Two decades of blackbox optimization applications

EURO Journal on Computational Optimization - Tập 9 - Trang 100011 - 2021
Stéphane Alarie1, Charles Audet2, Aïmen E. Gheribi3, Michael Kokkolaras4, Sébastien Le Digabel2
1Hydro-Québec and IREQ, Canada
2GERAD and Polytechnique Montréal, Canada
3CRCT and Polytechnique Montréal, Canada
4GERAD and McGill University, Canada

Tài liệu tham khảo

Aasi, 2013, Einstein@Home all-sky search for periodic gravitational waves in LIGO S5 data, Phys. Rev. D, 87, 042001, 10.1103/PhysRevD.87.042001 Abramson, 2002 Abramson, 2004, Mixed variable optimization of a load-bearing thermal insulation system using a filter pattern search algorithm, Optim. Eng., 5, 157, 10.1023/B:OPTE.0000033373.79886.54 Abramson, 2012, An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions, Struct. Multidiscip. Optim., 45, 53, 10.1007/s00158-011-0658-3 Abramson, 2009, Mesh adaptive direct search algorithms for mixed variable optimization, Optim. Lett., 3, 35, 10.1007/s11590-008-0089-2 Abramson, 2009, OrthoMADS: a deterministic MADS instance with orthogonal directions, SIAM J. Optim., 20, 948, 10.1137/080716980 Abramson, M., Booker, A., Cramer, E., Simonis, J., 2017. Search and poll method for solving multifidelity optimization problems. Patent US 2017/0011143 A1, https://lens.org/095-460-083-532-225. Adjengue, 2014, A variance-based method to rank input variables of the mesh adaptive direct search algorithm, Optim. Lett., 8, 1599, 10.1007/s11590-013-0688-4 Al-Handawi, 2020, Scalable set-based design optimization and remanufacturing for meeting changing requirements, ASME J. Mech. Des., 143 Alarie, 2015, Global optimization with NOMAD for the simultaneous tuning of several power system stabilizers Alarie, 2019, Optimization of noisy blackboxes with adaptive precision Alarie, 2013, Snow water equivalent estimation using blackbox optimization, Pac. J. Optim., 9, 1 Alarie, 2013, Positionnement de stations GMON avec inversion du modèle HUT Aspentech, Accessed: 2020-11-06. Aspen chemical engineering simulator. https://www.aspentech.com. Audet, 2014, A survey on direct search methods for blackbox optimization and their applications, 31 Audet, 2008, Spent potliner treatment process optimization using a MADS algorithm, Optim. Eng., 9, 143, 10.1007/s11081-007-9030-2 Audet, 2008, Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search, J. Glob. Optim., 41, 299, 10.1007/s10898-007-9234-1 Audet, 2020, Binary, unrelaxable and hidden constraints in blackbox optimization, Oper. Res. Lett., 48, 467, 10.1016/j.orl.2020.05.011 Audet, 2020, Monotonic grey box optimization, Optim. Lett., 14, 3, 10.1007/s11590-019-01497-8 Audet, 2019, Dynamic improvements of static surrogates in direct search optimization, Optim. Lett., 13, 1433, 10.1007/s11590-019-01452-7 Audet, 2001, Pattern search algorithms for mixed variable programming, SIAM J. Optim., 11, 573, 10.1137/S1052623499352024 Audet, 2004, A pattern search filter method for nonlinear programming without derivatives, SIAM J. Optim., 14, 980, 10.1137/S105262340138983X Audet, 2006, Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., 17, 188, 10.1137/040603371 Audet, 2009, A progressive barrier for derivative-free nonlinear programming, SIAM J. Optim., 20, 445, 10.1137/070692662 Audet, 2008, Parallel space decomposition of the mesh adaptive direct search algorithm, SIAM J. Optim., 19, 1150, 10.1137/070707518 Audet, 2013, Metamaterial design by mesh adaptive direct search, Vol. 127, 71 Audet, 2021, Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates, Comput. Optim. Appl., 79, 1, 10.1007/s10589-020-00249-0 Audet, 2017, Derivative-Free and Blackbox Optimization, 10.1007/978-3-319-68913-5 Audet, 2014, Reducing the number of function evaluations in mesh adaptive direct search algorithms, SIAM J. Optim., 24, 621, 