This work describes the application of a multiobjective cuckoo search method for turbomachinery design optimization of an axial pump. Maximization of the total efficiency and minimization of the required net positive suction head of the pump are the two objective functions considered for the optimization problem. The optimization process is carried out on a range of imposed volumetric flow rates, with taking into account at each discretized radius between the hub and tip of the rotor: the profile camber, rotor wall thickness, angular deviation, and the solidity, regarded as geometrical constraints and nominal flow rate as mechanical constraint. Two strategies are proposed in order to solve the problem. In the first one, three forms of mono-objective model with two variables, total efficiency and net positive suction head, are considered. In the second one, a multiobjective model with nondominated sorting scheme is adopted. A comparative evaluation of results obtained from the proposed approach with those of a reference machine and genetic algorithm allowed us to validate the present work.
SrinivasNDebK. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolut Comput1994; 2: 221–248.
2.
CoelloCAC, et al.A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl Inf Syst1999; 1: 129–156.
3.
Massardo A and Satta A. Axial flow compressor design optimization. part I: Pitchline analysis and multivariable objective function influence. Journal of Turbomachinery 1990; 112(3): 399–404.
4.
Massardo A, Satta A and Marini M. Axial flow compressor design optimization: Part ii-throughflow analysis. Journal of Turbomachinery 1990; 112(3): 405–410.
5.
Kipouros T, Jaeggi D, Dawes B, et al. Multi-objective optimisation of turbomachinery blades using tabu search. In: International conference on evolutionary multi-criterion optimization, pp.897–910. Berlin: Springer.
6.
BeniniE. Three-dimensional multi-objective design optimization of a transonic compressor rotor. J Propul Power2004; 20: 559–565.
7.
SamadAKimK. Shape optimization of an axial compressor blade by multi-objective genetic algorithm. Proc IMechE, Part A: J Power and Energy2008; 222: 599–611.
8.
BonaiutiDZangenehM. On the coupling of inverse design and optimization techniques for the multiobjective, multipoint design of turbomachinery blades. J Turbomach2009; 131: 021014.
9.
KimJHChoiJHHusainA, et al.Performance enhancement of axial fan blade through multi-objective optimization techniques. J Mech Sci Technol2010; 24: 2059–2066.
10.
Takayama Y and Watanabe H. Multi-objective design optimization of a mixed-flow pump. In: ASME 2009 fluids engineering division summer meeting, pp.371–379. New York: American Society of Mechanical Engineers.
11.
WangXHirschCKangS, et al.Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model. Comput Methods Appl Mech Eng2011; 200: 883–895.
12.
ZhangJZhuHYangC, et al.Multi-objective shape optimization of helico-axial multiphase pump impeller based on NSGA-II and ANN. Energy Convers Manag2011; 52: 538–546.
13.
ChenxingZLWSHQianZ. Multi-objective optimization design and experimental investigation of centrifugal fan performance. Chin J Mech Eng2013; 26: 1.
14.
MengFDongQWangP, et al.Multiobjective optimization for the impeller of centrifugal fan based on response surface methodology with grey relational analysis method. Adv Mech Eng2014; 6: 614581.
15.
StadlerMSchmitzMBLauferW, et al.Inverse aeroacoustic design of axial fans using genetic optimization and the lattice-Boltzmann method. J Turbomach2014; 136: 041011.
16.
YangWXiaoR. Multiobjective optimization design of a pump–turbine impeller based on an inverse design using a combination optimization strategy. J Fluids Eng2014; 136: 014501.
17.
HuangRLuoXJiB, et al.Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm. Sci China Technol Sci2015; 58: 2122–2130.
18.
SmithAECoitDWBaeckT, et al.Penalty functions. Evolut Comput2000; 2: 41–48.
19.
DebK. Multi-objective optimization using evolutionary algorithms, New York: John Wiley & Sons Inc., 2001.
20.
Ait ChikhMABelaidiIKhelladiS, et al.Efficiency of bio-and socio-inspired optimization algorithms for axial turbomachinery design. Appl Soft Comput2018; 64: 282–306.
21.
Robert R, Ricardo N and Bakir F. Pompes rotodynamiques – aérohydrodynamique des profils et aubages de pompes hélices. Techniques de l'Ingénieur, Réf: BM4304 V1, 2013.
22.
Robert R, Ricardo N and Bakir F. Pompes rotodynamiques – dimensionnement et analyse des performances des pompes hélices. Techniques de l'Ingénieur, Réf: BM4305, 2013.
23.
NadirMGhenaietACarcasciC. Thermo-economic optimization of heat recovery steam generator for a range of gas turbine exhaust temperatures. Appl Therm Eng2016; 106: 811–826.
24.
Grodzevich O and Romanko O. Normalization and other topics in multi-objective optimization. In: Proceedings of the Fields MITACS industrial problems workshop, pp.89–102. Toronto: The Fields Institute.
25.
DebKPratapAAgarwalS, et al.A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput2002; 6: 182–197.
26.
YangXSDebS. Engineering optimisation by cuckoo search. Int J Math Model Numer Optim2010; 1: 330–343.
27.
Yang XS and Deb S. Cuckoo search via Lévy flights. In: World congress on nature & biologically inspired computing, 2009. NaBIC 2009, pp.210–214. New York: IEEE.
Wang Q, Liu S, Wang H et al. Multi-objective cuckoo search for the optimal design of water distribution systems. In Civil engineering and urban planning 2012. American Society of Civil Engineers, 2012. pp. 402–405.
31.
Rani KA, Malek MFA, Neoh SC, et al. Hybrid multiobjective optimization using modified cuckoo search algorithm in linear array synthesis. In: Antennas and propagation conference (LAPC), 2012 Loughborough, pp.1–4. New York: IEEE.
32.
FisterIJrYangXSFisterD, et al.Cuckoo search: a brief literature review. In: Yang Xin-She (ed.) Cuckoo search and firefly algorithm,, Berlin: Springer, 2014, pp. 49–62. .
33.
He XS, Li N and Yang XS. Non-dominated sorting cuckoo search for multiobjective optimization. In: 2014 IEEE symposium on Swarm intelligence (SIS), pp.1–7. New York: IEEE.
Reyes-SierraMCoelloCC. Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res2006; 2: 287–308.
36.
YaoXLiuYLinG. Evolutionary programming made faster. IEEE Trans Evolut Comput1999; 3: 82–102.
37.
LagunaMMartíR. Experimental testing of advanced scatter search designs for global optimization of multimodal functions. J Global Optim2005; 33: 235–255.
38.
Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1985. (pp. 93–100). Lawrence Erlbaum Associates. Inc., Publishers.
39.
FonsecaCMFlemingPJ. An overview of evolutionary algorithms in multiobjective optimization. Evolut Comput1995; 3: 1–16.
CheikhMJarbouiBLoukilT, et al.A method for selecting pareto optimal solutions in multiobjective optimization. J Informat Math Sci2010; 2: 51–62.
42.
Deb K, Chaudhuri S and Miettinen K. Estimating nadir objective vector quickly using evolutionary approaches. Technical report, Technical Report KanGAL Report, Kanpur India, 2005.
43.
Deb K, Miettinen K and Sharma D. A hybrid integrated multi-objective optimization procedure for estimating nadir point. In: International conference on evolutionary multi-criterion optimization, pp.569–583. Berlin: Springer.
44.
Bechikh S, Said LB and Ghedira K. Estimating nadir point in multi-objective optimization using mobile reference points. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp.1–9. New York: IEEE.
