Minimize the average mean first passage time of random walk in complex networks by genetic algorithm

We investigate the methods of rewiring a given connected network so that the average mean first passage time (AMFPT) for random walk processes can be reduced. Two rewiring mechanisms are used, which we call the zeroth order method (Z) and the higher order method (H) according to the series expansion analysis of the first passage time. We aim at finding the optimal sequence of rewiring action of k units long composed of the Z and H methods that yields the maximal reduction of average mean first passage time. We use both the simple genetic algorithm (SGA) and mutation only genetic algorithm (MOGA) and the results show in general MOGA produces networks with higher reduction of AMFPT for benchmark tests on all three major classes of complex networks (ER, BA, WS). In general, the higher order method appears more often in the networks with large clustering coefficient. The networks with small clustering coefficient will develop to regular networks through the zeroth order rewiring method, while the networks with initially large clustering coefficient have preference to reduce the number of small loops through the higher order rewiring method. We also apply our rewiring sequence of three steps on real networks (IEEE30, IEEE 57) and produce remarkable reduction on the AMFPT. This indicates that our method of analysis can be of practical importance for engineering.