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Chaotic quasi-oppositional arithmetic optimization algorithm for thermo-economic design of a shell and tube condenser running with different refrigerant mixture pairs

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Abstract

This theoretical research study proposes a novel Chaotic Quasi-Oppositional Arithmetic Optimization Algorithm (COAOA) for thermo-economic optimization of a shell and tube condenser working with refrigerant mixtures. Arithmetic Optimization Algorithm (AOA) is a recently emerged metaheuristic algorithm considering different mathematical operators to optimize the candidate solutions over a wide range of search domains. The effectiveness the COAOA is assessed by applying it to a set of benchmark optimization problems and comparing the obtained solutions with that of the original AOA and its quasi-oppositional variant. The COAOA has been employed to acquire the minimum value of the total annual cost of the shell and tube condenser by iteratively varying nine decision variables of mass flow rate, shell diameter, the tube inside diameter, tube length, number of tube passes, tube layout, tube pitch ratio, the total number of baffles, and diameter ratio. Three different case studies are solved using different refrigerant pairs used for in-tube flow to show the proposed metaheuristic optimizer’s efficiency and effectivity on real-world mixed-integer optimization problem. Optimal results retrieved for different mixture pairs with varying mass fractions are compared with each other, and parametric configuration yielding the minimum total cost is decided. Finally, a comprehensive sensitivity analysis is performed to investigate the influences of the design variables over the considered problem objective. Overall analysis results indicate that COAOA can be an excellent optimizer to obtain a shell and tube condenser’s optimal configuration within a reasonable computation time.

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Abbreviations

A :

Heat exchange area (m2)

A s :

Cross-sectional area normal to the shell flow direction (m2)

B :

Baffle spacing (m)

C e :

Energy cost (€/kWh)

C i :

Capital investment cost (€)

C min :

Heat capacity (J/K)

C o :

Annual operating cost (€/year)

C od :

Total discounted operating cost (€)

C p :

Specific heat (J/kgK)

C tot :

Total annual cost (€)

D e :

Equivalent shell diameter (m)

D s :

Shell diameter (m)

d :

Tube diameter (m)

f :

Friction factor

G :

Mass velocity (kg/m2s)

g :

Gravitational acceleration (m/s2)

H :

Annual operating hours (h/year)

h :

Heat transfer coefficient (W/m2K)

i :

Annual discount rate (%)

K 1 :

Model coefficient

k :

Thermal conductivity (W/mK)

L :

Total tube length (m)

\(\dot{m}\) :

Mass flow rate (kg/s)

ny :

Equipment life (year)

n 1 :

Model coefficient

N tube :

Number of tubes

N pass :

Number of tube passes

NTU :

Number of transfer units

p crit :

Critical pressure (Pa)

P t :

Tube pitch (m)

PP :

Pumping power (W)

Pr :

Prandtl number

p r :

Reduced pressure

p sat :

Saturation pressure (Pa)

Q :

Heat load (W)

Re :

Reynolds number

R fs :

Shell side fouling factor (m2K/W)

R ft :

Tube side fouling factor (m2K/W)

STHE :

Shell and tube heat exchanger

T :

Temperature (K)

U o :

Overall heat transfer coefficient (W/m2K)

v :

Fluid velocity (m/s)

x :

Vapor quality

x:

Mass fraction of the refrigerant in the mixture

∆p frict :

Frictional pressure drop (Pa)

∆p mom :

Momentum pressure drop (Pa)

∆p static :

Static pressure drop (Pa

ε :

Void fraction

η :

Pump efficiency

μ :

Viscosity (Pa.s)

ρ :

Density (kg/m3)

σ :

Surface tension (N/m

cond:

Condensation

e :

Equivalent

i :

Inlet

in :

Inner

l :

Liquid

o :

Outlet

out:

Outer

s :

Shell side

t :

Tube side

v :

Vapor

w :

Wall

References

  1. Mohanty DP (2016) Application of firefly algorithm for design optimization of a shell and tube heat exchanger from economic point of view. Int J Therm Sci 102:228–238

    Article  Google Scholar 

  2. Şahin AŞ, Kılıç B, Kılıç U (2011) Design and economic optimization of shell and tube exchangers using Artificial Bee Colony (ABC) algorithm. Energ Convers Manage 52:3356–3362

    Article  Google Scholar 

  3. Yang J, Oh SR, Liu W (2014) Optimization of shell and tube heat exchangers using a general design approach motivated by constructal theory. Int J Heat Mass Transf 77:1144–1154