10.1137/120895056 Audet, 2018, Robust optimization of noisy blackbox problems using the mesh adaptive direct search algorithm, Optim. Lett., 12, 675, 10.1007/s11590-017-1226-6 Audet, 2018, Order-based error for managing ensembles of surrogates in mesh adaptive direct search, J. Glob. Optim., 70, 645, 10.1007/s10898-017-0574-1 Audet, 2012, The mesh adaptive direct search algorithm for periodic variables, Pac. J. Optim., 8, 103 Audet, 2015, Linear equalities in blackbox optimization, Comput. Optim. Appl., 61, 1, 10.1007/s10589-014-9708-2 Audet, 2021, NOMAD version 4: nonlinear optimization with the MADS algorithm Audet, 2016, Dynamic scaling in the mesh adaptive direct search algorithm for blackbox optimization, Optim. Eng., 17, 333, 10.1007/s11081-015-9283-0 Audet, 2019, The mesh adaptive direct search algorithm for granular and discrete variables, SIAM J. Optim., 29, 1164, 10.1137/18M1175872 Audet, 2006, Finding optimal algorithmic parameters using derivative-free optimization, SIAM J. Optim., 17, 642, 10.1137/040620886 Audet, 2008, Multiobjective optimization through a series of single-objective formulations, SIAM J. Optim., 19, 188, 10.1137/060677513 Audet, 2010, A mesh adaptive direct search algorithm for multiobjective optimization, Eur. J. Oper. Res., 204, 545, 10.1016/j.ejor.2009.11.010 Audet, 2018, Mesh-based Nelder-Mead algorithm for inequality constrained optimization, Comput. Optim. Appl., 71, 331, 10.1007/s10589-018-0016-0 Aziz, 2020, Multi-fidelity algorithms for the horizontal alignment problem in road design, Eng. Optim., 52, 1848, 10.1080/0305215X.2019.1691547 Bahrami, 2017, Application of a territorial-based filtering algorithm in turbomachinery blade design optimization, Eng. Optim., 49, 216, 10.1080/0305215X.2016.1165994 Bahrami, 2016, Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm, Appl. Math. Model., 40, 1650, 10.1016/j.apm.2015.09.008 Bale, 2016, Reprint of: FactSage thermochemical software and databases, 2010-2016, Calphad, 55, 1, 10.1016/j.calphad.2016.07.004 Barris, 2015, Simulation-based optimization of the control strategy for isolated power grids via blackbox software Bayoumy, 2020, A relative adequacy framework for multi-model management in design optimization, ASME J. Mech. Des., 1 Bayoumy, 2020, A relative adequacy framework for multimodel management in multidisciplinary design optimization, Struct. Multidiscip. Optim., 62, 1701, 10.1007/s00158-020-02591-7 Bayoumy, 2020, Multi-model management for time-dependent multidisciplinary design optimization problems, Struct. Multidiscip. Optim., 61, 1821, 10.1007/s00158-020-02572-w Beaudoin, 2013, Decompose Zoltan: doing domain decomposition in parallel Bellavia, 2004, STRSCNE: a scaled trust-region solver for constrained nonlinear equations, Comput. Optim. Appl., 28, 31, 10.1023/B:COAP.0000018878.95983.4e Bollas, G., Kyle, K. P., Prasad, D., Jacobson, C., Maljanian Jr, J., Poisson, R., Park, Y., 2019. Plate-fin heat exchanger fouling identification. Patent US 10495547 B2, https://lens.org/145-576-524-862-964. Booker, 1999, A rigorous framework for optimization of expensive functions by surrogates, Struct. Multidiscip. Optim., 17, 1, 10.1007/BF01197708 Brochu, 2017, Enjeux reliés à l’intégration des énergies renouvelables en réseaux autonomes Browne, 2016, Stochastic simulators based optimization by Gaussian process metamodels - application to maintenance investments planning issues, Qual. Reliab. Eng. Int., 32, 2067, 10.1002/qre.2028 Chamseddine, 2018, Design optimization of tumor vasculature-bound nanoparticles, Sci. Rep., 8, 10.1038/s41598-018-35675-y Chamseddine, 2020, Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles, Sci. Rep., 10, 10.1038/s41598-020-65162-2 Chamseddine, 2018, Nanoparticle optimization for enhanced targeted anticancer drug delivery, ASME J. Biomech. Eng., 