Abstract
In recent years, there has been a growing interest in multiobjective evolutionary algorithms (MOEAs) with a selection mechanism different from Pareto dominance. This interest has been mainly motivated by the poor performance of Pareto-based selection mechanisms when dealing with problems having more than three objectives (the so-called many-objective optimization problems). Two viable alternatives for solving many-objective optimization problems are decomposition-based and indicator-based MOEAs. However, it is well-known that the performance of decomposition-based MOEAs (and also of indicator-based MOEAs designed around R2) heavily relies on the scalarizing function adopted. In this paper, we propose an approach for generating novel scalarizing functions using genetic programming. Using our proposed approach, we were able to generate two new scalarizing functions (called AGSF1 and AGSF2), which were validated using an indicator-based MOEA designed around R2 (MOMBI-II). This validation was conducted using a set of standard test problems and two performance indicators (hypervolume and s-energy). Our results indicate that AGSF1 has a similar performance to that obtained when using the well-known Achievement Scalarizing Function (ASF). However, AGSF2 provided a better performance than ASF in most of the test problems adopted. Nevertheless, our most remarkable finding is that genetic programming can indeed generate novel (and possible more competitive) scalarizing functions.
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 grant no. 2016-01-1920 (Investigación en Fronteras de la Ciencia 2016) and from a SEP-Cinvestav grant (application no. 4).
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Notes
- 1.
Source code for ELGP is available at: https://github.com/lacava/ellen.
- 2.
The source code of MOMBI-II is available at:
https://www.cs.cinvestav.mx/~EVOCINV/software/MOMBI-II/MOMBI-II.html.
- 3.
The source code of our approach is available at:
http://www.computacion.cs.cinvestav.mx/~abernabe/scalarizing_functions.
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Bernabé Rodríguez, A.V., Coello Coello, C.A. (2020). Generation of New Scalarizing Functions Using Genetic Programming. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12270. Springer, Cham. https://doi.org/10.1007/978-3-030-58115-2_1
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