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2017 | OriginalPaper | Buchkapitel

Multi-objective Optimisation with Multiple Preferred Regions

verfasst von : Md. Shahriar Mahbub, Markus Wagner, Luigi Crema

Erschienen in: Artificial Life and Computational Intelligence

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Neighbourhood Analysis: A Case Study on Google Machine Reassignment Problem

Nächstes Kapitel An Adaptive Memetic Algorithm for the Architecture Optimisation Problem

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.

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.

Number of decision variables is 12 for DTLZ2/3, as set in the jMetal framework.

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).

We do not report other indicator values, such as inverted generational distance (IGD) [20] or the Hausdorff distance [19] due to space constraints.

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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Titel: Multi-objective Optimisation with Multiple Preferred Regions
verfasst von: Md. Shahriar Mahbub
Markus Wagner
Luigi Crema
Verlag: Springer International Publishing
Buch: Artificial Life and Computational Intelligence
Print ISBN: 978-3-319-51690-5

Electronic ISBN: 978-3-319-51691-2

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-51691-2_21

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