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Soft Computing

, Volume 22, Issue 6, pp 1763–1771 | Cite as

Mathematical analysis of schema survival for genetic algorithms having dual mutation

  • Apoorva Mishra
  • Anupam Shukla
Foundations

Abstract

Genetic algorithms are widely used in the field of optimization. Schema theory forms the foundational basis for the success of genetic algorithms. Traditional genetic algorithms involve only a single mutation phase per iteration of the algorithm. In this paper, a novel concept of genetic algorithms involving two mutation steps per iteration is proposed. The purpose of adding a second mutation phase is to improve the explorative power of the genetic algorithms. All the possible cases regarding the working of the proposed variant of the genetic algorithms are explored. After a meticulous analysis of all these cases, three lemmas are proposed regarding the survival of a schema after the application of the dual mutation. Based on these three lemmas, a theorem is proved, and a mathematical expression representing the probability of survival of a schema after the application of the crossover and dual mutation is derived. This expression provides a new insight about the penetration of a schema for such scenario and improves our understanding of the functioning of this modified form of the genetic algorithm.

Keywords

Genetic algorithms Crossover Dual mutation Schema Schema survival 

Notes

Acknowledgements

The authors are grateful to Prof. S.G. Deshmukh, Director, ABV-Indian Institute of Information Technology and Management (an autonomous institute of Government of India), Gwalior (M.P), for providing a cordial atmosphere of research in the institute.

Compliance with ethical standards

Conflict of interest

Prof. Anupam Shukla has received the funds from the Department of Electronics and Information Technology, Ministry of Communication and Information Technology, Government of India, under Grant No. 23011/22/2013-R&D in CC & BT.

References

  1. Banerjee A (2013) A novel probabilistically-guided context-sensitive crossover operator for clustering. Swarm Evol Comput. doi: 10.1016/j.swevo.2013.05.007 Google Scholar
  2. Basagoiti MBR, Rodriguez IRV (2016) A modified genetic algorithm applied to the elevator dispatching problem. Soft Comput. doi: 10.1007/s00500-015-1718-1 Google Scholar
  3. Faraji R, Naji HR (2014) An efficient crossover architecture for hardware parallel implementation of genetic algorithm. Neurocomputing. doi: 10.1016/j.neucom.2013.08.035 Google Scholar
  4. Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, ReadingzbMATHGoogle Scholar
  5. Hsu C, Cho H (2015) A genetic algorithm for the maximum edge-disjoint paths problem. Neurocomputing. doi: 10.1016/j.neucom.2012.10.046
  6. Li Y, Yu J, Tao D (2014) Genetic algorithm for spanning tree construction in P2P distributed interactive applications. Neurocomputing. doi: 10.1016/j.neucom.2014.02.035 Google Scholar
  7. Mehboob U, Qadir J, Ali S, Vasilakos A (2016) Genetic algorithms in wireless networking: techniques, applications, and issues. Soft Comput. doi: 10.1007/s00500-016-2070-9 Google Scholar
  8. Mishra A, Shukla A (2016) Mathematical analysis of the cumulative effect of novel ternary crossover operator and mutation on probability of survival of a schema. Theor Comput Sci. doi: 10.1016/j.tcs.2016.07.035 zbMATHGoogle Scholar
  9. Nogueira B, Maciel P, Tavares E, Silva RMA, Andrade E (2016) Multi-objective optimization of multimedia embedded systems using genetic algorithms and stochastic simulation. Soft Comput. doi: 10.1007/s00500-016-2061-x Google Scholar
  10. Pawar R, Saini JS, Gopal M, Mittal AP (2011) Towards generalized expression for schemata count. Appl Soft Comput J. doi: 10.1016/j.asoc.2010.07.012
  11. Qiongbing Z, Lixin D (2016) A new crossover mechanism for genetic algorithms with variable-length chromosomes for path optimization problems. Expert Syst Appl. doi: 10.1016/j.eswa.2016.04.005 Google Scholar
  12. Shih CC, Horng MF, Pan TS, Pan JS, Chen CY (2016) A genetic-based effective approach to path-planning of autonomous underwater glider with upstream-current avoidance in variable oceans. Soft Comput. doi: 10.1007/s00500-016-2122-1 Google Scholar
  13. Shukla A, Tiwari R, Kala R (2010) Towards hybrid and adaptive computing studies in computational intelligence. Computational intelligence. Springer, Berlin. ISBN: 9783642143434. doi: 10.1007/978-3-642-14344-1
  14. Thi N, Quyen P, Chen JC (2016) Hybrid genetic algorithm to solve resource constrained assembly line balancing problem in footwear manufacturing. Soft Comput. doi: 10.1007/s00500-016-2181-3 Google Scholar
  15. Uzor CJ, Gongora M, Coupland S, Passow BN (2016) Adaptive-mutation compact genetic algorithm for dynamic environments. Soft Comput. doi: 10.1007/s00500-016-2195-x
  16. White D (2014) An overview of schema theory. Neural Evol Comput (cs.NE) 1–27. arXiv:1401.2651

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Soft Computing and Expert System LaboratoryABV -Indian Institute of Information Technology and ManagementGwaliorIndia

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