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The hypervolume indicator is one of the most used set-quality indicators for the assessment of stochastic multiobjective optimizers, as well as for selection in evolutionary multiobjective optimization algorithms.
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A New Analysis of the LebMeasure Algorithm for Calculating Hypervolume. In Evolutionary Multi-Criterion Optimization (Lecture Notes in Computer Science) , Carlos A. Coello Coello et al
Lyndon While. 2005 · 2005
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Heuristics for optimizing the calculation of hypervolume for multi-objective optimization problems. In CEC 2005, IEEE Congress on Evolutionary Computation , Vol. 3. IEEE, 2225–2232
Lyndon While, Lucas Bradstreet, Luigi Barone, and Phil Hingston. 2005 · 2005
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Faster S-metric calculation by considering dominated hypervolume as Klee’s measure problem
Nicola Beume and Günter Rudolph. 2006 · 2006
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Maximising Hypervolume for Selection in Multi-objective Evolutionary Algorithms. In CEC 2006, IEEE Congress on Evolutionary Computation . 1744–1751
Lucas Bradstreet, Luigi Barone, and Lyndon While. 2006 · 2006
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An improved dimension-sweep algorithm for the hypervolume indicator. In CEC 2006, IEEE Congress on Evolutionary Computation . 1157–1163
Carlos M. Fonseca, Luís Paquete, and Manuel López-Ibáñez. 2006 · 2006
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A faster algorithm for calculating hypervolume
Lyndon While, Philip Hingston, Luigi Barone, and Simon Huband. 2006 · 2006
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Incrementally maximising hypervolume for selection in multi-objective evolutionary algorithms. In CEC 2007, IEEE Congress on Evolutionary Computation . 3203–3210
Lucas Bradstreet, Lyndon While, and Luigi Barone. 2007 · 2007
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Covariance Matrix Adaptation for Multi-objective Optimization
Christian Igel, Nikolaus Hansen, and Stefan Roth. 2007 · 2007
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A Fast Algorithm for Computing the Contribution of a Point to the Hypervolume. In Third International Conference on Natural Computation (ICNC 2007) , Vol. 4. 415–420
Xiuling Zhou, Ning Mao, Wenjuan Li, and Chengyi Sun. 2007 · 2007
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The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration. In Evolutionary Multi-Criterion Optimization (Lecture Notes in Computer Science) , Shigeru Obayashi et al
Eckart Zitzler, Dimo Brockhoff, and Lothar Thiele. 2007 · 2007
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A Fast Incremental Hypervolume Algorithm
Lucas Bradstreet, Lyndon While, and Luigi Barone. 2008 · 2008
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Karl Bringmann and Tobias Friedrich. 2008 · 2008
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A (slightly) faster algorithm for Klee’s measure problem. In Proceedings of the Twenty-fourth Annual Symposium on Computational Geometry (SoCG ’08) . ACM, New York, NY, USA, 94–100
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Quality Assessment of Pareto Set Approximations . Lecture Notes in Computer Science, Vol. 5252
Eckart Zitzler, Joshua Knowles, and Lothar Thiele. 2008 · 2008
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S-metric calculation by considering dominated hypervolume as Klee’s measure problem
Nicola Beume. 2009 · 2009
Cited alongside, same era.
On the Complexity of Computing the Hypervolume Indicator
Nicola Beume, Carlos M. Fonseca, Manuel López-Ibáñez, Luís Paquete, and Jan Vahrenhold. 2009 · 2009
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Updating exclusive hypervolume contributions cheaply. In CEC 2009, IEEE Congress on Evolutionary Computation . 538–544
Lucas Bradstreet, Luigi Barone, and Lyndon While. 2009a · 2009
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Correction to “A Fast Incremental Hypervolume Algorithm"
Lucas Bradstreet, Lyndon While, and Luigi Barone. 2009b · 2009
Cited alongside, same era.
A new way of calculating exact exclusive hypervolumes
Logarithmic-Time Updates in SMS-EMOA and Hypervolume-Based Archiving
Iris Hupkens and Michael Emmerich. 2013 · 2013
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Convergence of Hypervolume-Based Archiving Algorithms
Karl Bringmann and Tobias Friedrich. 2014 · 2014
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Two-dimensional Subset Selection for Hypervolume and Epsilon-indicator. In Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation (GECCO ’14) . ACM, New York, NY, USA, 589–596
Karl Bringmann, Tobias Friedrich, and Patrick Klitzke. 2014 · 2014
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Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms
Tobias Friedrich and Frank Neumann. 2014 · 2014
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Quick Hypervolume
Luís M. S. Russo and Alexandre P. Francisco. 2014 · 2014
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Lucas Bradstreet, Lyndon While, and Luigi Barone. 2009c · 2009
Cited alongside, same era.
Many-Objective Optimization and Hypervolume Based Search
Dimo Brockhoff. 2009 · 2009
Cited alongside, same era.
Theoretically Investigating Optimal μ \mu -Distributions for the Hypervolume Indicator: First Results for Three Objectives
Anne Auger, Johannes Bader, and Dimo Brockhoff. 2010 · 2010
Cited alongside, same era.
