The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point
Open accessAbstract
The hypervolume indicator is a set measure used in evolutionary multiobjective optimization to evaluate the performance of search algorithms and to guide the search. Multiobjective evolutionary algorithms using the hypervolume indicator transform multiobjective problems into single objective ones by searching for a finite set of solutions maximizing the corresponding hypervolume indicator. In this paper, we theoretically investigate how those optimal μ--distributions-finite sets of μ solutions maximizing the hypervolume indicator-are spread over the Pareto front of biobjective problems. This problem is of high importance for practical applications as these sets characterize the preferences that the hypervolume indicator encodes, i.e., which types of Pareto set approximations are favored.
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Cites
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Zitzler, E., Deb, K., & Thiele, L. (2000) · Evolutionary Computation · doi:10.1162/106365600568202 · Cited by 5,697
Self-citationPerformance assessment of multiobjective optimizers: an analysis and review
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., & da Fonseca, V. G. (2003) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2003.810758 · Cited by 4,330
Self-citationMultiobjective optimization using evolutionary algorithms — A comparative case study
Zitzler, E., & Thiele, L. (1998) · Lecture Notes in Computer Science · doi:10.1007/bfb0056872 · Cited by 2,262
Self-citationIndicator-Based Selection in Multiobjective Search
Zitzler, E., & Künzli, S. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-30217-9_84 · Cited by 2,259
Self-citationSMS-EMOA: Multiobjective selection based on dominated hypervolume
Beume, N., Naujoks, B., & Emmerich, M. (2007) · European Journal of Operational Research · doi:10.1016/j.ejor.2006.08.008 · Cited by 2,048
Scalable Test Problems for Evolutionary Multiobjective Optimization
Deb, K., Thiele, L., Laumanns, M., & Zitzler, E. (2005) · Advanced Information and Knowledge Processing · doi:10.1007/1-84628-137-7_6 · Cited by 2,010
Self-citationKnowles, J. (2006) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2005.851274 · Cited by 1,254
Covariance Matrix Adaptation for Multi-objective Optimization
Igel, C., Hansen, N., & Roth, S. (2007) · Evolutionary Computation · doi:10.1162/evco.2007.15.1.1 · Cited by 788
Evaluating the CMA Evolution Strategy on Multimodal Test Functions
Hansen, N., & Kern, S. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-30217-9_29 · Cited by 758
An evolutionary algorithm for multiobjective optimization: the strength Pareto approach
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Self-citation
Cited by
Particle swarm optimization for feature selection in classification: a multi-objective approach
Xue, B., Zhang, M., & Browne, W. N. (2013) · IEEE Transactions on Cybernetics · doi:10.1109/tsmcb.2012.2227469 · Cited by 1,282
A Survey on the Hypervolume Indicator in Evolutionary Multiobjective Optimization
Shang, K., Ishibuchi, H., He, L., & Pang, L. M. (2021) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2020.3013290 · Cited by 380
Pareto front feature selection based on artificial bee colony optimization
Hancer, E., Xue, B., Zhang, M., Karaboga, D., & Akay, B. (2018) · Information Sciences · doi:10.1016/j.ins.2017.09.028 · Cited by 325
Decomposition-Based Algorithms Using Pareto Adaptive Scalarizing Methods
Wang, R., Zhang, Q., & Zhang, T. (2016) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2016.2521175 · Cited by 283
Metadata
- Authors
- Auger, A., Bader, J., Brockhoff, D., & Zitzler, E.
- Venue
- Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
- Publisher
- ACM
- Published
- 2009-01-09
- Pages
- 87-102
- OpenAlex
- W2148615815
- Cited by
- 375
- References
- 21
- FWCI
- 15.31
- Type
- conference paper
- Language
- en
- Open access
- green
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- Auger, A., Bader, J., Brockhoff, D., & Zitzler, E. (2009). Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point. Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms. https://doi.org/10.1145/1527125.1527138
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