Abstract
The Dissipative Lozi chaotic map is embedded in the discrete self organising migrating algorithm (DSOMA), as a pseudorandom generator. This novel chaotic based algorithm is applied to the constraint based lot-streaming flowshop scheduling problem. Two new and unique data sets generated using the Lozi and Delayed Logistic maps are used to compare the chaos embedded DSOMA and the generic DSOMA utilising the venerable Mersenne Twister. In total, 100 data sets were tested by these two algorithms, for the idling and the non-idling case. From the obtained results, the chaos variant algorithm is shown to significantly improve the performance of generic DSOMA.













Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Alatas B, Akin E, Ozer A (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals 40(4):1715–1734
Caponetto R, Fortuna L, Fazzino S, Xibilia M (2003) Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans Evol Comput 7(3):289–304
Chang JL, Gong DW, Ma XP (2007) A heuristic genetic algorithm for no-wait flowshop scheduling problem. J China Univ Min Technol 17(4):582–586
Davendra D (2009) Chaotic attributes and permutative optimization. Ph.D. thesis, Tomas Bata University in Zlin, Zlin
Davendra D (2012) Flowshop lot-streaming problem data sets. http://mrl.cs.vsb.cz/people/davendra/research.html
Davendra D, Bialic-Davendra M (2013) Scheduling flow shops with blocking using a discrete self-organising migrating algorithm. Int J Prod Res 51(8):2200–2218. doi:10.1080/00207543.2012.711968
Davendra D, Zelinka I, Senkerik R, Bialic-Davendra M (2010) Chaos driven evolutionary algorithm for the traveling salesman problem. In: Davendra D (ed) Traveling salesman problem, theory and applications. InTech Publishing, Croatia, pp 55–70
Davendra D, Zelinka I, Bialic-Davendra M, Senkerik R, Jasek R (2013) Discrete self-organising migrating algorithm for flow-shop scheduling with no-wait makespan. Math Comput Model 57(12):100–110. doi:10.1016/j.mcm.2011.05.029
Davendra D, Zelinka I, Senkerik R (2010) Chaos driven evolutionary algorithms for the task of pid control. Comput Math Appl 60(4):1088–1104
Hennon M (1979) A two-dimensional mapping with a strange attractor. Commun Math Phys 50:69–77
Herring C, Julian P (1989) Random number generators are chaotic. ACM SIGPLAN 11:1–4
Hilborn R (2000) Chaos and nonlinear dynamics: an introduction for scientists and engineers. OUP, Oxford
Lehmer D (1951) Mathematical methods in large-scale computing units. Ann Comput Lab (Harvard University) 26:141–146
Lozi R (2008) New enhanced chaotic number generators. Indian J Ind Appl Math 1(1):1–23
Lozi R (2009) Chaotic pseudo random number generators via ultra weak coupling of chaotic maps and double threshold sampling sequences. In: ICCSA 2009 the 3rd international conference on complex systems and applications. University of Le Havre, France, pp 1–5
Lu Y, Zhou J, Qin H, Wang Y, Zhang Y (2011) Chaotic differential evolution methods for dynamic economic dispatch with valve-point effects. Eng Appl Artif Intell 24(2):378–387
Matsumoto M (2012) Mersenne twister webpage. http://www.math.sci.hiroshima-u.ac.jp/m-mat/MT/ARTICLES/earticles.html
Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans Model Comput Simul 8(1):3–30
Ozer A (2010) Cide: chaotically initialized differential evolution. Expert Syst Appl 37(6):4632–4641
Palmore J, McCauley J (1987) Shadowing by computable chaotic orbits. Phys Lett A 121:399
Pan QK, Fatih Tasgetiren M, Suganthan PN, Chua TJ (2011) A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem. Inf Sci 181(12):2455–2468. doi:10.1016/j.ins.2009.12.025
Pan QK, Ruiz R (2012) An estimation of distribution algorithm for lot-streaming flow shop problems with setup times. Omega 40(2):166–180
Potts CN, Baker KR (1989) Flow shop scheduling with lot streaming. Oper Res Lett 8(6):297–303
Price K (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimisation. McGraw Hill International, UK
Sarin SC, Jaiprakash P (2007) Flow shop lot streaming. Springer, Berlin
Stojanovski T, Kocarev L (2001) Chaos-based random number generators part I: analysis. IEEE Trans Circuits Syst I Fundam Theory Appl 48(3):281–288
Yavuz M (2010) Fuzzy lead time management. In: Kahraman C, Yavuz M (eds) Production engineering and management under fuzziness, studies in fuzziness and soft computing, vol 252. Springer, Berlin/Heidelberg, pp 77–94
Yuan X, Cao B, Yang B, Yuan Y (2008) Hydrothermal scheduling using chaotic hybrid differential evolution. Energy Convers Manag 49(12):3627–3633
Zelinka I (2004) Soma—self organizing migrating algorithm. In: Onwubolu G, Babu B (eds) New optimization techniques in engineering. Springer-Verlag, Germany
Zuo X, Fan Y (2006) A chaos search immune algorithm with its application to neuro-fuzzy controller design. Chaos Solitons Fractals 30(1):94–109
Acknowledgments
Donald Davendra was supported by the Technology Agency of the Czech Republic under the Project TE01020197 and Michal Pluhacek was supported by the Internal Grant Agency of Tomas Bata University under the project No. IGA/FAI/2013/012.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by I. Zelinka.
Rights and permissions
About this article
Cite this article
Davendra, D., Senkerik, R., Zelinka, I. et al. Utilising the chaos-induced discrete self organising migrating algorithm to solve the lot-streaming flowshop scheduling problem with setup time. Soft Comput 18, 669–681 (2014). https://doi.org/10.1007/s00500-014-1219-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-014-1219-7