algorithm converges to a stationary point under the maximum iteration . The settings of and the initial points are the same with the above Setting 1. The setting of is as follows. Set at Step 2) as follows: where is an iteration when the center is newly updated at Step 4) and such as . Thus we have to add the following rules about to the Algorithm: •(Step 1) . •(Step 4) If then . Future works The algorithms with the above settings are deterministic. Thus, incorporating some random operations make this algorithm powerful for global optimization. Cruz-Duarte et al. demonstrated it by including stochastic disturbances in spiral searching trajectories. However, this door remains open to further studies. To find an appropriate balance between diversification and intensification spirals depending on the target problem class (including ) is important to enhance the performance. Extended works Many extended studies have been conducted on the SPO due to its simple structure and concept; these studies have helped improve its global search performance and proposed novel applications. References Collective intelligence Multi-agent systems Evolutionary algorithms Optimization algorithms and methods