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Multifactorial evolutionary algorithm for solving clustered tree problems: competition among Cayley codes

Case studies on the clustered shortest-path tree problem and the minimum inter-cluster routing cost clustered tree problem

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Abstract

The Multifactorial Evolutionary Algorithm (MFEA) has emerged as an effective variant of the evolutionary algorithm. MFEA has been successfully applied to deal with various problems with many different types of solution encodings. Although clustered tree problems play an important role in real life, there haven’t been much research on exploiting the strengths of MFEA to solve these problems. One of the challenges in applying the MFEA is to build specific evolutionary operators of the MFEA algorithm. To exploit the advantages of the Cayley Codes in improving the MFEA’s performance, this paper introduces MFEA with representation scheme based on the Cayley Code to deal with the clustered tree problems. The new evolutionary operators in MFEA have two different levels. The purpose of the first level is to construct a spanning tree which connects to a vertex in each cluster, while the objective of the second one is to determine the spanning tree for each cluster. We focus on evaluating the efficiency of the new MFEA algorithm on known Cayley Codes when solving clustered tree problems. In the aspect of the execution time and the quality of the solutions found, each encoding type of the Cayley Codes is analyzed when performed on both single-task and multi-task to find the solutions of one or two different clustered tree problems respectively. In addition, we also evaluate the effect of those encodings on the convergence speed of the algorithms. Experimental results show the level of effectiveness for each encoding type and prove that the Dandelion Code outperforms the remaining encoding mechanisms when solving clustered tree problems.

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Acknowledgements

This research was sponsored by the U.S. Army Combat Capabilities Development Command (CCDC) Pacific and CCDC Army Research Laboratory (ARL) under Contract Number W90GQZ-93290007. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the CCDC Pacific and CCDC ARL and the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.

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Authors and Affiliations

  1. Faculty of Natural Science and Technology, Taybac University, Son La, Vietnam

    Thanh Pham Dinh

  2. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Binh Huynh Thi Thanh, Trung Tran Ba & Long Nguyen Binh

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  1. Thanh Pham Dinh
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  2. Binh Huynh Thi Thanh
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Correspondence to Binh Huynh Thi Thanh.

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Dinh, T.P., Thanh, B.H.T., Ba, T.T. et al. Multifactorial evolutionary algorithm for solving clustered tree problems: competition among Cayley codes. Memetic Comp. 12, 185–217 (2020). https://doi.org/10.1007/s12293-020-00309-2

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