Design of a parallel genetic algorithm for continuous and pattern-free heliostat field optimization


The heliostat field of solar power tower plants can suppose up to 50% of investment costs and 40% of energy loss. Unfortunately, obtaining an optimal field requires facing a complex non-convex, continuous, large-scale, and constrained optimization problem. Although pattern-based layouts and iterative deployment are popular heuristics to simplify the problem, they limit flexibility and might be suboptimal. This work describes a new genetic algorithm for continuous and pattern-free heliostat field optimization. Considering the potential computational cost of the objective function and the necessity of broad explorations, it has been adapted to run in parallel on shared-memory environments. It relies on elitism, uniform crossover, static penalization of infeasibility, and tournament selection. Interesting experimental results show an optimization speedup up to 15\(\times \) with 16 threads. It could approximately reduce a one year runtime, at complete optimization, to a month only. The optimizer has also been made available as a generic C++ library.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    Alexopoulos S, Hoffschmidt B (2017) Advances in solar tower technology. WIREs Energy Environ 6(1):1–19

    Article  Google Scholar 

  2. 2.

    Behar O, Khellaf A, Mohammedi K (2013) A review of studies on central receiver solar thermal power plants. Renew Sustain Energy Rev 23:12–39

    Article  Google Scholar 

  3. 3.

    Besarati SM, Goswami DY (2014) A computationally efficient method for the design of the heliostat field for solar power tower plant. Renew Energy 69:226–232

    Article  Google Scholar 

  4. 4.

    Buck R (2014) Heliostat field layout improvement by nonrestricted refinement. J SolEnergy Eng 136(2):1–6

    Google Scholar 

  5. 5.

    Camacho EF, Berenguel M, Rubio FR, Martínez D (2012) Control of solar energy systems. Springer, Berlin

    Google Scholar 

  6. 6.

    Carrizosa E, Domínguez-Bravo C, Fernández-Cara E, Quero M (2015) A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems. Comput Oper Res 57:109–122

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Collado FJ, Guallar J (2013) A review of optimized design layouts for solar power tower plants with campo code. Renew Sustain Energy Rev 20:142–154

    Article  Google Scholar 

  8. 8.

    Cruz NC, Redondo JL, Berenguel M, Álvarez JD, Becerra-Terón A, Ortigosa PM (2017) High performance computing for the heliostat field layout evaluation. J Supercomput 73(1):259–276

    Article  Google Scholar 

  9. 9.

    Cruz NC, Redondo JL, Berenguel M, Álvarez JD, Ortigosa PM (2017) Review of software for optical analyzing and optimizing heliostat fields. Renew Sustain Energy Rev 72:1001–1018

    Article  Google Scholar 

  10. 10.

    Duffie JA, Beckman WA (2013) Solar engineering of thermal processes. Wiley, London

    Google Scholar 

  11. 11.

    Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Michigan Press, Ann Arbor

    Google Scholar 

  12. 12.

    Johnson A (2012) Clipper—an open source freeware polygon clipping library. Accessed July 2017

  13. 13.

    Lipps F, Vant-Hull L (1978) A cellwise method for the optimization of large central receiver systems. Sol Energy 20(6):505–516

    Article  Google Scholar 

  14. 14.

    Lutchman S, Gauché P, Groenwold A (2014) On selecting a method for heliostat field layout optimization. In: 2nd Southern African Solar Energy Conference (SASEC)

  15. 15.

    Lutchman SL (2014) Heliostat field layout optimization for a central receiver. Master’s thesis, Stellenbosch University

  16. 16.

    Lutchman SL, Groenwold AA, Gauché P, Bode S (2014) On using a gradient-based method for heliostat field layout optimization. Energy Procedia 49:1429–1438

    Article  Google Scholar 

  17. 17.

    Mutuberria A, Pascual J, Guisado MV, Mallor F (2015) Comparison of heliostat field layout design methodologies and impact on power plant efficiency. Energy Procedia 69:1360–1370

    Article  Google Scholar 

  18. 18.

    Noone CJ, Torrilhon M, Mitsos A (2012) Heliostat field optimization: a new computationally efficient model and biomimetic layout. Sol Energy 86(2):792–803

    Article  Google Scholar 

  19. 19.

