Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
Convergence of stochastic search algorithms to finite size pareto set approximations
Journal of Global Optimization
Approximating the Least Hypervolume Contributor: NP-Hard in General, But Fast in Practice
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Effects of 1-Greedy $\mathcal{S}$-Metric-Selection on Innumerably Large Pareto Fronts
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Approximating the volume of unions and intersections of high-dimensional geometric objects
Computational Geometry: Theory and Applications
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
On sequential online archiving of objective vectors
EMO'11 Proceedings of the 6th 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
Convergence of hypervolume-based archiving algorithms ii: competitiveness
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Bounding the effectiveness of hypervolume-based (µ+λ)-archiving algorithms
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
| Hi-index | 0.00 |
The core of hypervolume-based multi-objective evolutionary algorithms is an archiving algorithm which performs the environmental selection. A (μ+λ)-archiving algorithm defines how to choose μ children from μ parents and λ offspring together. We study theoretically (μ+λ)-archiving algorithms which never decrease the hypervolume from one generation to the next. Zitzler, Thiele, and Bader (IEEE Trans. Evolutionary Computation, 14:58--79, 2010) proved that all (μ+1)-archiving algorithms are ineffective, which means there is an initial population such that independent of the used reproduction rule, a set with maximum hypervolume cannot be reached. We extend this and prove that for λlocally optimal algorithms, which maximize the hypervolume in each step, are effective for λ=μ and can always find a population with hypervolume at least half the optimum for λ We also prove that there is no hypervolume-based archiving algorithm which can always find a population with hypervolume greater than 1 / (1 + 0.1338, ( 1/λ - 1/μ) ) times the optimum.