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

In this paper, two types of tness landscapes of the graph bi-partitioning problem are analyzed, and a memetic algorithm { a genetic algorithm incorporating local search { that nds near-optimum solutions eeciently is presented. A search space analysis reveals that the tness landscapes of geometric and non-geometric random graphs diier significantly , and within each type of graph there are also diierences 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 epis-tasis 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 nd (near) optimum solutions.