A fast many-objective hypervolume algorithm using iterated incremental calculations. In CEC 2010, IEEE Congress on Evolutionary Computation . 1–8
Lucas Bradstreet, Lyndon While, and Luigi Barone. 2010 · 2010
Cited alongside, same era.
Klee’s measure problem on fat boxes in time O ( n ( d + 2 ) / 3 ) O(n^{(d+2)/3}) . In Proceedings of the Twenty-sixth Annual Symposium on Computational Geometry (SoCG ’10) . ACM, New York, NY, USA, 222–229
Karl Bringmann. 2010 · 2010
Cited alongside, same era.
An Efficient Algorithm for Computing Hypervolume Contributions
Karl Bringmann and Tobias Friedrich. 2010 · 2010
Cited alongside, same era.
Optimal μ \mu -Distributions for the Hypervolume Indicator for Problems with Linear Bi-objective Fronts: Exact and Exhaustive Results
Dimo Brockhoff. 2010 · 2010
Cited alongside, same era.
A Theoretical Analysis of Volume Based Pareto Front Approximations. In Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation (GECCO ’14) . ACM, New York, NY, USA, 1415–1422
Pradyumn Kumar Shukla, Nadja Doll, and Hartmut Schmeck. 2014 · 2014
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Benchmarking Numerical Multiobjective Optimizers Revisited. In Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation (GECCO ’15) . ACM, New York, NY, USA, 639–646
Dimo Brockhoff, Thanh-Do Tran, and Nikolaus Hansen. 2015 · 2015
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A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems
Kerstin Dächert and Kathrin Klamroth. 2015 · 2015
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On the representation of the search region in multi-objective optimization
Kathrin Klamroth, Renaud Lacour, and Daniel Vanderpooten. 2015 · 2015
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Representative Systems and Decision Support for Multicriteria Optimization Problems
Tobias Kuhn. 2015 · 2015
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A GPU-Based Algorithm for a Faster Hypervolume Contribution Computation. In Evolutionary Multi-Criterion Optimization (Lecture Notes in Computer Science) , António Gaspar-Cunha et al
Edgar Manoatl Lopez, Luis Miguel Antonio, and Carlos A. Coello Coello. 2015 · 2015
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Experiments on Greedy and Local Search Heuristics for d d –dimensional Hypervolume Subset Selection. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’16) . ACM, New York, NY, USA, 541–548
Matthieu Basseur, Bilel Derbel, Adrien Goëffon, and Arnaud Liefooghe. 2016 · 2016
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Improving the IWFG algorithm for calculating incremental hypervolume. In CEC 2016, IEEE Congress on Evolutionary Computation . 3969–3976
W. Cox and L. While. 2016 · 2016
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Greedy Hypervolume Subset Selection in Low Dimensions
Andreia P. Guerreiro, Carlos M. Fonseca, and Luís Paquete. 2016 · 2016
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Hypervolume Subset Selection in Two Dimensions: Formulations and Algorithms
Tobias Kuhn, Carlos M. Fonseca, Luís Paquete, Stefan Ruzika, Miguel M. Duarte, and José Rui Figueira. 2016 · 2016
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Extending quick hypervolume
Luís M. S. Russo and Alexandre P. Francisco. 2016 · 2016
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Maximum Volume Subset Selection for Anchored Boxes. In 33rd International Symposium on Computational Geometry (SoCG 2017) . Dagstuhl Publishing, Schloss Dagstuhl Leibniz-Zentrum für Informatik, Germany, 22:1–22:15
Karl Bringmann, Sergio Cabello, and Michael T. M. Emmerich. 2017 · 2017
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Computing and Updating Hypervolume Contributions in Up to Four Dimensions
Andreia P. Guerreiro and Carlos M. Fonseca. 2018 · 2017
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A box decomposition algorithm to compute the hypervolume indicator
Renaud Lacour, Kathrin Klamroth, and Carlos M. Fonseca. 2017 · 2017
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New Performance guarantees for the greedy maximization of submodular set functions
Jussi Laitila and Atte Moilanen. 2017 · 2017
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Implicit enumeration strategies for the hypervolume subset selection problem
Ricardo J. Gomes, Andreia P. Guerreiro, Tobias Kuhn, and Luís Paquete. 2018 · 2018
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Portfolio Selection in Evolutionary Algorithms
Andreia P. Guerreiro. 2018 · 2018
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Improved quick hypervolume algorithm
Andrzej Jaszkiewicz. 2018 · 2018
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Greedily Excluding Algorithm for Submodular Maximization. In 2018 IEEE Conference on Control Technology and Applications (CCTA) . 1680–1685
Min-Guk Seo and Hyo-Sang Shin. 2018 · 2018
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Hypervolume Subset Selection with Small Subsets
Benoît Groz and Silviu Maniu. 2019 · 2019
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Quality Evaluation of Solution Sets in Multiobjective Optimisation: A Survey
Miqing Li and Xin Yao. 2019 · 2019
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Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. In CEC 2007, IEEE Congress on Evolutionary Computation . 2086–2093
Dimo Brockhoff and Eckart Zitzler. 2007 · 2093
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