With the popularity of multiple power domain (MPD) design, the multi-domain power network noise analysis and minimization is becoming important. This paper describes an efficient heuristic algorithm to arrange the power-up sequence in a multi-domain power network in order to minimize the noise. We present a formulation of this problem and show it is NP-complete. Therefore, we propose a simulated annealing (SA) based algorithm with preprocessing. Experimental results show that the proposed algorithm can minimize the noise close to the minimal values. In terms of efficiency, the SA algorithm is more than hundreds of times faster than the enumerating method and the running time scales well for these cases with the number of domains. In addition, we discuss the trade off between power-up efficiency and noise.