As migratory birds, geese exhibit a high degree of collaborative, energy-efficient, and dynamic adaptability in their flight behavior. This paper proposes a new Wild Goose Optimization Algorithm (WGOA), inspired by the natural behavior of geese. The algorithm constructs a mathematical model that incorporates dynamic formation weights, a leadership rotation mechanism, energy balance, and random perturbations. By simulating the behavioral characteristics of geese during migration, the algorithm achieves efficient search for complex optimization problems. The paper details the algorithm's individual representation, group structure, position update formula, energy regulation mechanism, and convergence conditions, providing theoretical support and mathematical foundations for nature-inspired optimization algorithms.