Bull Shark Optimization Algorithm

To address the problems of traditional swarm intelligence algorithms, such as susceptibility to local extrema, lack of unified dynamic interpretation of search mechanisms, and difficulty in theoretically characterizing convergence behavior in complex high-dimensional non-convex optimization problems, this paper proposes a Bull Shark optimization algorithm based on the modeling ideas of dynamic permeation fields and non-equilibrium dissipative systems. The algorithm treats individuals in the population as a particle system moving in an information permeation field. By constructing a global permeation potential function, it unifies the optimal solution attraction information, local gradient structure information, and population density distribution information under the same field function framework. Furthermore, a continuous-time stochastic dynamic system model is introduced, characterizing the search process as controlled stochastic differential equations. By defining a system energy function, a phase transition between reversible diffusion modes and irreversible compression modes is achieved. To enhance adaptability in high-dimensional spaces, a local curvature modulation diffusion mechanism based on discrete second-order differences is introduced. Simultaneously, a memory entropy control structure is constructed to avoid directional collapse, and a non-Gaussian impact transition mechanism is used to improve global search capability. Theoretical analysis shows that the proposed method has an interpretable dynamic structure and stability analysis space. Numerical experimental results demonstrate that the algorithm exhibits good convergence performance and robustness on multimodal complex functions and high-dimensional optimization problems.