A Fast Way of Calculating Exact Hypervolumes

By Lyndon While, Lucas Bradstreet, L. Barone. IEEE Transactions on Evolutionary Computation, 2012

432 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d3dc1a3056734a6b8d176c8d22ada75e7a4185f8

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Citations in the corpus

Consistencies and Contradictions of Performance Metrics in Multiobjective Optimization (2014, methodology): “For the fast approaches on calculating the exact HV, the reader is referred to [61] and [64]Ű[69].”
Many-Objective Evolutionary Algorithms (2015, methodology): “There has been some recent work on faster computation of the hypervolume indicator, such as hypervolume by slicing objectives (HSO) with worst-case complexity being O( N M − 1 ) [While et al. 2006], the WFG algorithm with worst-case complexity being O(2 N − 1 ) [While et al. 2012], and so forth.”
Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers (2016, methodology): “For problems having no more than ten objectives, HV is exactly calculated using the recently proposed WFG algorithm [59].”
Modified Distance Calculation in Generational Distance and Inverted Generational Distance (2015, neutral): “The use of the hypervolume indicator for those test problems is often impractical from a viewpoint of computation time whereas its fast calculation [17], [22] as well as its efficient approximation [1] has been actively studied.”
Improved Regularity Model-Based EDA for Many-Objective Optimization (2018, methodology): “Furthermore, Monte Carlo simulation [12] is applied for the calculation of HV when M ≥ 10, otherwise the exact approach proposed in [66] is utilized due to TABLE I SETTINGS FOR REFERENCE VECTORS AND POPULATION SIZE”
An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition (2015, methodology): “For 3- to 10-objective problems, we adopt the recently proposed WFG algorithm [29] to calculate the exact HV, whereas a Monte Carlo sampling [28] is applied to approximate HV in 15-objective cases.”
A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization (2019, methodology): “Otherwise the precise approach proposed in [45] is utilized.”
Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization (2014, background): “efforts to address this issue are being made [7], [74].”
A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “For problems with fewer than eight objectives, the recently proposed fast HV calculation method is adopted to calculate the exact HV [76], while for eight-objective and ten-objective problems, the Monte Carlo method [43] with 1 000 000 sampling points is adopted to obtain the approximate HV values.”
A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization (2017, methodology): “the exact HV metric (calculated by the WFG3 algorithm [44])”
A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization (2018, methodology): “To this end, we adopt the reference vector guided evolutionary algorithm (RVEA) [7] for many-objective optimization to be used as an evolutionary algorithm.”
Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes (2017, methodology): “We use a fast calculation method of the exact hypervolume value proposed in [49] for all test problems with 3, 5, 8, and 10 objectives.”
IGD Indicator-Based Evolutionary Algorithm for Many-Objective Optimization Problems (2018, methodology): “Because the computational cost increases sig-niﬁcantly as the number of objectives grows, Monte Carlo simulation [34] 2 is applied for the calculation when m ≥ 10, otherwise the exact approach proposed in [67] is utilized.”