Spiral Optimization Algorithm Using Periodic Descent Directions

A few years ago, the authors proposed a nature-inspired metaheuristic concept, the spiral optimization algorithm, which was inspired by spiral phenomena in nature. The principal idea of the algorithm is to utilize spiral trajectories generated by multiple generalized spiral models for search applications. The generalized spiral model is composed of a spiral matrix defined by a composite rotation matrix and a convergence rate parameter. The setting of the spiral matrix with each initial point placement is important for its search performance, because it characterizes each spiral trajectory. This paper proposes 1) the concept of periodic descent directions for a spiral trajectory that is appropriate for optimization; 2) sufficient conditions, with examples, for the generalized spiral model to generate the periodic descent directions; 3) a setting method for the composite rotation matrix with initial search points to satisfy the conditions in the algorithm; and 4) a method for setting the convergence rate parameter to utilize the periodic descent directions effectively for its search performance. The effectiveness of the proposed method is confirmed by conducting numerical experiments under various conditions.