Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
G-Metric: an M-ary quality indicator for the evaluation of non-dominated sets
Proceedings of the 10th annual conference on Genetic and evolutionary computation
The Journal of Machine Learning Research
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
Investigating and exploiting the bias of the weighted hypervolume to articulate user preferences
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Multiplicative approximations and the hypervolume indicator
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Steady-state selection and efficient covariance matrix update in the multi-objective CMA-ES
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
Improved step size adaptation for the MO-CMA-ES
Proceedings of the 12th annual conference on Genetic and evolutionary computation
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Tight bounds for the approximation ratio of the hypervolume indicator
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
An EMO algorithm using the hypervolume measure as selection criterion
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Running time analysis of a multiobjective evolutionary algorithm on simple and hard problems
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Properties of an adaptive archiving algorithm for storing nondominated vectors
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
GECCO 2012 tutorial on evolutionary multiobjective optimization
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Approximation quality of the hypervolume indicator
Artificial Intelligence
GECCO 2013 tutorial on evolutionary multiobjective optimization
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Speeding up many-objective optimization by Monte Carlo approximations
Artificial Intelligence
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It was recently proven that sets of points maximizing the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new "logarithmic hypervolume indicator" and prove that it achieves a close-to-optimal multiplicative approximation ratio. This is experimentally verified on several benchmark functions by comparing the approximation quality of the multi-objective covariance matrix evolution strategy (MO-CMA-ES) with the classic hypervolume indicator and the MO-CMA-ES with the logarithmic hypervolume indicator.