Abstract
Optimisers for multi- or many-objective optimisation problems can be categorised as scalarisation and meta-heuristic approaches. Many of the approaches from both groups require to use a set of weighting vectors, which are expected to be as evenly distributed as possible. The current practice employs the normal-boundary intersection (NBI) method which has one disadvantage in that the number of sampling points must be the number of k-combination. This work proposes a numerical scheme called clustering-based hyperplane sampling (CBHS) to deal with such a weak point. The method is based on random sampling on a hyperplane and clustering. The classical NBI method and some of its extended versions are used to examine the performance of the proposed algorithm. The comparative results reveal that CBHS is the best performer with using longer computing time. Moreover, its real advantage is the capability of generating a set of weighting vectors with any sample size.
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The authors are grateful for financial support from Thailand Research Funds (TRF), Grant Number RTA6180010.
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Bureerat, S., Pholdee, N. A simple numerical scheme for generation of weighting factors for multiobjective optimisation. Soft Comput 25, 1631–1646 (2021). https://doi.org/10.1007/s00500-020-05249-0
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DOI: https://doi.org/10.1007/s00500-020-05249-0