A Novel Approach to Optimization Problem without Objective Function

For optimization problem in complex systems, normally, the objective funtion is hardly obtained or quantified. In this paper, a novel approach is presented. Its first procedure is to model the objective function by fitting complete data with NN. Secondly, global optimization solutions would be searched for the fitted objective function with genetic algorithm (GA). Moreover, Peaks function inside MATLAB and actual PID control system were selected to demostrate the approach, respectively. The results show that the optimal values and the correspnding solutions between original function and fitted function were both very close. Therefore, the methodology, which combines modeling approach NN with global optimization algorithm GA, could effectively solve optimization problem without objective function.