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Multi-objective Minimum Spanning Trees

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Abstract

In this chapter, we analyze multi-objective evolutionary algorithms (MOEAs) on an NP-hard multi-objective combinatorial optimization problem, namely the multi-objective minimum spanning tree problem. Many successful evolutionary algorithms have been proposed for this problem (Knowles and Corne, 2001; Zhou and Gen, 1999). In Chapter 5, we showed that stochastic search algorithms are able to compute minimum spanning trees in expected polynomial time. The analysis is based on the investigation of the expected multiplicative distance decrease (where the distance is measured as the weight difference between the current solution and an optimal one) and serves as a starting point for the analysis of the multi-objective minimum spanning tree problem.

Keywords

  • Span Tree
  • Extremal Point
  • Connected Graph
  • Pareto Front
  • Minimum Span Tree

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-16544-3_10
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References

  • Knowles J D, Corne D (2001) A comparison of encodings and algorithms for multiobjective spanning tree problems. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’01), IEEE Press, 544–551

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  • Zhou G, Gen M (1999) Genetic algorithm approach on multi-criteria minimum spanning tree problem. European Journal of Operational Research 114:141–152

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Correspondence to Carsten Witt .

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© 2010 Springer-Verlag Berlin Heidelberg

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Neumann, F., Witt, C. (2010). Multi-objective Minimum Spanning Trees. In: Bioinspired Computation in Combinatorial Optimization. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16544-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-16544-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16543-6

  • Online ISBN: 978-3-642-16544-3

  • eBook Packages: Computer ScienceComputer Science (R0)