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


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.


Genetic algorithms Crossover Dual mutation Schema Schema survival 



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.


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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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