    Article  Google Scholar 

  4. Yang J, Oh SR, Liu W, Jacobi AM (2014) Optimization of shell-and-tube heat exchangers conforming to TEMA standards with general design approach motivated by constructal theory. Energ Convers Manage 78:468–476

    Article  Google Scholar 

  5. Selbas O, Kızılkan M, Reppich A (2006) New design approach for shell-and-tube heat exchangers using genetic algorithms from economic point of view. Chem Eng Process 35:268–275

    Article  Google Scholar 

  6. Fettaka S, Thibault J, Gupta Y (2013) Design of shell-and-tube heat exchangers using multi objective optimization. Int J Heat Mass Transf 60:343–354

    Article  Google Scholar 

  7. Amini M, Bazargan M (2014) Two objective optimization in shell-and-tube heat exchangers using genetic algorithm. Appl Therm Eng 69:278–285

    Article  Google Scholar 

  8. Ravagnani MASS, Silva AP, Biscaiac EC, Caballero JA (2009) Optimal design of shell and tube heat exchangers using particle swarm optimization. Ind Chem Eng Res 48:2927–2935

    Article  Google Scholar 

  9. Sadeghzadeh H, Ehyaei MA, Rosen MA (2016) Techno-economic optimization of a shell and tube heat exchanger by genetic and particle swarm algorithms. Energ Convers Manage 93:888–899

    Google Scholar 

  10. Mohanty DP (2016) Gravitational search algorithm for economic optimization design of a shell and tube heat exchanger. Appl Therm Eng 107:184–193

    Article  Google Scholar 

  11. Hadidi A, Hadidi M, Nazari A (2013) A new design approach for shell-and-tube heat exchangers using imperialist competitive algorithm (ICA) from economic point of view. Energ Convers Manage 67:66–74

    Article  Google Scholar 

  12. Rao RV, Patel V (2013) Multi-objective optimization of heat exchangers using a modified teaching- learning-based optimization algorithm. Appl Math Model 37:1147–1162

    Article  MathSciNet  MATH  Google Scholar 

  13. Rao RV, Saroj A (2017) Constrained economic optimization of shell-and-tube heat exchangers using elitist-Jaya algorithm. Energy 128:785–800

    Article  Google Scholar 

  14. Sai JP, Rao BN (2020) Efficiency and economic optimization of shell and tube heat exchanger using bacteria foraging algorithm. SN Appl Sci 2:13

    Article  Google Scholar 

  15. Iyer VH, Mahesh S, Malpani R, Sapre M, Kulkarni AJ (2019) Adaptive range genetic algorithm: a hybrid optimization approach and its application in the design and economic optimization of shell-and-tube heat exchanger. Eng Appl Artif Intel 85:444–461

    Article  Google Scholar 

  16. Kulkarni AJ, Durugkar LP, Kumar M (2013) Cohort Intelligence: self supervised learning behavior. In: Proceedings of the 2013 IEEE International Conference on Systems, Man, and Cybernetics, Manchester, pp.1396–1400

  17. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. Int Conf Comput Intell Modell, Control Autom 1:695–701

    Google Scholar 

  18. Tizhoosh HR (2005) Reinforcement learning based on actions and opposite actions. In: ICGST International Conference on Artificial Intelligence and Machine Learning, Cairo, Egypt.

  19. Tizhoosh HR (2006) Opposition-based reinforcement learning. J Adv Comput Intell Intell Inform 10(3):578–585

    Article  Google Scholar 

  20. Ventresca M, Tizhoosh HR (2006) Improving the convergence of backpropagation by opposite transfer functions. In: IEEE World Congress on Computational Intelligence, Vancouver, BC, Canada, pp. 9527–9534

  21. Yu X, Xu W, Li C (2021) Opposition-based learning grey wolf optimizer for global optimization. Knowl-Based Syst 226:107139

    Article  Google Scholar 

  22. Gupta S, Deep K, Heidari AA, Moayedi H, Wang M (2020) Opposition-based learning Harris hawks optimization with advanced transition rules: principles and analysis. Expert Syst Appl 158:113510

    Article  Google Scholar 

  23. Fan Q, Huang H, Yang K, Zhang S, Yao L, Xiong Q (2021) A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Syst Appl 170:114575

    Article  Google Scholar 

  24. Ewees AA, Abd-Elaziz M, Houssein EH (2018) Improved grasshopper optimization algorithm using opposition-based learning. Expert Syst Appl 112:156–172

    Article  Google Scholar 

  25. Roy PK, Paul C, Sultana S (2014) Oppositional teaching and learning based optimization approach for combined heat and power dispatch. Int J Elec Power 57:392–403

