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Computational Intelligence in Expensive Optimization Problems pp 423–452Cite as

Evolutionary Algorithms for the Multi Criterion Minimum Spanning Tree Problem

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Part of the book series: Adaptation Learning and Optimization ((ALO,volume 2))

Abstract

In many real world network problems several objectives have to be optimized simultaneously. To solve such problems, it is often appropriate to use the multi-criterion minimum spanning tree (MCMST) model, a combinatorial optimization problem that has been shown to be NP-Hard. In Pareto Optimization of the model no polynomial time algorithm is known to find the Pareto front for all instances of the MCMST problem. Researchers have therefore developed deterministic and evolutionary algorithms. However, these exhibit a number of shortcomings such as lack of scalability and large CPU times. Therefore, the hybridised Knowledge-based Evolutionary Algorithm (KEA) has been proposed, which does not have the limitations of previous algorithms because of its speed, its scalability to more than 500 nodes in the bi-criterion case and scalability to the multicriterion case, and its ability to find both the supported and non-supported optimal solutions. KEA is faster and more efficient than NSGA-II in terms of spread and number of solutions found. The only weakness of KEA is the dominated middle of its Pareto front. In order to overcome this deficiency, a number of modifications have been tested including KEA-M, KEA-G and KEA-W. Experimental results show that when time is expensive KEA is preferable to all other algorithms tested.

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Author information

Authors and Affiliations

  1. School of Systems Engineering, University of Reading, Pepper Lane, Reading, RG6 6AY, UK

    Madeleine Davis-Moradkhan

  2. Senior Lecturer, Victoria University of Wellington, New Zealand

    Will Browne

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  1. Madeleine Davis-Moradkhan
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  2. Will Browne
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Editors and Affiliations

  1. Department of Mechanical Engineering and Science-Faculty of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-Ku,, 606-8501, Kyoto, Japan

    Yoel Tenne

  2. Advanced Technology Centre, Rolls-Royce Singapore Pte Ltd, 50 Nanyang Avenue, Block N2, Level B3C,Unit 05-08, 639798, Singapore

    Chi-Keong Goh

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Davis-Moradkhan, M., Browne, W. (2010). Evolutionary Algorithms for the Multi Criterion Minimum Spanning Tree Problem. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_17

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  • DOI: https://doi.org/10.1007/978-3-642-10701-6_17

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