A novel convergent filled function algorithm for multi-dimensional global optimization

As we all know, the filled function method as an effective algorithm to solve global optimization problems can overcome the defect that the non-linear algorithm is trapped in the local minimizer and cannot jump to attach the global minimizer, which has attracted the attention of researchers. However, when solving multi-dimensional global optimization problems, the filled function often lacks good properties such as mandatory, convexity and continuity, which makes the conventional filled function algorithm to always encounter the difficulty that its convergence cannot be guaranteed. In view of this, a novel convergent filled function algorithm for multi-dimensional global optimization is proposed. In this algorithm, by the way of the coordinates rotate, the multi-dimensional global optimization problem is transformed into several one-dimensional sub-problems, and then the new filled function with good properties is constructed to solve the one-dimensional sub-problem, which leads to attachment of the convergence in algorithm. Finally, compared with the existing algorithms on test optimization problems in NETLIB library, the effectiveness of the algorithm is verified by numerical experiments.