Brown Frog Optimization Algorithm

In the fields of continuous optimization and swarm intelligence research, most existing optimization algorithms assume that the search behavior is continuous and low-cost in the time dimension, thus performing position updates in each iteration. However, in high-dimensional complex optimization problems or situations where the objective function evaluation cost is high, this assumption of "continuous updates" often leads to a large amount of ineffective search and wasted computational resources. To address this issue, this paper proposes a novel swarm intelligence optimization method—the Brown Frog Optimization Algorithm. This algorithm does not simply introduce a new biological metaphor, but rather starts from the essence of optimization decision-making, treating the search behavior as a sparse and expensive discrete decision event. By introducing fitness uncertainty perception, event-triggered jump mechanism, decomposable multimodal transition operator, and reflexive threshold learning mechanism, this paper constructs an uncertainty-aware driven sparse decision optimization paradigm. This paradigm emphasizes that "when to search" takes precedence over "how to search," providing a new theoretical perspective for swarm intelligence optimization algorithms. This paper systematically elaborates on the algorithm's mathematical modeling, dynamic evolution mechanism, and theoretical significance, and analyzes its potential advantages in complex optimization problems.