Flip-Sunfish Optimization Algorithm

To address the problems of local extremum traps, dimensional coupling imbalances, and premature swarm convergence in high-dimensional complex optimization problems, a non-equilibrium dynamics-based optimization algorithm for pufferfish overturning is proposed. The algorithm uses the core evolutionary framework of "inertial propulsion—energy compression—curvature modulation flipping—anisotropic recovery—information flow field coupling—swarm phase transition" as its core evolutionary framework. The stagnation process is formalized as an accumulative energy variable, and a structure-aware direction flipping mechanism is executed under energy threshold triggering. An adaptive amplitude control is achieved by constructing a curvature modulation operator through numerical approximation of the local diagonal curvature of the objective function; submanifold contraction is achieved by constructing an anisotropic recovery tensor through gradient magnitude; swarm-level potential field coupling is achieved by constructing a global information flow field through kernel function superposition; and a phase transition perturbation mechanism is introduced when the swarm variance decreases to enhance global exploration capabilities. The algorithm as a whole can be represented as a multinomial coupled nonlinear discrete dynamic system. Theoretical analysis shows that the proposed method possesses boundedness and asymptotic convergence trend under local Lipschitz continuity conditions. The proposed framework provides a new modeling approach for swarm intelligence algorithms based on a non-equilibrium energy release mechanism.