Simulated Annealing

Step 0. Initialize X_o,Y_o=f_o(X_o), T_o>0 and k=0.

Step1. Generate a candidate point W_k+1 using a specific direction generator and step size generator.

Step2. Update the new point with acceptance probability.

Step 3. Update temperature according to a cooling schedule.

Step 4. If the stopping criterion is met, stop. Else increment k and continue from Step1.

The acceptance probability is determined by Metropolis criterion, i.e. the candidate point is accepted with probability 1 if it is improving and with probabiity exp{[fo(X)-f(W)]/T_k} if it is not improving. The cooling schedule adopted here has the form

T_i+1=bT_i

where b is the temeperature reduction factor and is set empirically to 0.6. The number of iterations between each temeperature iteration depends on the dimension of the problem and is set in the program. The initial temeprature value can be specified by the user, or a default option of 300 is also available.

Reference: Neogi, S., Zabinsky, Z.B. and Tuttle, M.E. "Constrained Global Optimization with Continuous and Discrete Variables using Simulated Annealing", under preparation