Global Nonlinear Optimization Based on Wave Function and Wave Coefficient Equation

Abstract

A method was developed for deriving the approximate global optimum of a nonlinear objective function with multiple local optimums. The objective function is expanded into a linear wave coefficient equation, so the problem of maximizing the objective function is reduced to that of maximizing a quadratic function with respect to the wave coefficients. Because a wave function expressed by the wave coefficients is used in the algorithm for maximizing the quadratic function, the algorithm is equivalent to a full search algorithm, i.e., one that searches in parallel for the global optimum in the whole domain of definition. Therefore, the global optimum is always derived. The method was evaluated for various objective functions, and computer simulation showed that a good approximation of the global optimum for each objective function can always be obtained.