Using Genetic Algorithms to Find Good K-Tree Subgraphs

Many combinatorial problems which are (NP) hard on general graphs yield to polynomial algorithms when restricted to k-trees which are graphs that can be reduced to the k-complete graph by repeatedly removing degree k vertices having completely connected neighbors. We present a genetic algorithm which seeks a heuristic optimum solution by generating an evolving population of k-tree subgraphs. Each is evaluated by computing an exact optimum over the subgraph, which provides a feasible solution over the original graph. Then we validate our algorithm by testing it on the task of finding a minimum total cost 3-tree in a complete graph.

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