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Evolutionary many-objective optimization based on linear assignment problem transformations

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Abstract

The selection mechanisms that are most commonly adopted by multi-objective evolutionary algorithms (MOEAs) are based on Pareto optimality. However, recent studies have provided theoretical and experimental evidence regarding the unsuitability of Pareto-based selection mechanisms when dealing with problems having four or more objectives. In this paper, we propose a novel MOEA designed for solving many-objective optimization problems. The selection mechanism of our approach is based on the transformation of a multi-objective optimization problem into a linear assignment problem, which is solved by the Kuhn–Munkres’ (Hungarian) algorithm. Our proposed approach is compared with respect to three state-of-the-art MOEAs, designed for solving many-objective optimization problems (i.e., problems having four or more objectives), adopting standard test problems and performance indicators taken from the specialized literature. Since one of our main aims was to analyze the scalability of our proposed approach, its validation was performed adopting test problems having from two to nine objective functions. Our preliminary experimental results indicate that our proposal is very competitive with respect to all the other MOEAs compared, obtaining the best results in several of the test problems adopted, but at a significantly lower computational cost.

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Notes

  1. The source code of our proposed approach is available for download at: https://www.cs.cinvestav.mx/~EVOCINV/software/LAP/LAP.html.

  2. The source code of CMA-PAES-HAGA was provided to us by Shahin Rostamin in Python, but it is also available at: https://github.com/shahinrostami/CMA-HAGA-release.

  3. The source code of \(\theta \)-DEA was provided to us by Yuan Yuan in Java and is available at: http://www.cs.bham.ac.uk/~xin/papers/TEVC2016FebManyEAs.zip.

  4. We used the version of NSGA-III that was included in the source code provided to us by Yuan Yuan, and which is also available at: http://www.cs.bham.ac.uk/~xin/papers/TEVC2016FebManyEAs.zip.

  5. This apparent inconsistency in the population sizes for 7 and 9 objectives arises due to the procedure adopted to compute the number of weight vectors when using the simplex-lattice method.

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Authors and Affiliations

  1. Computer Science Department, CINVESTAV-IPN, Av. Instituto Politécnico Nacional 2508, Gustavo A. Madero, San Pedro Zacatenco, 07360, Mexico City, Mexico

    Luis Miguel Antonio, José A. Molinet Berenguer & Carlos A. Coello Coello

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  1. Luis Miguel Antonio
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  2. José A. Molinet Berenguer
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  3. Carlos A. Coello Coello
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Correspondence to Luis Miguel Antonio.

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The authors declare that they have no conflict of interest.

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We hereby submit the paper entitled “Evolutionary Many-objective Optimization based on Linear Assignment Problem Transformations,” which is submitted for possible publication in this journal. This is an original contribution and is not being considered for possible publication in any other journal.

Additional information

Communicated by X. Li.

The third author acknowledges support from CONACyT Project No. 221551.

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Antonio, L.M., Berenguer, J.A.M. & Coello, C.A.C. Evolutionary many-objective optimization based on linear assignment problem transformations. Soft Comput 22, 5491–5512 (2018). https://doi.org/10.1007/s00500-018-3164-3

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