Noncooperative Population-Based Search Relying on Spatial and/or Temporal Scale-Free Behaviors of Individuals

Abstract

Although individuals of species engaging in cooperative foraging behaviors are often modeled as swarm intelligence optimization algorithms, there are also several species whose individuals take noncooperative foraging behaviors. Some such species exhibit common behaviors, which we call scale-free behaviors in this study. A type of scale-free behavior is spatial scale-free behavior, in which the moving distance of an individual from the present food source follows a power-law distribution. Second, the staying duration of an individual at the current food source follows a power-law distribution, and this behavior is called temporal scale-free behavior. We propose two types of noncooperative population-based search methods, based on the two types of scale-free behaviors. We also conducted simulations to compare the two methods, assuming static and dynamic environments in which the position of the food source did not change and changed, respectively. The simulation results showed that temporal scale-free behavior is suitable for specific problems in which individuals around the global optimum can be eliminated probabilistically, and spatial scale-free behavior is suitable for problems in which such elimination never occurs. In other words, the two types of scale-free behaviors are complementary. Next, we first assume problems for which we cannot know if the probabilistic elimination of individuals occurs in advance, and then propose a search method that selects an appropriate type of scale-free behavior for individuals during the search. The simulation results showed that this method demonstrates a good search performance, on average, for such problems.