Andean Condor Algorithm for cell formation problems

Article

Abstract

This paper proposes a novel population based optimization algorithm called Andean Condor Algorithm (ACA) for solving cell formation problems. The ACA metaheuristic is inspired by the movement pattern of the Andean Condor when it searches for food. This pattern of movement corresponds to the flight distance traveled by the Andean Condor from its nest to the place where food is found. This distance varies depending on the seasons of the year. The ACA metaheuristic presents a balance of its population through a performance indicator based on the average quality of the population’s fitness. This balance determines the number of Andean Condors that will perform an exploration or intensification movements. ACA metaheuristics have a flexible design. It allows to easily integrate specific heuristics according to the optimization problem to be solved. Two types of computational experiments have been performed. According to the results obtained it has been possible to determine that ACA is an algorithm with an outstanding RPD% in relation to the algorithms BAT, MBO and PSO, robust and with a convergence which tends not to be trapped in the local optimums. Besides, according to the non-parametric multiple comparison, results have been obtained in which the ACA metaheuristic has significant differences in relation to the BAT, MBO and PSO algorithms.

Keywords

Andean Condor Algorithm Cell formation problem Metaheuristics Nature-inspired algorithms Animal behavior 

Notes

Acknowledgements

Boris Almonacid is supported by Animal Behavior Society, USA (Developing Nations Research Awards 2016); by Postgraduate Grant Pontificia Universidad Católica de Valparaíso, Chile (VRIEA 2016 and INF-PUCV 2015) and by Ph.D (h.c) Sonia Alvarez, Chile. Ricardo Soto is supported by Grant CONICYT / FONDECYT / REGULAR / 1160455. Also, we thank the anonymous reviewers for their constructive comments.

