Fast stochastic global optimization

A new stochastic optimization strategy is introduced which cascades many Metropolis-like procedures to sample a Boltzmann distribution at fixed temperatures. Global optimization of an objective f(x) in a certain class is shown to require O((Δ/T_low) ²) computational effort where Δ=max_x,x´(f(x)-f(x´)) and T_low is a low enough temperature that the Boltzmann function of f at T_low acceptably small except for optimal x. This theoretical advantage is confirmed by experimental results which are presented for a problem in vector quantization and for seven standard test problems in nonlinear optimization