A Memetic Algorithm for the Minimum Conductance Graph Partitioning Problem

TL;DR

This paper introduces a memetic algorithm for solving the NP-hard minimum conductance graph partitioning problem, combining local search and evolutionary strategies to improve solution quality on real-world networks.

Contribution

The paper presents a novel memetic algorithm with an efficient local search and evolutionary framework specifically designed for the minimum conductance graph partitioning problem.

Findings

The memetic algorithm outperforms other stochastic approaches.

It effectively finds high-quality partitions in real-world networks.

The approach demonstrates robustness across diverse network datasets.

Abstract

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.