References

  1. Almonacid B (2018a) Appendix: Andean Condor Algorithm for cell formation problems.  https://doi.org/10.6084/m9.figshare.5805360. https://figshare.com/s/ed10f7ae1739e21ea352. Accessed 21 Jan 2018
  2. Almonacid B (2018b) Dataset: Andean Condor Algorithm for cell formation problems.  https://doi.org/10.6084/m9.figshare.5808780. https://figshare.com/s/b6dfee83cd7d619339ce. Accessed 21 Jan 2018
  3. Almonacid B, Aspée F, Soto R, Crawford B, Lama J (2016) Solving manufacturing cell design problem using modified binary firefly algorithm and Egyptian vulture optimization algorithm. IET Software, LondonGoogle Scholar
  4. Asktn RG, Subramantan SP (1987) A cost-based heuristic for group technology configuration. Int J Prod Res 25(1):101–113CrossRefGoogle Scholar
  5. Badgerow JP, Hainsworth FR (1981) Energy savings through formation flight? a re-examination of the vee formation. J Theor Biol 93(1):41–52CrossRefGoogle Scholar
  6. Boctor F (1991a) A linear formulation of the machine-part cell formation problem. Int J Prod Res 29(2):343–356CrossRefGoogle Scholar
  7. Boctor FF (1991b) A jinear formulation of the machine-part cell formation problem. Int J Prod Res 29(2):343–356CrossRefGoogle Scholar
  8. Boe WJ, Cheng CH (1991) A close neighbour algorithm for designing cellular manufacturing systems. Int J Prod Res 29(10):2097–2116CrossRefMATHGoogle Scholar
  9. Breves C (2008) Plumaje de color anormal en Cóndor Andino (Vultur gryphus) en Chile central. Abnormal plumage color in Andean Condor (Vultur gryphus) in central Chile. Boletin Chileno de Ornitología 14(1):52–55Google Scholar
  10. Carrie A (1973) Numerical taxonomy applied to group technology and plant layout. Int J Prod Res 11(4):399–416CrossRefGoogle Scholar
  11. Chan H, Milner D (1982) Direct clustering algorithm for group formation in cellular manufacture. J Manuf Syst 1(1):65–75CrossRefGoogle Scholar
  12. Chandrasekar C et al (2013) An optimized approach of modified bat algorithm to record deduplication. Int J Comput Appl 62(1):10–15Google Scholar
  13. Chandrasekharan MP, Rajagopalan R (1986a) An ideal seed non-hierarchical clustering algorithm for cellular manufacturing. Int J Prod Res 24(2):451–463CrossRefMATHGoogle Scholar
  14. Chandrasekharan M, Rajagopalan R (1986b) Modroc: an extension of rank order clustering for group technology. Int J Prod Res 24(5):1221–1233CrossRefGoogle Scholar
  15. Chandrasekharan M, Rajagopalan R (1987) Zodiac-an algorithm for concurrent formation of part-families and machine-cells. Int J Prod Res 25(6):835–850CrossRefMATHGoogle Scholar
  16. Chandrasekharan M, Rajagopalan R (1989) Groupabil1ty: an analysis of the properties of binary data matrices for group technology. Int J Prod Res 27(6):1035–1052CrossRefGoogle Scholar
  17. Crawford B, Soto R, Zuñiga G, Monfroy E, Paredes F (2014) Modeling manufacturing cell design problems: Cp vs mh. In: International conference on human–computer interaction. Springer, pp. 498–502Google Scholar
  18. Donázar J, Feijóo JE (2002) Social structure of Andean Condor roosts: influence of sex, age, and season. The Condor 104(4):832CrossRefGoogle Scholar
  19. Duman E, Uysal M, Alkaya AF (2012) Migrating birds optimization: a new metaheuristic approach and its performance on quadratic assignment problem. Inf Sci 217:65–77MathSciNetCrossRefGoogle Scholar
  20. Durán O, Rodriguez N, Consalter LA (2010) Collaborative particle swarm optimization with a data mining technique for manufacturing cell design. Expert Syst Appl 37(2):1563–1567CrossRefGoogle Scholar
  21. Fister I, Rauter S, Yang XS, Ljubič K (2015) Planning the sports training sessions with the bat algorithm. Neurocomputing 149:993–1002CrossRefGoogle Scholar
  22. Gaing ZL (2003) Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst 18(3):1187–1195CrossRefGoogle Scholar
  23. Gao X, Alvo M (2008) Nonparametric multiple comparison procedures for unbalanced two-way layouts. J Stat Plan Inference 138(12):3674–3686MathSciNetCrossRefMATHGoogle Scholar
  24. Gao X, Alvo M, Chen J, Li G (2008) Nonparametric multiple comparison procedures for unbalanced one-way factorial designs. J Stat Plan Inference 138(8):2574–2591MathSciNetCrossRefMATHGoogle Scholar
  25. Hollander M, Wolfe DA, Chicken E (2013) Nonparametric statistical methods. Wiley, New YorkMATHGoogle Scholar
  26. Hummel D, Beukenberg M (1989) Aerodynamische interferenzeffekte beim formationsflug von vögeln. Journal für Ornithologie 130(1):15–24CrossRefGoogle Scholar
  27. Kennedy J (2011) Particle swarm optimization. In: Sammut C, Webb G (eds) Encyclopedia of machine learning. Springer, Berlin, pp 760–766Google Scholar
  28. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995. Proceedings, vol 4, pp. 1942–1948Google Scholar
  29. King JR (1980) Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm. Int J Prod Res 18(2):213–232MathSciNetCrossRefGoogle Scholar
