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Abstract: Simple central force optimization (SCFO) algorithm is a novel physically-inspired optimization algorithm as simulating annealing (SA). To enhance the global search ability of SCFO and accelerate its convergence, a novel extended/enhanced central force optimization (ECFO) algorithm is proposed through both adding the historical information and defining an adaptive mass. SCFO and ECFO are all motivated by gravitational kinematics, in which the compound gravitation impels particles to the optima. The convergence of ECFO is proved based on a more complex characteristic equation than SCFO, i.e. the second order difference equation. The stability theory of discrete-time-linear system is used to analyze the motion equations of particles. Stability conditions limit their eigenvalues inside the unit cycle in complex plane and corresponding convergence conditions are deduced related with ECFO’s parameters. Finally, ECFO are tested against a suite of benchmark functions with deterministic and excellent results. Experiments results show that ECFO converges faster than SCFO with higher global searching ability. [Copyright &y& Elsevier]