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An Edge-Set Representation Based on a Spanning Tree for Searching Cut Space

The encoding or representation scheme in evolutionary algorithms is very important because it can greatly affect their performance. Most previous evolutionary algorithms for solving graph problems have traditionally used a vertex-based encoding in which each gene corresponds to a vertex. In this paper, addressing the well-known maximum cut problem, we introduce an edge-set encoding based on the spanning tree – a kind of edge-based encoding. In our encoding scheme, each gene corresponds to an edge subset derived from a spanning tree.

In contrast to a traditional edge-based encoding in which each gene corresponds to only one edge, our encoding scheme has the advantage of representing only feasible solutions, so there is no need to apply a repair step. We present a genetic algorithm based on this new encoding. We have conducted various experiments on a large set of test graphs including commonly used benchmark graphs and have obtained performance improvement on sparse graphs, which frequently appear in real-world applications such as social networks and systems biology, in comparison with a scheme using a vertex-based encoding.

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