  30. King JR, Nakornchai V (1982) Machine-component group formation in group technology: review and extension. Int J Prod Res 20(2):117–133CrossRefGoogle Scholar
  31. Kumar KR, Vannelli A (1986) Strategic subcontracting for efficient disaggregated manufacturing. BEBR faculty working paper no. 1252Google Scholar
  32. Kumar KR, Kusiak A, Vannelli A (1986) Grouping of parts and components in flexible manufacturing systems. Eur J Oper Res 24(3):387–397CrossRefMATHGoogle Scholar
  33. Kusiak A, Cho M (1992) Similarity coefficient algorithms for solving the group technology problem. Int J Prod Res 30(11):2633–2646CrossRefGoogle Scholar
  34. Kusiak A, Chow WS (1987) Efficient solving of the group technology problem. J Manuf Syst 6(2):117–124CrossRefGoogle Scholar
  35. Lambertucci SA, Trejo A, Di Martino S, Sánchez-zapata JA, Donázar JA, Hiraldo F (2009) Spatial and temporal patterns in the diet of the Andean condor: ecological replacement of native fauna by exotic species. Anim Conserv 12(4):338–345CrossRefGoogle Scholar
  36. Lemma TA, Hashim FBM (2011) Use of fuzzy systems and bat algorithm for exergy modeling in a gas turbine generator. In: IEEE colloquium on humanities, science and engineering (CHUSER), 2011. IEEE, pp. 305–310Google Scholar
  37. Lissaman P, Shollenberger CA (1970) Formation flight of birds. Science 168(3934):1003–1005CrossRefGoogle Scholar
  38. McCormick WT Jr, Schweitzer PJ, White TW (1972) Problem decomposition and data reorganization by a clustering technique. Oper Res 20(5):993–1009CrossRefMATHGoogle Scholar
  39. McGahan J (1973) Flapping flight of the Andean condor in nature. J Exp Biol 58:239–253Google Scholar
  40. Mosier C, Taube L (1985a) The facets of group technology and their impacts on implementation-a state-of-the-art survey. Omega 13(5):381–391CrossRefGoogle Scholar
  41. Mosier C, Taube L (1985b) Weighted similarity measure heuristics for the group technology machine clustering problem. Omega 13(6):577–579CrossRefGoogle Scholar
  42. Naveda-Rodríguez A et al (2016) Andean Condor (Vultur gryphus) in Ecuador: geographic distribution, population size and extinction risk. PLOS One 11(3):e0151,827CrossRefGoogle Scholar
  43. Nethercote N, Stuckey PJ, Becket R, Brand S, Duck GJ, Tack G (2007) Minizinc: towards a standard cp modelling language. In: Bessière C (ed) Principles and practice of constraint programming—CP 2007. Springer, Berlin, Heidelberg, pp 529–543CrossRefGoogle Scholar
  44. Niroomand S, Hadi-Vencheh A, Şahin R, Vizvari B (2015) Modified migrating birds optimization algorithm for closed loop layout with exact distances in flexible manufacturing systems. Expert Syst Appl 42:6586–6597CrossRefGoogle Scholar
  45. Pan QK, Dong Y (2014) An improved migrating birds optimisation for a hybrid flowshop scheduling with total flowtime minimisation. Inf Sci 277:643–655MathSciNetCrossRefMATHGoogle Scholar
  46. Park JB, Lee KS, Shin JR, Lee KY (2005) A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans Power Syst 20(1):34–42CrossRefGoogle Scholar
  47. Pavez EF (2008) Patrón de movimiento de dos cóndores andinos vultur gryphus (aves: Cathartidae) en los andes centrales de chile y argentina. Boletín Chileno de Ornitología 20((1–2)):1–12Google Scholar
  48. Rayner J (1979) A new approach to animal flight mechanics. J Exp Biol 80(1):17–54Google Scholar
  49. Reddy VU, Manoj A (2012) Optimal capacitor placement for loss reduction in distribution systems using bat algorithm. IOSR J Eng 2(10):23–27CrossRefGoogle Scholar
  50. Robinson J, Rahmat-Samii Y (2004) Particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407MathSciNetCrossRefMATHGoogle Scholar
  51. Royston JP (1982a) An extension of Shapiro and Wilk’s W test for normality to large samples. J R Stat Soc Ser C (Appl Stat) 2:115–124MATHGoogle Scholar
  52. Royston JP (1982b) Algorithm as 181: the w test for normality. J R Stat Soc Ser C (Appl Stat) 31(2):176–180Google Scholar
  53. Royston P (1992) Approximating the Shapiro–Wilk W-test for non-normality. Stat Comput 2(3):117–119CrossRefGoogle Scholar
  54. Royston P (1995) Remark as r94: a remark on algorithm as 181: the w-test for normality. J R Stat Soc Ser C (Appl Stat) 44(4):547–551Google Scholar
  55. Salman A, Ahmad I, Al-Madani S (2002) Particle swarm optimization for task assignment problem. Microprocessors Microsyst 26(8):363–371CrossRefGoogle Scholar
  56. Seifoddini H (1989) A note on the similarity coefficient method and the problem of improper machine assignment in group technology applications. Int J Prod Res 27(7):1161–1165CrossRefGoogle Scholar
  57. Seifoddini H, Wolfe PM (1986) Application of the similarity coefficient method in group technology. IIE Trans 18(3):271–277CrossRefGoogle Scholar
  58. Selvakumar AI, Thanushkodi K (2007) A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst 22(1):42–51CrossRefGoogle Scholar
  59. Shen L, Asmuni H, Weng F (2014) A modified migrating bird optimization for university course timetabling problem. Jurnal Teknologi 72(1):89–96Google Scholar
