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Convergence analysis of some multiobjective evolutionary algorithms when discovering motifs

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Abstract

An important issue in multiobjective optimization is the study of the convergence speed of algorithms. An optimization problem must be defined as simple as possible to minimize the computational cost required to solve it. In this work, we study the convergence speed of seven multiobjective evolutionary algorithms: DEPT, MO-VNS, MOABC, MO-GSA, MO-FA, NSGA-II, and SPEA2; when solving an important biological problem: the motif discovery problem. We have used twelve instances of four different organisms as benchmark, analyzing the number of fitness function evaluations required by each algorithm to achieve reasonable quality solutions. We have used the hypervolume indicator to evaluate the solutions discovered by each algorithm, measuring its quality every 100 evaluations. This methodology also allows us to study the hit rates of the algorithms over 30 independent runs. Moreover, we have made a deeper study in the more complex instance of each organism. In this study, we observe the increase of the archive (number of non-dominated solutions) and the spread of the Pareto fronts obtained by the algorithm in the median execution. As we will see, our study reveals that DEPT, MOABC, and MO-FA provide the best convergence speeds and the highest hit rates.

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Acknowledgments

This work was partially funded by the Spanish Ministry of Economy and Competitiveness and the ERDF (European Regional Development Fund), under the contract TIN2012-30685 (BIO project). Thanks also to the Fundación Valhondo for the economic support offered to David L. González-Álvarez. Álvaro Rubio-Largo is supported by the research Grant PRE09010 from Gobierno de Extremadura (Spain) and the European Social Fund (ESF).

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Authors and Affiliations

  1. Department of Technologies of Computers and Communications, ARCO Research Group, Escuela Politécnica, University of Extremadura, Campus Universitario s/n, 10003 , Cáceres, Spain

    David L. González-Álvarez, Miguel A. Vega-Rodríguez & Álvaro Rubio-Largo

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  1. David L. González-Álvarez
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  2. Miguel A. Vega-Rodríguez
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  3. Álvaro Rubio-Largo
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Correspondence to David L. González-Álvarez.

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Communicated by G. Acampora.

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González-Álvarez, D.L., Vega-Rodríguez, M.A. & Rubio-Largo, Á. Convergence analysis of some multiobjective evolutionary algorithms when discovering motifs. Soft Comput 18, 853–869 (2014). https://doi.org/10.1007/s00500-013-1103-x

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