    Article  Google Scholar 

  26. Ekinci S, Hekimoğlu B, Izci D (2021) Opposition based Hengy gas solubility optimization as a novel algorithm for PID control of DC motor. Eng Sci Technol 24:331–342

    Google Scholar 

  27. Rahnamayan S, Tizhoosh HR, Salama MMA (2007) Quasi-oppositional differential evolution, in: 2007 IEEE Congress on Evolutionary Computation, pp.2229–2236

  28. Guha D, Roy PK, Banerjee S (2016) Quasi-oppositional differential search algorithm applied to load frequency control. Eng Sci Technol 19:1635–1654

    Google Scholar 

  29. Chen H, Li W, Yang X (2020) A whale optimization algorithm with chaos mechanism based on quasi-opposition for global optimization problems. Expert Syst Appl 158:113612

    Article  Google Scholar 

  30. Basu M (2016) Quasi-oppositional differential evolution for optimal reactive power dispatch. Elec Power Energy Syst 78:29–40

    Article  Google Scholar 

  31. Warid W, Hizam H, Mariun N, Abdul-Wahab NI (2018) A novel quasi-oppositional modified Jaya algorithm for multi-objective optimal power flow solution. Appl Soft Comput 65:360–373

    Article  Google Scholar 

  32. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2020) The arithmetic optimization algorithm. Comput Method Appl M 376:113609

    Article  MathSciNet  MATH  Google Scholar 

  33. Allen B, Gosselin L (2008) Optimal geometry and flow arrangement for minimizing the cost of shell-and-tube condensers. Int J Energy Res 32:958–969

    Article  Google Scholar 

  34. Haseli Y, Dincer I, Natarer GF (2008) Optimum temperatures in a shell and tube condenser with respect to exergy. Int J Heat Mass Transf 51:2462–2470

    Article  MATH  Google Scholar 

  35. Khalifeh Soltan B, Saffar-Avval M, Damangir E (2004) Minimizing capital and operating costs of shell and tube condensers using optimum baffle spacing. Appl Therm Eng 24:2801–2810

    Article  Google Scholar 

  36. Hajabdollahi H, Ahmadi P, Dincer I (2011) Thermoeconomic optimization of a shell and tube condenser using both genetic algorithm and particle swarm. Int J Refrig 34:1066–1076

    Article  Google Scholar 

  37. Haseli Y, Dincer I, Natarer GF (2010) Exergy efficiency of two-phase flow in a shell and tube condenser. Heat Transf Eng 31:17–24

    Article  Google Scholar 

  38. Kern DQ (1950) Process heat transfer. McGraw-Hill

    Google Scholar 

  39. Shah MM (1979) A general correlation for heat transfer during film condensation inside pipes. Int J Heat Mass Transf 22:547–556

    Article  Google Scholar 

  40. Shah RK, Dusan PS (2003) Fundamentals of heat exchanger design. Wiley, New York

    Book  Google Scholar 

  41. Müller-Steinhagen H, Heck K (1986) A simple friction pressure drop correlation for two phase flow in pipes. Chem Eng Process 20:297–308

    Article  Google Scholar 

  42. Rouhani SZ, Axelsson E (1970) Calculation of void volume fraction in the subcooled and quality boiling regions. Int J Heat Mass Transf 13:383–393

    Article  Google Scholar 

  43. Caputo AC, Pelagagge PM, Salini P (2008) Heat exchanger design based on economic optimization. Appl Therm Eng 28:1151–1159

    Article  Google Scholar 

  44. Peters MS, Timmerhaus KD (1991) Plant design and economics for chemical engineering. McGraw-Hill, New-york, NY, USA

    Google Scholar 

  45. Abualigah L (2021) Group search optimizer: a nature-inspired meta-heuristic optimization algorithm with its results, variants, and applications. Neural Comput Appl 33:2949–2972

    Article  Google Scholar 

  46. Jiang F, Wang K, Dong L, Pan C, Xu W, Yang K (2019) Deep-learning-based joint resource scheduling algorithms for hybrid MEC networks. IEEE Internet Things J 7:6252–6265

    Article  Google Scholar 

  47. Jiang F, Wang K, Dong L, Pan C, Xu W, Yang K (2020) AI driven heteroheneous MEC system with UAV assistance for dynamic environment: challenges and solutions. IEEE Netw 35:400–408

    Article  Google Scholar 

  48. Rahnamayan S, Tizhoosh HR, Salma MMA (2008) Opposition versus randomness in soft computing technique. Appl Soft Comput 8(2):906–918

