Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
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
Multicriteria Optimization
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
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
Approximating the Volume of Unions and Intersections of High-Dimensional Geometric Objects
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
An EMO algorithm using the hypervolume measure as selection criterion
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
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
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Simultaneous use of different scalarizing functions in MOEA/D
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Some comments on GD and IGD and relations to the Hausdorff distance
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
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
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Illustration of fairness in evolutionary multi-objective optimization
Theoretical Computer Science
The logarithmic hypervolume indicator
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Information Sciences: an International Journal
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications
Theoretical Computer Science
Approximation quality of the hypervolume indicator
Artificial Intelligence
A fast approximation-guided evolutionary multi-objective algorithm
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Aircraft morphing wing design by using partial topology optimization
Structural and Multidisciplinary Optimization
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Indicator-based algorithms have become a very popular approach to solve multi-objective optimization problems. In this paper, we contribute to the theoretical understanding of algorithms maximizing the hypervolume for a given problem by distributing μ points on the Pareto front. We examine this common approach with respect to the achieved multiplicative approximation ratio for a given multi-objective problem and relate it to a set of μ points on the Pareto front that achieves the best possible approximation ratio. For the class of linear fronts and a class of concave fronts, we prove that the hypervolume gives the best possible approximation ratio. In addition, we examine Pareto fronts of different shapes by numerical calculations and show that the approximation computed by the hypervolume may differ from the optimal approximation ratio.