Fishing for interactions: A network science approach to modeling fish school search

Computational swarm intelligence has been demonstrably shown to efficiently solve high-dimensional optimization problems due to its flexibility, robustness, and (low) computational cost. Despite these features, swarm-based algorithms are black boxes whose dynamics may be hard to understand. In this paper, we delve into the Fish School Search (FSS) algorithm by looking at how fish interact within the fish school. We find that the network emerging from these interactions is structurally invariant to the optimization of three benchmark functions: Rastrigin, Rosenbrock and Schwefel. However, at the same time, our results also reveal that the level of social interactions among the fish depends on the problem. We show that the absence of highly-influential fish leads to a slow-paced convergence in FSS and that the changes in the intensity of social interactions enable good performance on both unimodal and multimodal problems. Finally, we examine two other swarm-based algorithms - -the Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO) algorithms - -and find that for the same three benchmark functions, the structural invariance characteristic only occurs in the FSS algorithm. We argue that FSS, ABC, and PSO have distinctive signatures of interaction structure and flow.