Optimization of the critical diameter and average path length of social networks

Optimizing average path length (APL) by adding shortcut edges has been widely discussed in connection with social networks, but the relationship between network diameter and APL is generally ignored in the dynamic optimization of APL. In this paper, we analyze this relationship and transformthe problem of optimizing APL into the problem of decreasing diameter to 2.We propose a mathematic model based on a memetic algorithm. Experimental results show that our algorithm can efficiently solve this problem as well as optimize APL.