Evolutionary Algorithms and Matroid Optimization Problems

Joachim Reichel and Martin Skutella

Algorithmica, to appear. An extended abstract appeared in Proceedings of the 9th Genetic and Evolutionary Computation Conference (GECCO'07), 947-954, 2007.

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evolutionary algorithms, matroids, minimum weight basis, matroid intersection, randomized search heuristics

We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NP-hard combinatorial optimization problems (including many well-known examples such as minimum spanning tree and maximum bipartite matching). We obtain very promising bounds on the expected running time and quality of the computed solution. Our results establish a better theoretical understanding of why randomized search heuristics yield empirically good results for many real-world optimization problems.

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