The minimum conductance problem is an NP-hard graph partitioning problem. Apart from the search for bottlenecks in complex networks, the problem is very closely related to the popular area of network community detection. In this paper, we tackle the minimum conductance problem as a pseudo-Boolean optimisation problem and propose a memetic algorithm to solve it. An efficient local search strategy is established. Our memetic algorithm starts by using this local search strategy with different random strings to sample a set of diverse initial solutions. This is followed by an evolutionary phase based on a steady-state framework and two intensification subroutines. We compare the algorithm to a wide range of multi-start local search approaches and classical genetic algorithms with different crossover operators. The experimental results are presented for a diverse set of real-world networks. These results indicate that the memetic algorithm outperforms the alternative stochastic approaches.