Geometric crossover for multiway graph partitioning

Abstract

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. Our new genetic algorithm outperforms existing ones.

Quotient geometric crossovers and redundant encodings

“…Corollary 1 then guarantees that this crossover can be understood as a geometric crossover GY associated with the phenotype space (Y, d Y ). As anticipated, the presented IQX coincides to the labeling-independent crossover presented in [21].…”

“…As a preliminary work [21,27], we presented a well-designed metric suitable for the multiway graph partitioning problem, which presents a redundant encoding, and designed a geometric crossover defined on the corresponding metric space successfully. However, the idea of the previous work is applicable only to a specific problem (multiway graph partitioning) and does not apply to other problems with redundant encoding.…”

Vertex Ordering, Clustering, and Their Application to Graph Partitioning

“…We made experiments on the six graphs that have been used in many studies [3,5,8,9,10,11,12,15]. The different classes of graphs are briefly described below.…”

“…They have also been successfully used to solve the graph partitioning problem [3,5,8,9,10,11,12]. Kim et al [6] presents a deep survey of genetic approaches for graph partitioning.…”

Linkage-Based Distance Metric in the Search Space of Genetic Algorithms

“…Different metrics produce different topologies and thus change the shape of the search space. When a space is to be searched by a genetic algorithm (GA), a good distance metric facilitates navigation of the space [2][3][4][5] and can also improve the effectiveness of search [6][7][8][9][10][11][12]. Hamming distance is a popular metric in a discrete space that is to be searched by a GA. Hamming distance has also been widely used in analyses of solution spaces [13][14][15].…”