    Pitz-Paal R, Botero NB, Steinfeld A (2011) Heliostat field layout optimization for high-temperature solar thermochemical processing. Sol Energy 85(2):334–343

    Article  Google Scholar 

  20. 20.

    Ramos A, Ramos F (2012) Strategies in tower solar power plant optimization. Sol Energy 86(9):2536–2548

    Article  Google Scholar 

  21. 21.

    Ramos A, Ramos F (2014) Heliostat blocking and shadowing efficiency in the video-game era. arXiv preprint arXiv:1402.1690

  22. 22.

    Salhi S (2017) Heuristic search: the emerging science of problem solving. Springer, Cham

    Google Scholar 

  23. 23.

    Sanchez M, Romero M (2006) Methodology for generation of heliostat field layout in central receiver systems based on yearly normalized energy surfaces. Sol Energy 80(7):861–874

    Article  Google Scholar 

  24. 24.

    Stine WB, Geyer M (2001) Power from the sun. Accessed July 2017

  25. 25.

    Tonatiuh Project Website (2013) Tonatiuh, ray tracing for solar energy. Accessed July 2017

  26. 26.

    Wang K, He YL (2017) Thermodynamic analysis and optimization of a molten salt solar power tower integrated with a recompression supercritical CO\(_2\) brayton cycle based on integrated modeling. Energy Convers Manage 135:336–350

    Article  Google Scholar 

  27. 27.

    Wendelin T, Dobos A, Lewandowski A (2013) SolTrace: a ray-tracing code for complex solar optical systems. Technical report NREL/TP-5500-59163, NREL

  28. 28.

    Yao Y, Hu Y, Gao S (2015) Heliostat field layout methodology in central receiver systems based on efficiency-related distribution. Sol Energy 117:114–124

    Article  Google Scholar 

  29. 29.

    Yeniay Ö (2005) Penalty function methods for constrained optimization with genetic algorithms. Math Comput Appl 10(1):45–56

    MathSciNet  Google Scholar 

  30. 30.

    Zhang H, Juchlia I, Favrat D, Pelet X (2007) Multi-objective thermo-economic optimisation of the design of heliostat field of solar tower power plants. In: Engineering for sustainable energy in developing countries. Rio de Janeiro, Brazil

  31. 31.

    Zhang HL, Baeyens J, Degrève J, Cacères G (2013) Concentrated solar power plants: review and design methodology. Renew Sustain Energy Rev 22:466–481

    Article  Google Scholar 

  32. 32.

    Zhang M, Yang L, Xu C, Du X (2016) An efficient code to optimize the heliostat field and comparisons between the biomimetic spiral and staggered layout. Renew Energy 87:720–730

    Article  Google Scholar 

  33. 33.

    Zhou Y, Zhao Y (2014) Heliostat field layout design for solar tower power plant based on GPU. IFAC Proc Vol 47(3):4953–4958

    Article  Google Scholar 

Download references


This work has been funded by Grants from the Spanish Ministry of Economy, Industry and Competitiveness (TIN2015-66680-C2-1-R and ENERPRO DPI 2014-56364-C2-1-R), Junta de Andalucía (P12-TIC301). N. C. Cruz (FPU14/01728) is supported by an FPU Fellowship from the Spanish Ministry of Education. J. L. Redondo (RYC-2013-14174) and J. D. Álvarez (RYC-2013-14107) are fellows of the Spanish ‘Ramón y Cajal’ contract program, co-financed by the European Social Fund. The authors also wish to thank Juan José Moreno Riado for his technical support.

Author information



Corresponding author

Correspondence to N. C. Cruz.

Complementary material

Complementary material

A C++ library with the proposed optimizer and the description of a new heuristic to generate sets of initial solutions can be found at

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cruz, N.C., Salhi, S., Redondo, J.L. et al. Design of a parallel genetic algorithm for continuous and pattern-free heliostat field optimization. J Supercomput 75, 1268–1283 (2019).

Download citation


  • Genetic algorithm
  • Parallel computing
  • Heliostat field optimization
  • Solar power tower