140, 10.1115/1.4038202 Chamseddine, 2020, A dual nanoparticle delivery strategy for enhancing drug distribution in cancerous tissue, ASME J. Biomech. Eng., 142, 10.1115/1.4047657 Characklis, 2006, Developing portfolios of water supply transfers, Water Resour. Res., 42, 10.1029/2005WR004424 Chen, 2018, A smoothing direct search method for Monte Carlo-based bound constrained composite nonsmooth optimization, SIAM J. Sci. Comput., 40, A2174, 10.1137/17M1116714 Choi, 2000, Optimization of automotive valve train components with implicit filtering, Optim. Eng., 1, 9, 10.1023/A:1010071821464 Choquette, Y., Lavigne, P., Ducharme, P., Houdayer, A., Martin, J.-P., 2010. Apparatus and method for monitoring snow water equivalent and soil moisture content using natural gamma radiation. US Patent No. 7800051 B2. Clarke, 1983 Conn, 2013, Use of quadratic models with mesh-adaptive direct search for constrained black box optimization, Optim. Methods Softw., 28, 139, 10.1080/10556788.2011.623162 Conn, 2009, Introduction to Derivative-Free Optimization Côté, 2020, Combining historical data and domain expert knowledge using optimization to model electrical equipment reliability, 1 Custódio, 2017, Methodologies and software for derivative-free optimization Delavari, 2018, Simscape power systems benchmarks for education and research in power grid dynamics and control, 1 Diest, 2013, Numerical Methods for Metamaterial Design, Vol. 127 Drews, 2020, Spontaneous reversal of stenosis in tissue-engineered vascular grafts, Sci. Transl. Med., 12, 10.1126/scitranslmed.aax6919 Drumheller, M., 2010. Constraint-based method of designing a route for a transport element. Patent US 7647211 B2, https://lens.org/109-649-319-705-23X. Erignac, C., Drumheller, M., 2010. Adaptive distance field constraint for designing a route for a transport element. Patent US 7668700 B2, https://lens.org/112-901-768-864-121. Feingesicht, M., Polyakov, A., Kerherve, F., Richard, J.-P., 2018. Device for active control of the readhesion of a flow on a profile. Patent WO 2018/229442 A1, https://lens.org/084-049-298-871-25X. Fleischman, D., Atwater, H., 2018a. Narrowband light filters. Patent US 2018/0308888 A1, https://lens.org/029-259-096-576-421. Fleischman, D., Atwater, H., 2018b. Narrowband light filters. Patent WO 2018/200593 A1, https://lens.org/137-184-878-006-724. Fortin, 2001, Distributed watershed model compatible with remote sensing and GIS Data. I: description of model, J. Hydrol. Eng., 6, 91, 10.1061/(ASCE)1084-0699(2001)6:2(91) Fortin, 1999, Le Modèle Météo-Apport HSAMI: Historique, Théorie et Application Gérin-Lajoie, 1999, Hydro-Québec experience with PSS tuning, Vol. 1, 88 Gheribi, 2012, Calculating optimal conditions for alloy and process design using thermodynamic and properties databases, the FactSage software and the Mesh Adaptive Direct Search algorithm, CALPHAD Comput. Coupling Phase Diagr. Thermochem., 36, 135, 10.1016/j.calphad.2011.06.003 Gheribi, 2016, Use of a biobjective direct search algorithm in the process design of material science applications, Optim. Eng., 17, 27, 10.1007/s11081-015-9301-2 Gheribi, 2013, Identifying optimal conditions for magnesium based alloy design using the mesh adaptive direct search algorithm, Thermochim. Acta, 559, 107, 10.1016/j.tca.2013.02.004 Gheribi, 2018, On the prediction of low-cost high entropy alloys using new thermodynamic multi-objective criteria, Acta Mater., 161, 73, 10.1016/j.actamat.2018.09.001 Gheribi, 2020, Determination of optimal compositions and properties for phase change materials in a solar electric generating station, Sol. Energy Mater. Sol. Cells, 210, 110506, 10.1016/j.solmat.2020.110506 Gheribi, 2011, Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm, J. Chem. Thermodyn., 43, 1323, 10.1016/j.jct.2011.03.021 Griebel, 1998 