    Article  Google Scholar 

  49. Chen X, Yu K, Du W, Zhao W, Liu G (2016) Parameters identification of solar cell models using generalized oppositional teaching-learning based optimization. Energy 99:170–180

    Article  Google Scholar 

  50. Shekhawat S, Saxena A (2020) Development and applications of an intelligent crow search algorithm based on opposition based learning. ISA Trans 99:210–230

    Article  Google Scholar 

  51. Gong L, Shaoqian L (2020) Chaotic spreading sequences with multiple access performance better than random sequences. IEEE Trans Circuits Syst I Fundam Theory Appl 47(3):394–397

    Article  Google Scholar 

  52. Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng 5(4):458–472

    Google Scholar 

  53. Mitic M, Vukovic N, Petrovic M, Mijkovic Z (2015) Chaotic fruit fly optimization algorithm. Knowl-Based Syst 89:446–458

    Article  Google Scholar 

  54. Arora S, Anand P (2019) Chaotic grasshopper optimization algorithm for global optimization. Neural Comput Appl 31:4385–4405

    Article  Google Scholar 

  55. Sayed GI, Hassanien AE, Azar AT (2019) Feature selection via a novel chaotic crow search algorithm. Neural Comput Appl 31:171–188

    Article  Google Scholar 

  56. Wang GG, Guo L, Gandomi AH, Hao GS, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci 274:17–34

    Article  MathSciNet  Google Scholar 

  57. Kaur G, Arora S (2018) Chaotic Whale Optimization algorithm. J Comput Des Eng 5(3):275–284

    Google Scholar 

  58. Gagnon I, April A, Abran A (2020) An investigation of the effects of chaotic maps on the performance of metaheuristics. Eng Rep 3:e12369

    Google Scholar 

  59. May R (1976) Simple mathematical models with very complicated dynamics. Nature 261(5560):459–467

    Article  MATH  Google Scholar 

  60. Jessa M (2006) Designing security for number sequences generated by means of sawtooth chaotic map. IEEE Trans Circuits Syst I Fundam Theory Appl 53(5):1140–1150

    Article  MathSciNet  MATH  Google Scholar 

  61. Konno H, Kondo T (1997) Iterative chaotic map as a random number generator. Ann Nucl Energy 24(14):1183–1188

    Article  Google Scholar 

  62. Mansouri A, Wang X (2020) A novel one dimensional sine powered chaotic map and its application in a new image encryption scheme. Inf Sci 520:46–62

    Article  MathSciNet  MATH  Google Scholar 

  63. Peitgen HO, Jurgens H, Saupe D (1992) Chaos and Fractals. Springer, Berlin, Germany

    Book  MATH  Google Scholar 

  64. Kennedy J, Eberhart R (1995) Particle Swarm Optimization, In: Proceedings of ICNN’95- International Conference on Neural Networks, Perth, WA, Australia

  65. Moosavi SHS, Bardsiri VK (2019) Poor and Rich Optimization Algorithm: A new human-based and multi populiations algorithm. Eng Appl Artif Intel 86:165–181

    Article  Google Scholar 

  66. Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MAA, Gandomi AH (2021) Aquila Optimizer: A novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250

    Article  Google Scholar 

  67. Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H, Musirin I, Daud MR (2018) Barnacles Mating Optimizer: An Evolutionary Algorithm for Solving Optimization, In: 2018 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS), Shah Alam, Malaysia

  68. Steven Brown J (2013) Introduction to hydrofluoro-olefin alternatives for high global warming potential hydrofluorocarbon refrigerants. HVAC&R Res 19:693–704

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Ege University, Bornova, Izmir, Turkey

    Mert Sinan Turgut

  2. Department of Industrial Engineering, Faculty of Engineering and Architecture, Izmir Bakircay University, Menemen, Izmir, Turkey

    Oguz Emrah Turgut

  3. Faculty of Computer Sciences and Informatics, Amman Arab University, Amman, 11953, Jordan

    Laith Abualigah

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  1. Mert Sinan Turgut
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Correspondence to Oguz Emrah Turgut.

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Turgut, M.S., Turgut, O.E. & Abualigah, L. Chaotic quasi-oppositional arithmetic optimization algorithm for thermo-economic design of a shell and tube condenser running with different refrigerant mixture pairs. Neural Comput & Applic 34, 8103–8135 (2022). https://doi.org/10.1007/s00521-022-06899-x

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  • DOI: https://doi.org/10.1007/s00521-022-06899-x

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