A fuzzy global optimization method for parallel computation

Using the capacity of multiple operated relatively low speed or slack computers instead of expensive supercomputers for the numerical solution of complex problems become popular on the last few years. In this study a fuzzy global optimization algorithm modified for parallel computation is proposed. The main motivation of this study lies in the use of an ordinary controller to find the roots of an objective function by means of a closed loop control system approach. If a transfer function of a plant, in a closed loop control system with a reference input r, is replaced by the objective function f(x) then the output of a properly designed controller driving the plant converges the solution of the equation f(x)-r=0 at the steady-state. The algorithm can also be used to find the roots of the derivative of the objective function that represent the local minimum or maximum. The references will then point to these extremums of the objective function. In a multi-computer environment a master computer dynamically shares and updates the search intervals and the reference levels between the subscribers on the network, resulting in the increase in the search speed. When a slave finds a better local solution while others are trying to solve the equation, this new value is set as a new reference for the other computers. This will increase their errors resulting the output of their respective controllers vary faster than single computer case. By enabling the division of the search space into many sub-intervals, this method offers an increase in the performance of the algorithm.