Group, E., Accessed: 2020-11-06. OpenFOAM - the open source CFD toolbox. https://www.openfoam.com/. Guay, 2015, A global portrait of hydrological changes at the 2050 horizon for the province of Québec, Can. Water Resour. J. Rev. Can. Ressour. Hydr., 40, 285, 10.1080/07011784.2015.1043583 Gundert, 2012, Optimization of cardiovascular stent design using computational fluid dynamics, J. Biomech. Eng., 134, 011002, 10.1115/1.4005542 Gundert, 2012, Identification of hemodynamically optimal coronary stent designs based on vessel caliber, IEEE Trans. Biomed. Eng., 59, 1992, 10.1109/TBME.2012.2196275 Harvey, 2014, Process simulation and control optimization of a blast furnace using classical thermodynamics combined to a direct search algorithm, Metall. Mater. Trans. B, 45, 307, 10.1007/s11663-013-0004-9 Heidari, M., Druckman, M., Nakhjavani, O., 2016. Methods for optimized engine balancing based on flight data. Patent US 9347321 B2, https://lens.org/163-726-408-033-724. Hibberd, 2020, Project lyra: catching 1I/‘oumuamua - mission opportunities after 2024, Acta Astronaut., 170, 136, 10.1016/j.actaastro.2020.01.018 Huot, 2019 Huot, 2014, Assessment of blackbox optimization methods for efficient calibration of computationally intensive hydrological models Huot, 2019, A hybrid optimization approach for efficient calibration of computationally intensive hydrological models, Hydrol. Sci. J., 64, 1204, 10.1080/02626667.2019.1624922 Huot, 2019, Low-cost and representative surrogate hydrological models. Part I – Construction of surrogates Huot, 2019, Low-cost and representative surrogate hydrological models. Part II – use within calibration frameworks Hydro-Québec, 2019. Setting new sights with our clean energy, annual report. https://www.hydroquebec.com/about/financial-results/annual-report.html. Jahn, 2007 Kokkolaras, 2020, When, why, and how can derivative-free optimization be useful to computational engineering design?, ASME J. Mech. Des., 142, 10.1115/1.4045043 Kokkolaras, 2001, Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system, Optim. Eng., 2, 5, 10.1023/A:1011860702585 Kolda, 2003, Optimization by direct search: new perspectives on some classical and modern methods, SIAM Rev., 45, 385, 10.1137/S003614450242889 Komljenovic, 2021, Asset management in electrical utilities in the context of business and operational complexity Laboratories, S. N., Accessed: 2020-11-06. Zoltan: parallel partitioning, load balancing and data-management services. https://cs.sandia.gov/Zoltan/. Lainé, 2019, Blackbox optimization for aircraft engine blades with contact interfaces, J. Eng. Gas Turb. Power, 141, 10.1115/1.4042808 Lakhmiri, 2021, HyperNOMAD: hyperparameter optimization of deep neural networks using mesh adaptive direct search, ACM Trans. Math. Softw., 47, 10.1145/3450975 Larson, 2019, Derivative-free optimization methods, Acta Numer., 28, 287, 10.1017/S0962492919000060 Le Digabel, 2011, Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm, ACM Trans. Math. Softw., 37, 44:1, 10.1145/1916461.1916468 Le Digabel, 2010, Parallel versions of the MADS algorithm for black-box optimization Leclaire, 2015, Massive distribution of black box calculation for model calibration Lewis, 2000, Direct search methods: then and now, J. Comput. Appl. Math., 124, 191, 10.1016/S0377-0427(00)00423-4 Li, 2019, A method for automatically recreating the horizontal alignment geometry of existing railways, Comput. Aided Civ. Infrastruct. Eng., 34, 71, 10.1111/mice.12392 Li, 2017, Mountain railway alignment optimization with bidirectional distance transform and genetic algorithm, Comput. Aided Civ. Infrastruct. Eng., 32, 691, 10.1111/mice.12280 Li, 2016, Methodology for optimizing constrained 3-dimensional railway alignments in mountainous terrain, Transp. Res. Part C Emerg. Technol., 68, 549, 