  60. Soto R, Kjellerstrand H, Durán O, Crawford B, Monfroy E, Paredes F (2012a) Cell formation in group technology using constraint programming and boolean satisfiability. Expert Syst. Appl. 39(13):11423–11427CrossRefGoogle Scholar
  61. Soto R, Kjellerstrand H, Gutiérrez J, López A, Crawford B, Monfroy E (2012b) Solving manufacturing cell design problems using constraint programming. In: International conference on industrial, engineering and other applications of applied intelligent systems. Springer, pp. 400–406Google Scholar
  62. Soto R, Crawford B, Almonacid B, Paredes F (2015a) A migrating birds optimization algorithm for machine-part cell formation problems. In: Advances in artificial intelligence and soft computing. pp. 270–281, SpringerGoogle Scholar
  63. Soto R, Crawford B, Almonacid B, Paredes F (2015b) A migrating birds optimization algorithm for machine-part cell formation problems. In: Mexican international conference on artificial intelligence. Springer, pp. 270–281Google Scholar
  64. Soto R, Crawford B, Vega E, Paredes, F (2015c) Solving manufacturing cell design problems using an artificial fish swarm algorithm. In: Mexican international conference on artificial intelligence. Springer, pp. 282–290Google Scholar
  65. Soto R, Crawford B, Alarcón A, Zec C, Vega E, Reyes V, Araya I, Olguín E (2016a) Solving manufacturing cell design problems by using a bat algorithm approach. In: International conference in swarm intelligence. Springer, pp. 184–191Google Scholar
  66. Soto R, Crawford B, Almonacid B (2016b) Efficient leader exchange for migrating birds optimization when solving machine-part cell formation problems. In: 11th Iberian conference on information systems and technologies (CISTI), 2016. IEEE, pp. 1–7Google Scholar
  67. Soto R, Crawford B, Almonacid B, Paredes F (2016c) Efficient parallel sorting for migrating birds optimization when solving machine-part cell formation problems. Sci Program 2016:21Google Scholar
  68. Soto R, Crawford B, Carrasco C, Almonacid B, Reyes V, Araya I, Misra S, Olguín E (2016d) Solving manufacturing cell design problems by using a dolphin echolocation algorithm. In: International conference on computational science and its applications. Springer, pp. 77–86Google Scholar
  69. Soto R, Crawford B, Castillo C, Paredes F (2016e) Solving the manufacturing cell design problem via invasive weed optimization. In: Artificial intelligence perspectives in intelligent systems. Springer, pp. 115–126Google Scholar
  70. Soto R, Crawford B, Lama J, Almonacid B (2016f) A firefly algorithm to solve the manufacturing cell design problem. In: 11th Iberian conference on information systems and technologies (CISTI), 2016. IEEE, pp. 1–7Google Scholar
  71. Soto R, Crawford B, Vega E, Johnson F, Paredes F (2016g) Solving manufacturing cell design problems using a shuffled frog leaping algorithm. In: The 1st international conference on advanced intelligent system and informatics (AISI2015), 28–30 Nov 2015, Beni Suef, Egypt. Springer, pp. 253–261Google Scholar
  72. Speziale KL, Lambertucci SA, Olsson O (2008) Disturbance from roads negatively affects Andean condor habitat use. Biol Conserv 141(7):1765–1772CrossRefGoogle Scholar
  73. Srinlvasan G, Narendran T, Mahadevan B (1990) An assignment model for the part-families problem in group technology. Int J Prod Res 28(1):145–152CrossRefGoogle Scholar
  74. Stanfel LE (1985) Machine clustering for economic production. Eng Costs Prod Econ 9(1):73–81CrossRefGoogle Scholar
  75. Stuckey PJ, Feydy T, Schutt A, Tack G, Fischer J (2014) The MiniZinc challenge 2008–2013. AI Mag 35(2):55–60CrossRefGoogle Scholar
  76. Tsai PW, Pan JS, Liao BY, Tsai MJ, Istanda V (2012) Bat algorithm inspired algorithm for solving numerical optimization problems. In: Chang G (ed) Applied mechanics and materials, vol 148, pp. 134–137. Trans Tech PublGoogle Scholar
  77. Waghodekar P, Sahu S (1984) Machine-component cell formation in group technology: mace. Int J Prod Res 22(6):937–948CrossRefGoogle Scholar
  78. Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp. 65–74Google Scholar
  79. Yang XS (2011) Bat algorithm for multi-objective optimisation. Int J Bio Inspir Comput 3(5):267–274CrossRefGoogle Scholar
  80. Yang XS, He X (2013) Bat algorithm: literature review and applications. Int J Bio Inspir Comput 5(3):141–149CrossRefGoogle Scholar
  81. Yang XS, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483CrossRefGoogle Scholar
  82. Zhang JW, Wang GG (2012) Image matching using a bat algorithm with mutation. In: Du Z, Liu B (eds) Applied mechanics and materials, vol 203, pp. 88–93. Trans Tech PublGoogle Scholar
  83. Zhang B, Pan Q, Gao L, Zhang X, Sang H, Li J (2017) An effective modified migrating birds optimization for hybrid flowshop scheduling problem with lot streaming. Appl Soft Comput 52:14–27CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Pontificia Universidad Católica de ValparaísoValparaísoChile

Personalised recommendations