Population-based Search Relying on Spatial and/or Temporal Scale-free Behaviors of Individuals

We develop two types of simple population-based search algorithms that model two types of scale-free behaviors of individuals. The scale-free behavior is a particular behavior of individuals of species that search for food not cooperatively but independently. One type of the scale-free behaviors is that a moving distance of an individual from the present food source follows a power low distribution, which is called the spatial scale-free behavior. The other is that a staying duration of an individual at the preset food source follows a power low distribution, which is called the temporal scale-free behavior. We assume static and dynamic problems in which a position of the best food source (the global optimum) is not changed and changed, respectively. In addition, we assume a special event that individuals near the best food source are probabilistically eliminated. We compare the two search algorithms and show that they are complementary with respect to suitable problems. Therefore, we develop a search algorithm that initially includes both types of individuals in a population and evolutionarily adaptively increases an appropriate type of individuals in it. The algorithm is shown to be not the best but work quite well for any problems used.