10.1016/j.trc.2016.05.010 Liang, X., Xie, Y., Zhang, Z., Niu, T., 2020. Method and apparatus for optimizing blocking grating for cone beam CT image scattering correction. Patent US 10722205 B2, https://lens.org/074-553-279-373-132. Lonchampt, 2017, VME a tool for probabilistic models valuation in engineering asset management, 1158 Lucidi, 2005, An algorithm model for mixed variable programming, SIAM J. Optim., 15, 1057, 10.1137/S1052623403429573 Lupuleac, 2020, Optimization of fastener pattern in airframe assembly, Assembl. Autom., 40, 723, 10.1108/AA-03-2019-0040 Marsden, 2013, Simulation based planning of surgical interventions in pediatric cardiology, Phys. Fluids, 25, 101303, 10.1063/1.4825031 Marsden, 2008, A computational framework for derivative-free optimization of cardiovascular geometries, Comput. Methods Appl. Mech. Eng., 197, 1890, 10.1016/j.cma.2007.12.009 Marsden, 2007, Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation, J. Fluid Mech., 572, 13, 10.1017/S0022112006003235 Marwaha, 2015, System-of-systems approach to air transportation design using nested optimization and direct search, Struct. Multidiscip. Optim., 51, 885, 10.1007/s00158-014-1180-1 MathWorks, 2018a. power_AsynchronousMachineParams. https://www.mathworks.com/help/releases/R2018a/physmod/sps/powersys/ref/power_asynchronousmachineparams.html. MathWorks, 2018b. Simscape power systems release notes. https://www.mathworks.com/help/releases/R2018a/physmod/sps/release-notes.html. Mehrgan, 2019, A 40 billion solar-mass black hole in the extreme core of holm 15A, the central galaxy of abell 85, Astrophys. J., 887, 195, 10.3847/1538-4357/ab5856 Minville, 2014, Improving process representation in conceptual hydrological model calibration using climate simulations, Water Resour. Res., 50, 5044, 10.1002/2013WR013857 Miracle, 2017, A critical review of high entropy alloys and related concepts, Acta Mater., 122, 448, 10.1016/j.actamat.2016.08.081 Mondal, 2015, Optimizing horizontal alignment of roads in a specified corridor, Comput. Oper. Res., 64, 130, 10.1016/j.cor.2015.05.018 Moré, 2014, Do you trust derivatives or differences?, J. Comput. Phys., 273, 268, 10.1016/j.jcp.2014.04.056 Neureiter, 2020, SMART: a new implementation of Schwarzschild’s orbit Superposition technique for triaxial galaxies and its application to an N-body merger simulation, Mon. Not. R. Astron. Soc., 500, 1437 Pourbagian, 2015, Constrained problem formulations for power optimization of aircraft electro-thermal anti-icing systems, Optim. Eng., 16, 663, 10.1007/s11081-015-9282-1 Pullano, 2021, Underdetection of cases of COVID-19 in France threatens epidemic control, Nature, 590, 134, 10.1038/s41586-020-03095-6 Ramachandra, 2017, Gradual loading ameliorates maladaptation in computational simulations of vein graft growth and remodelling, J. R. Soc. Interface, 14, 20160995, 10.1098/rsif.2016.0995 Ramakrishnan, 2019, Nuclear kinematics in nearby AGN - I. An ALMA perspective on the morphology and kinematics of the molecular CO(2-1) emission, Mon. Not. R. Astron. Soc., 487, 444, 10.1093/mnras/stz1244 Renaud, 2011, Thermodynamic evaluation and optimization of the Li, Na, K, Mg, Ca, Sr // F, Cl reciprocal system, J. Chem. Thermodyn., 43, 1286, 10.1016/j.jct.2011.03.015 Rossi, 2017 Rossi, 2016, Parametric optimization of a hall effect thruster magnetic circuit, Trans. Jpn. Soc. Aeronaut. Space Sci. Aerosp. Technol. Jpn., 14, Pb197 Sankaran, 2010, A method for stochastic constrained optimization using derivative-free surrogate pattern search and colLocation, J. Comput. Phys., 229, 4664, 10.1016/j.jcp.2010.03.005 Sankaran, 2013, An efficient framework for optimization and parameter sensitivity analysis in arterial growth and remodeling computations, Comput. Methods Appl. Mech. Eng., 256, 200, 10.1016/j.cma.2012.12.013 Selvan, 2013, Spherical