design variables decrease gradually. After each times of orthogonal design, one-dimension search is also employed to improve search precision, the search direction is determined by the central point and the best (or worst) design points. This algorithm need less times of objective function calculation and is easy to make program. Two numerical optimization problem and a trajectory optimization problem of a rocket-powered horizontal-launched single-stage-to-orbit vehicle were solved to test this algorithm. These examples show when the peak of the objection function is less than the number of experimental points provided by the orthogonal table, orthogonal direction algorithm can often find the global optimization solution with small calculation.