A population-based optimization method using Newton fractal

Abstract

We propose a deterministic population-based method for a global optimization, a Newton particle optimizer (NPO). The algorithm uses the Newton method with a guiding function and drives particles toward the current best positions. The particles’ movements are influenced by the fractal nature of the Newton method and are greatly diversified in the approach to the temporal best optimums. As a result, NPO generates a wide variety of searching paths, achieving a balance between exploration and exploitation. NPO differs from other metaheuristic methods in that it combines an exact mathematical operation with heuristics and is therefore open to more rigorous analysis. The local and global search of the method can be separately handled as properties of an associated multidimensional mapping.