mesh adaptive direct search for separating quasi-uncorrelated sources by range-based independent component analysis, Neural Comput., 25, 2486, 10.1162/NECO_a_00485 Shukla, 2009, Solar water heaters with phase change material thermal energy storage medium: a review, Renew. Sustain. Energy Rev., 13, 2119, 10.1016/j.rser.2009.01.024 Solnik, 2017, Bayesian optimization for a better dessert Szafron, 2019, Optimization of tissue engineered vascular graft design using computational modeling, Tissue Eng. Part C Methods, 25, 561, 10.1089/ten.tec.2019.0086 Talgorn, B., 2016. NoHiMDO, a non hierarchical solver for MDO problems. https://github.com/bastientalgorn/NoHiMDO, https://github.com/bastientalgorn/NoHiMDO. Talgorn, 2018, Locally weighted regression models for surrogate-assisted design optimization, Optim. Eng., 19, 213, 10.1007/s11081-017-9370-5 Talgorn, 2017, Compact implementation of non-hierarchical analytical target cascading for coordinating distributed multidisciplinary design optimization problems, Struct. Multidiscip. Optim., 56, 1, 10.1007/s00158-017-1726-0 Talgorn, 2017, Numerical investigation of non-hierarchical coordination for distributed multidisciplinary design optimization with fixed computational budget, Struct. Multidiscip. Optim., 55, 205, 10.1007/s00158-016-1489-z Talgorn, 2015, Statistical surrogate formulations for simulation-based design optimization, J. Mech. Des., 137, 10.1115/1.4028756 Temple, B., Armstrong, J., Bueschern, K., Favorite, J., 2015. Radiograph and passive data analysis using mixed variable optimization. Patent US 9047397 B1, https://lens.org/142-391-310-092-570. Tolson, 2007, Dynamically dimensioned search algorithm for computationally efficient watershed model calibration, Water Resour. Res., 43, 10.1029/2005WR004723 Torczon, 1997, On the convergence of pattern search algorithms, SIAM J. Optim., 7, 1, 10.1137/S1052623493250780 Tournemenne, 2017, Optimization of brass wind instruments based on sound simulations, J. Acoust. Soc. Am., 145, 3795, 10.1121/1.5111346 Tournemenne, 2017, Brass instruments design using physics-based sound simulation models and surrogate-assisted derivative-free optimization, J. Mech. Des., 139, 10.1115/1.4035503 Van Dyke, 2013, Using QR decomposition to obtain a new instance of mesh adaptive direct search with uniformly distributed polling directions, J. Optim. Theory Appl., 159, 805, 10.1007/s10957-013-0356-y Vázquez-Méndez, 2018, A 3D model for optimizing infrastructure costs in road design, Comput. Aided Civ. Infrastruct. Eng., 33, 423, 10.1111/mice.12350 Verma, 2020, A concurrent implementation of the surrogate management framework with application to cardiovascular shape optimization, Optim. Eng., 21, 1487, 10.1007/s11081-020-09483-1 Vicente, 2012, Analysis of direct searches for discontinuous functions, Math. Program., 133, 299, 10.1007/s10107-010-0429-8 Vincent, P., Grechy, L., Corbett, R., 2017. A device for maintaining vascular connections. Patent WO 2017/148836 A1, https://lens.org/049-785-433-011-823. Xi, 2020, Survey of derivative-free optimization, Numer. Algebra Control Optim., 10, 537, 10.3934/naco.2020050 Xu, 2016, Optimal adaptive sequential designs for crossover bioequivalence studies, Pharm. Stat., 15, 15, 10.1002/pst.1721 Yang, 2010, Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise, Comput. Methods Appl. Mech. Eng., 199, 2135, 10.1016/j.cma.2010.03.012 Yang, 2013, Optimization of a Y-graft design for improved hepatic flow distribution in the Fontan circulation, J. Biomech. Eng., 135, 011002, 10.1115/1.4023089 Ypma, A., Van Der Schaar, M., Tsirogiannis, G., Karssemeijer, L., Fan, C.-H., 2018. Apparatus and method for inferring parameters of a model of a measurement structure for a patterning process. Patent US 2018/0239851 A1, https://lens.org/124-692-152-146-241.