page_title: Spiral optimization algorithm
section_title: Algorithm
hierarchical_section_title: Spiral optimization algorithm / Algorithm
caption_attribution_description: English: Spiral Optimization (SPO) algorithm
context_page_description: The spiral optimization algorithm is an uncomplicated search concept inspired by spiral phenomena in nature.
  The first SPO algorithm was proposed for two-dimensional unconstrained optimization
  based on two-dimensional spiral models. This was extended to n-dimensional problems by generalizing the two-dimensional spiral model to an n-dimensional spiral model.
  There are effective settings for the SPO algorithm: the periodic descent direction setting
  and the convergence setting.
context_section_description: The SPO algorithm is a multipoint search algorithm that has no objective function gradient, which uses multiple spiral models that can be described as deterministic dynamical systems. As search points follow logarithmic 
  spiral trajectories towards the common center, defined as the current best point, better solutions can be found and the common center can be updated.
  The general SPO algorithm for a minimization problem under the maximum iteration  (termination criterion) is as follows:
  0) Set the number of search points  and the maximum iteration number .
  1) Place the initial search points  and determine the center , ,and then set .
  2) Decide the step rate  by a rule.
  3) Update the search points: 
  4) Update the center:  where .
  5) Set . If  is satisfied then terminate and output . Otherwise, return to Step 2).
caption: Spiral Optimization (SPO) algorithm