Rainbow Trout Optimization Algorithm

To address the problems of traditional swarm intelligence algorithms, such as reliance on gradient or gradient-like information, conservative dynamic structures, and susceptibility to local optima, this paper proposes a rainbow trout optimization algorithm based on non-conservative induced flow field, curvature refraction modulation, topological backflow memory, entropy-driven splitting, and energy conservation violation mechanisms. This algorithm, from the perspective of fluid dynamics and non-equilibrium statistical physics, treats the objective function as the source term of the induced flow field. By introducing an antisymmetric curl coupling matrix, a non-conservative dynamic system is constructed, enabling the search trajectory to maintain a downward trend while possessing flow-around capability. Furthermore, a curvature refraction tensor is constructed to achieve anisotropic step-size modulation, and a continuous backflow kernel replaces the traditional skip-memory strategy. The algorithm as a whole adopts a second-order dynamic structure and combines swarm entropy and system energy evolution laws to achieve adaptive splitting and energy injection. Theoretical analysis shows that this method belongs to a dissipative non-equilibrium system at the dynamic system level, possessing stronger global exploration capabilities and structural representation capabilities. Finally, the algorithm's complexity and stability are analyzed to demonstrate its potential advantages in high-dimensional complex optimization problems.