After solving problems like Unit Commitment and Economic Dispatch it is important to consider some special constraint which come directly from nature of generators. These constraints which will mention are some related to temperate limits and other are related to dynamic of turbines. In this paper after solving the unit commitment problem and economic dispatch simultaneously, the main effect of this constraints and method for skip them will be tried. In the next part the main cost function will be detailed this kind of functions on problems which consider two cost function instead of one The main algorithm that used is nested PSO. The nested PSO can optimize two function which one is in the inner layer of other one.The second algorithm which will try the results is NSGA-II.