To address the common problems of premature convergence, dimensional imbalance, and local extrema in high-dimensional non-convex optimization problems, this paper proposes a swarm optimization algorithm based on non-equilibrium free energy and geometric structure regulation mechanisms—the Arapaima Energy-Driven Optimization Algorithm. This algorithm is grounded in the theory of non-equilibrium dissipative dynamic systems. By constructing individual free energy functions, it unifies the objective function term, kinetic energy term, swarm deviation term, and information entropy term into a single energy framework, thus formalizing the swarm optimization process as a free energy minimization problem. Furthermore, it introduces a local curvature approximation to construct an anisotropic step-size modulation mechanism and uses a covariance structure to construct an adaptive manifold compression mapping, achieving automatic alignment of the principal directions of the search space. Simultaneously, an irreversible dissipative memory field structure is designed to identify stagnant states and trigger asymmetric transitions. Theoretical analysis shows that the system belongs to a bounded dissipative dynamic system, with a monotonically decreasing free energy function under certain conditions and the existence of an attractor set. The algorithm possesses both physical interpretability and geometric adaptability, making it suitable for complex high-dimensional optimization problems.