Abstract
Recently, an increasing number of state-of-the-art Multi-objective Evolutionary Algorithms (MOEAs) have incorporated the so-called pair-potential functions (commonly used to discretize a manifold) to improve the diversity within their population. A remarkable example is the Riesz s-energy function that has been recently used to improve the diversity of solutions either as part of a selection mechanism as well as to generate reference sets. In this paper, we perform an extensive empirical study with respect to the usage of the Riesz s-energy function and other 6 pair-potential functions adopted as a backbone of a selection mechanism used to update an external archive which is integrated into MOEA/D. Our results show that these pair-potential-based archives are able to store solutions with high diversity discarded by the MOEA/D’s main population. Our experimental results indicate that the utilization of the pair-potential-based archives helps to circumvent the known MOEA/D’s performance dependence on the Pareto front shapes without meddling with the original definition of the algorithm.
The first author acknowledges support from CINVESTAV-IPN and CONACyT to pursue graduate studies. The third author acknowledges support from CONACyT grant no. 1920 and from SEP-Cinvestav grant (application no. 4).
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Change history
24 March 2021
The original version of this chapter was revised. Two equations in section 2.1 have been corrected.
Notes
- 1.
Given \(\varvec{x}, \varvec{y} \in \mathbb {R}^m\), \(\varvec{x}\) is said to Pareto dominate \(\varvec{y}\) (denoted as \(\varvec{x} \prec \varvec{y}\)) if and only if \(x_i \le y_i\) for all \(i=1, \dots , m\) and \(\exists j \in \{1, \dots , m\}\) such that \(x_i < y_i\).
- 2.
The source code is available at http://computacion.cs.cinvestav.mx/~jfalcon/PairPotentials/.
- 3.
All the IGD and PD graphs are available at http://computacion.cs.cinvestav.mx/~jfalcon/PairPotentials/.
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Falcón-Cardona, J.G., Covantes Osuna, E., Coello Coello, C.A. (2021). An Overview of Pair-Potential Functions for Multi-objective Optimization. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_32
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