Abstract
The typical goal in multi-objective optimization is to find a set of good and well-distributed solutions. It has become popular to focus on specific regions of the objective space, e.g., due to market demands or personal preferences.
In the past, a range of different approaches has been proposed to consider preferences for regions, including reference points and weights. While the former technique requires knowledge over the true set of trade-offs (and a notion of “closeness”) in order to perform well, it is not trivial to encode a non-standard preference for the latter.
With this article, we contribute to the set of algorithms that consider preferences. In particular, we propose the easy-to-use concept of “preferred regions” that can be used by laypeople, we explain algorithmic modifications of NSGAII and AGE, and we validate their effectiveness on benchmark problems and on a real-world problem.
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- 1.
Consequently, our pNSGAII is somewhat equivalent to an island model approach for multi-objective optimization, with islands being responsible for preferred regions. In contrast to existing island model-MOO approaches (e.g. [2]), we are focussing on user-defined parts of the search space that are defined in an easy-to-use way.
- 2.
The ZDT functions are used as provided by the jMetal framework. The number of decision variables is 30 for ZDT1/2/3 and 10 for ZDT4/6.
- 3.
Number of decision variables is 12 for DTLZ2/3, as set in the jMetal framework.
- 4.
If we use \(\mu =30\) for typical MOEA (please see Table 1) then it is less probable to find adequate number of solutions in preferred regions, that makes it difficult to compare with pMOEA. In addition, compared in terms of FE, MOEA uses 50 less function evaluations than pMOEA only because the number is compatible with \(\mu \) (no extra function evaluations after completing last generation).
- 5.
- 6.
We uploaded all code and results to https://github.com/shaikatcse/pMOEAs. This includes pSPEA2 as an algorithm and also IGD indicator values.
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Acknowledgements
This work has been supported by the ARC Discovery Early Career Researcher Award DE160100850.
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Mahbub, M.S., Wagner, M., Crema, L. (2017). Multi-objective Optimisation with Multiple Preferred Regions. In: Wagner, M., Li, X., Hendtlass, T. (eds) Artificial Life and Computational Intelligence. ACALCI 2017. Lecture Notes in Computer Science(), vol 10142. Springer, Cham. https://doi.org/10.1007/978-3-319-51691-2_21
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