Speeding up many-objective optimization by Monte Carlo approximations

Auger, 2005, Performance evaluation of an advanced local search evolutionary algorithm, 1777 Bader, 2011, HypE: An algorithm for fast hypervolume-based many-objective optimization, Evol. Comput., 19, 45, 10.1162/EVCO_a_00009 Beume, 2009, S-metric calculation by considering dominated hypervolume as Kleeʼs measure problem, Evol. Comput., 17, 477, 10.1162/evco.2009.17.4.17402 Beume, 2007, SMS-EMOA: Multiobjective selection based on dominated hypervolume, Eur. J. Oper. Res., 181, 1653, 10.1016/j.ejor.2006.08.008 Beyer, 2007, Evolution strategies, Scholarpedia, 2, 1965, 10.4249/scholarpedia.1965 Bradstreet, 2008, A fast incremental hypervolume algorithm, IEEE Trans. Evol. Comput., 12, 714, 10.1109/TEVC.2008.919001 Bringmann, 2012, An improved algorithm for Kleeʼs measure problem on fat boxes, Comput. Geom., 45, 225, 10.1016/j.comgeo.2011.12.001 Bringmann, 2009, Approximating the least hypervolume contributor: NP-hard in general, but fast in practice, vol. 5467, 6 Bringmann, 2010, Approximating the volume of unions and intersections of high-dimensional geometric objects, Comput. Geom., 43, 601, 10.1016/j.comgeo.2010.03.004 Bringmann, 2010, An efficient algorithm for computing hypervolume contributions, Evol. Comput., 18, 383, 10.1162/EVCO_a_00012 Bringmann, 2012, Approximating the least hypervolume contributor: NP-hard in general, but fast in practice, Theor. Comput. Sci., 425, 104, 10.1016/j.tcs.2010.09.026 Bringmann, 2013, Parameterized average-case complexity of the hypervolume indicator, 575 Bringmann, 2013, Approximation quality of the hypervolume indicator, Artif. Intell., 195, 265, 10.1016/j.artint.2012.09.005 Brockhoff, 2011, Theoretical aspects of evolutionary multiobjective optimization, 101 Coello Coello, 2007 Deb, 2001 Deb, 2002, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 182, 10.1109/4235.996017 Deb, 2002, Scalable multi-objective optimization test problems, 825 Ehrgott, 2010 Eiben, 2008 Emmerich, 2011, Computing hypervolume contributions in low dimensions: Asymptotically optimal algorithm and complexity results, vol. 6576, 121 2004, vol. 78 Friedrich, 2011, The logarithmic hypervolume indicator, 81 Hansen, 2001, Completely derandomized self-adaptation in evolution strategies, Evol. Comput., 9, 159, 10.1162/106365601750190398 Hansen, 2010, Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009, 1689 Huband, 2003, An evolution strategy with probabilistic mutation for multi-objective optimisation, 2284 Igel, 2007, Covariance matrix adaptation for multi-objective optimization, Evol. Comput., 15, 1, 10.1162/evco.2007.15.1.1 Igel, 2007, Steady-state selection and efficient covariance matrix update in the multi-objective CMA-ES, vol. 4403, 171 Igel, 2008, Shark, J. Mach. Learn. Res., 9, 993 Impagliazzo, 1999, The complexity of k-SAT, 237 Kern, 2004, Learning probability distributions in continuous evolutionary algorithms – A comparative review, Nat. Comput., 3, 77, 10.1023/B:NACO.0000023416.59689.4e Miettinen, 1999, Nonlinear Multiobjective Optimization, vol. 12 Sawaragi, 1985, Theory of Multiobjective Optimization, vol. 176 Suttorp, 2009, Efficient covariance matrix update for variable metric evolution strategies, Mach. Learn., 75, 167, 10.1007/s10994-009-5102-1 Ursem, 2010 Voß, 2010, Scaling up indicator-based MOEAs by approximating the least hypervolume contributor: A preliminary study, 1975 Voß, 2010, Improved step size adaptation for the MO-CMA-ES, 487 While, 2012, A fast way of calculating exact hypervolumes, IEEE Trans. Evol. Comput., 16, 86, 10.1109/TEVC.2010.2077298 Wickramasinghe, 2010, Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization, 1857 Yıldız, 2012, On Kleeʼs measure problem for grounded boxes, 111 Zitzler, 2004, Indicator-based selection in multiobjective search, vol. 3242, 832 Zitzler, 1999, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput., 3, 257, 10.1109/4235.797969 Zitzler, 2003, Performance assessment of multiobjective optimizers: An analysis and review, IEEE Trans. Evol. Comput., 7, 117, 10.1109/TEVC.2003.810758