Track Field Line Fill Function

The optimization is a widely used discipline. The filled function is an effective method for solving global optimization problems. Different numerical algorithms have great effect on numerical calculation.The properties of the steepest descent field-lines are studied. The new filled function algorithm--tracing the steepest descent field-line for filled function is proposed. The problem is transformed into solving differential equations with initial value. The existence of differential equations’solution and the convergence of the algorithm under proper conditions are proved.Finally, the multi-functions are calculated. The feasibility of the algorithm is verified.