A new global optimization method, multicanonical jump walk annealing (MJWA), is proposed and applied to the geometric optimization of Lennard-Jones and Morse clusters and the hydrophobic (B), hydrophilic (L), and neutral (N) (BLN) protein model. The method efficiently finds the global minima of these systems. In four comparative studies, MJWA greatly outperforms the conventional simulated annealing in locating the global minima. Theoretical comparison with other global optimization methods is discussed. Through this paper, we demonstrate a criterion for devising stochastic global optimization schemes. Namely, a stochastic global optimization method must favor the global minimum thermodynamically and at the same time be able to cross the high energy barriers. (C) 2000 American Institute of Physics. [S0021-9606(00)00706-6].