Methods for multi-dimensional robustness optimization in complex embedded systems
EMSOFT '07 Proceedings of the 7th ACM & IEEE international conference on Embedded software
Reducing complexity of multiobjective design space exploration in VLIW-based embedded systems
ACM Transactions on Architecture and Code Optimization (TACO)
Quality Assessment of Pareto Set Approximations
Multiobjective Optimization
Implementation of scatter search for multi-objective optimization: a comparative study
Computational Optimization and Applications
Don't be greedy when calculating hypervolume contributions
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
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
Spread Assessment for Evolutionary Multi-Objective Optimization
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Objective reduction in evolutionary multiobjective optimization: Theory and applications
Evolutionary Computation
S-metric calculation by considering dominated hypervolume as klee's measure problem
Evolutionary Computation
Correction to "a fast incremental hypervolume algorithm"
IEEE Transactions on Evolutionary Computation
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Integrating decision space diversity into hypervolume-based multiobjective search
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
An efficient algorithm for computing hypervolume contributions**
Evolutionary Computation
Ectropy of diversity measures for populations in Euclidean space
Information Sciences: an International Journal
Hype: An algorithm for fast hypervolume-based many-objective optimization
Evolutionary Computation
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Achieving balance between proximity and diversity in multi-objective evolutionary algorithm
Information Sciences: an International Journal
Multi-level ranking for constrained multi-objective evolutionary optimisation
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
Theoretical Computer Science
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
Comparing multiobjective artificial bee colony adaptations for discovering DNA motifs
EvoBIO'12 Proceedings of the 10th European conference on Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics
On the performance metrics of multiobjective optimization
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part I
Expert Systems with Applications: An International Journal
Comparing multiobjective swarm intelligence metaheuristics for DNA motif discovery
Engineering Applications of Artificial Intelligence
Journal of Intelligent Manufacturing
Parameterized average-case complexity of the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows
Computers and Industrial Engineering
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
A math-heuristic for the warehouse location-routing problem in disaster relief
Computers and Operations Research
Annals of Mathematics and Artificial Intelligence
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We present an algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published. HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.