An Exact Random Number Generator for Visiting Distribution in Gsa

Global optimization is widely used in various aspects both in industry and academia. Although different methods in operations research have been proposed to solve the global optimization, simulated annealing and its variations have been favored for their simplicity in the implementation. In order to reach the global optimum from the current solution, a walking mechanism must be planned so that global optimum can be reached stochastically with high probability. The walking mechanism is the stochastic rule to find the next solution from the current solution. One of the most promising walking mechanisms is represented as Tsallis distribution. In this study, an exact simulation method is proposed for the Tsallis distribution that is used in performing generalized simulated annealing (GSA), a global optimization algorithm suggested by Tsallis (1996). First, the Tsallis variate (random variable) is transformed linearly into a standard Tsallis variate with one parameter v q . Then the structure of a t distribution variate is imitated to obtain the standard Tsallis variate. A ratio of a standard normal variate over a square root function of the Gamma variate with proper chosen parameters’ values renders the standard Tsallis distribution variate. This method is suitable for all v q in the range 1 to 3. Theoretical justification is provided in supporting the proposed method. A numerical example, given originally by Tsallis and Stariolo, on the GSA is studied on the effect to which the v q has on the convergence to the optimal solution. A conclusion can be drawn from the results that the development of the exact simulation method is crucial in obtaining the correct results by using GSA.