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A new indicator-based many-objective ant colony optimizer for continuous search spaces

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Abstract

In this paper, we propose a novel multi-objective ant colony optimizer (called iMOACO\(_{\mathbb {R}}\)) for continuous search spaces, which is based on ACO\(_{\mathbb {R}}\) and the R2 performance indicator. iMOACO\(_{\mathbb {R}}\) is the first multi-objective ant colony optimizer (MOACO) specifically designed to tackle continuous many-objective optimization problems (i.e., multi-objective optimization problems having four or more objectives). Our proposed iMOACO\(_{\mathbb {R}}\) is compared to three state-of-the-art multi-objective evolutionary algorithms (NSGA-III, MOEA/D and SMS-EMOA) and a MOACO algorithm called MOACO\(_{\mathbb {R}}\) using standard test problems and performance indicators taken from the specialized literature. Our experimental results indicate that iMOACO\(_{\mathbb {R}}\) is very competitive with respect to NSGA-III and MOEA/D and it is able to outperform SMS-EMOA and MOACO\(_{\mathbb {R}}\) in most of the test problems adopted.

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Notes

  1. Without loss of generality, we will assume only minimization problems.

  2. The source code and the complete study of iMOACO\(_{\mathbb {R}}\) are available at: http://computacion.cs.cinvestav.mx/~jfalcon/iMOACOR/imoacor.html.

  3. We used the implementation from 2007 for continuous search spaces: http://dces.essex.ac.uk/staff/zhang/webofmoead.htm.

  4. We used the implementation available at: http://web.ntnu.edu.tw/~tcchiang/publicstions/nsga3cpp/nsga3cpp.htm.

  5. The source code was provided by its author, Abel García-Nájera.

  6. According to Deb (2001), the parallel coordinates plot (also called value path plot) is a graphical method to show the objective values of high-dimensional nondominated fronts. The horizontal axis marks the identity of the objective function and, thus, must be ticked only at integers starting from 1 to m and a bar is put in each tick. The vertical axis will mark the objective function values. The plot provides the following information:

    1. 1.

      Qualitative assessment of the spread of the obtained solutions. An algorithm which spreads its solutions over the entire objective value axis is considered to be good at finding diverse solutions.

    2. 2.

      The extent to which the cross-lines “zig-zag” shows the trade-off among the objective functions captured by the obtained nondominated solutions. An algorithm having a large change of slope between two objective function bars is considered to be good in terms of finding good trade-off nondominated solutions.

  7. The election of these values is based on the analysis of diversification versus intensification of the search, made by Socha and Dorigo (2008) for ACO\(_{\mathbb {R}}\).

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Acknowledgements

The first author acknowledges support from CONACyT and CINVESTAV-IPN to pursue graduate studies in Computer Science. The second author gratefully acknowledges support from CONACyT Project No. 221551. Both authors thank the Referees for their valuable comments.

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  1. CINVESTAV-IPN (Evolutionary Computation Group), Av. IPN No. 2508, Col. San Pedro Zacatenco, 07300, Mexico City, Mexico

    Jesús Guillermo Falcón-Cardona & Carlos A. Coello Coello

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  1. Jesús Guillermo Falcón-Cardona
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  2. Carlos A. Coello Coello
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Correspondence to Jesús Guillermo Falcón-Cardona.

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Falcón-Cardona, J.G., Coello Coello, C.A. A new indicator-based many-objective ant colony optimizer for continuous search spaces. Swarm Intell 11, 71–100 (2017). https://doi.org/10.1007/s11721-017-0133-x

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