A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems

Abstract

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

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Acknowledgements

The research work of E. Filatovas was funded by a Grant (no. S-MIP-17-67) from the Research Council of Lithuania. The research work of J. L. Redondo and J. Fernández was funded by Grants from the Spanish Ministry of Economy and Competitiveness (MTM2015-70260-P, TIN2015-66680-C2-1-R, RTI2018-095993-B-100), Fundación Séneca (The Agency of Science and Technology of the Region of Murcia, 19241/PI/14 and 20817/PI/18), Junta de Andalucía (P12-TIC301, UAL18-TIC-A020-B), in part financed by the European Regional Development Fund (ERDF).

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Filatovas, E., Kurasova, O., Redondo, J.L. et al. A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems. TOP 28, 402–423 (2020). https://doi.org/10.1007/s11750-019-00535-z

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Keywords

  • Multiobjective optimization
  • Evolutionary algorithms
  • Preference-based EMO
  • NSGA-II
  • NBI
  • CHIM

Mathematics Subject Classification

  • 90C29
  • 90C26
  • 68W25
  • 90C59