Memetic Algorithms and the Fitness Landscape of the Graph Bi-Partitioning Problem

In this paper, two types of fitness landscapes of the graph bipartitioning problem are analyzed, and a memetic algorithm — a genetic algorithm incorporating local search — that finds near-optimum solutions efficiently is presented. A search space analysis reveals that the fitness landscapes of geometric and non-geometric random graphs differ significantly, and within each type of graph there are also differences with respect to the epistasis of the problem instances. As suggested by the analysis, the performance of the proposed memetic algorithm based on Kernighan-Lin local search is better on problem instances with high epistasis than with low epistasis. Further analytical results indicate that a combination of a recently proposed greedy heuristic and Kernighan-Lin local search is likely to perform well on geometric graphs. The experimental results obtained for non-geometric graphs show that the proposed memetic algorithm (MA) is superior to any other heuristic known to us. For the geometric graphs considered, only the initialization phase of the MA is required to find (near) optimum solutions.