Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Quality Assessment of Pareto Set Approximations
Multiobjective Optimization
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
On the complexity of computing the hypervolume indicator
IEEE Transactions on Evolutionary Computation
Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications
Theoretical Computer Science
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
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In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the R2 indicator exist. In this paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented.