Hybrid Bridge-Based Memetic Algorithms for Finding Bottlenecks in Complex Networks

We propose a memetic approach to find bottlenecks in complex networks based on searching for a graph partitioning with minimum conductance. Finding the optimum of this problem, also known in statistical mechanics as the Cheeger constant, is one of the most interesting NP-hard network optimisation problems. The existence of low conductance minima indicates bottlenecks in complex networks. However, the problem has not yet been explored in depth in the context of applied discrete optimisation and evolutionary approaches to solve it. In this paper, the use of a memetic framework is explored to solve the minimum conductance problem. The approach combines a hybrid method of initial population generation based on bridge identification and local optima sampling with a steady-state evolutionary process with two local search subroutines. These two local search subroutines have complementary qualities. Efficiency of three crossover operators is explored, namely one-point crossover, uniform crossover, and our own partition crossover. Experimental results are presented for both artificial and real-world complex networks. Results for Barabási–Albert model of scale-free networks are presented, as well as results for samples of social networks and protein–protein interaction networks. These indicate that both well-informed initial population generation and the use of a crossover seem beneficial in solving the problem in large-scale.