# A learning automata-based memetic algorithm

## Abstract

Combing a genetic algorithm (GA) with a local search method produces a type of evolutionary algorithm known as a memetic algorithm (MA). Combining a GA with a learning automaton (LA) produces an MA named GALA, where the LA provides the local search function. GALA represents chromosomes as object migration automata (OMAs), whose states represent the history of the local search process. Each state in an OMA has two attributes: the value of the gene (allele), and the degree of association with those values. The local search changes the degree of association between genes and their values. In GALA a chromosome’s fitness is computed using only the value of the genes. GALA is a Lamarckian learning model as it passes on the learned traits acquired by its local search method to offspring by a modification of the genotype. Herein we introduce a modified GALA (MGALA) that behaves according to a Baldwinian learning model. In MGALA the fitness function is computed using a chromosome’s fitness and the history of the local search recorded by the OMA states. In addition, in MGALA the learned traits are not passed to the offspring. Unlike GALA, MGALA uses all the information recorded in an OMA representation of the chromosome, i.e., the degree of association between genes and their alleles, and the value of a gene, to compute the fitness of genes. We used MGALA to solve two problems: object partitioning and graph isomorphism. MGALA outperformed GALA, a canonical MA, and an OMA-based method using computer simulations, in terms of solution quality and rate of convergence.

### Keywords

Learning automata (LA) Local search Memetic algorithm (MA) Object migration automata (OMA)### References

- 1.M. Weber, F. Neri, V. Tirronen, Distributed differential evolution with explorative–exploitative population families. Genet. Progr. Evolvable Mach.
**10**, 343–371 (2009)CrossRefGoogle Scholar - 2.K.W. Ku, M.-W. Mak, Empirical analysis of the factors that affect the Baldwin effect, in
*Parallel Problem Solving from Nature*—*PPSN V*(1998), pp. 481–490Google Scholar - 3.G.M. Morris, D.S. Goodsell, R.S. Halliday, R. Huey, W.E. Hart, R.K. Belew, A.J. Olson, Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J. Comput. Chem.
**19**, 1639–1662 (1998)CrossRefGoogle Scholar - 4.C. Xianshun, O. Yew-Soon, L. Meng-Hiot, T. Kay Chen, A multi-facet aurvey on memetic computation. IEEE Trans. Evol. Comput.
**15**, 591–607 (2011)CrossRefGoogle Scholar - 5.N. Krasnogor, J. Smith, A tutorial for competent memetic algorithms: model, taxonomy, and design issues. Evol. Comput. IEEE Trans.
**9**, 474–488 (2005)CrossRefGoogle Scholar - 6.K. Downing, Reinforced genetic programming. Genet. Progr. Evolvable Mach.
**2**, 259–288 (2001)MATHCrossRefGoogle Scholar - 7.K.S. Narendra, M.A.L. Thathachar,
*Learning automata: an introduction*(Prentice-Hall, Inc, Upper Saddle River, 1989)Google Scholar - 8.M.A.L. Thathachar, P.S. Sastry, Varieties of learning automata: an overview. IEEE Trans. Syst. Man Cybern. B Cybern.
**32**, 711–722 (2002)CrossRefGoogle Scholar - 9.M. Rezapoor, M.R. Meybodi, A hybrid algorithm for solving graph isomorphism problem, in
*Proceedings of the Second International Conference on Information and Knowledge Technology (IKT2005), Tehran, Iran*(2005)Google Scholar - 10.B.J. Oommen, D.C.Y. Ma, Deterministic learning automata solutions to the equipartitioning problem. IEEE Trans. Comput.
**37**, 2–13 (1988)MATHMathSciNetCrossRefGoogle Scholar - 11.M. Rezapoor, M.R. Meybodi, Improving GA+ LA algorithm for solving graph isomorphic problem, in
*Proceedings of the 11th Annual CSI Computer Conference of Iran, Tehran, Iran*(2006), pp. 474–483Google Scholar - 12.K. Asghari, A. Safari Mamaghani, F. Mahmoudi, M.R. Meybodi, A relational databases query optimization using hybrid evolutionary algorithm. J. Comput. Robot.
**1**, 28–39 (2008)Google Scholar - 13.K. Asghari, A. Safari Mamaghani, M.R. Meybodi, An evolutionary approach for query optimization problem in database, in
*Procceding of Internatinal Joint Conferance on Computers, Information and System Sciences, and Engineering (CISSE2007)*(University of Bridgeport, England, 2007)Google Scholar - 14.A. Safari Mamaghani, K. Asghari, M.R. Meybodi, F. Mahmoodi, A new method based on genetic algorithm for minimizing join operations cost in data base, in
*Proceedings of 13th Annual CSI Computer Conference of Iran, Kish Island, Iran*(2008)Google Scholar - 15.A. Safari Mamaghani, K. Asghari, F. Mahmoudi, and M. R. Meybodi, A novel hybrid algorithm for joint ordering problem in database queries, in
*Proceedings of 6th WSEAS international Conference on Computational Intelligence, Man*-*Machine Systems and Cybernetics, Tenerife, Spain*(2007), pp. 104–109Google Scholar - 16.B. Zaree, M. R. Meybodi, An evolutionary method for solving symmetric TSP, in
*Proceedings of the Third International Conference on Information and Knowledge Technology (IKT2007), Mashhad, Iran*(2007)Google Scholar - 17.B. Zaree, M.R. Meybodi, M. Abbaszadeh, A hybrid method for solving traveling salesman problem. IEEE/ACIS International Conference on Computer and Information Science, ICIS
**2007**, 394–399 (2007)Google Scholar - 18.B. Zaree, K. Asghari, M.R. Meybodi, A hybrid method based on clustering for solving large traveling salesman problem, in
*Proceedings of 13th Annual CSI Computer Conference of Iran, Kish Island, Iran*(2008)Google Scholar - 19.K. Asghari, M.R. Meybodi, Searching for Hamiltonian cycles in graphs using evolutionary methods, in
*Proceedings of the second Joint Congress on Fuzzy and Intelligent Systems, Tehran, Iran*(2008)Google Scholar - 20.B. Zaree, M.R. Meybodi, A hybrid method for sorting problem, in
*Proceedings of the Third International Conference on Information and Knowledge Technology (IKT2007), Mashhad, Iran*(2007)Google Scholar - 21.A. Safari Mamaghani, M.R. Meybodi, Hybrid algorithms (learning automata + genetic algorithm) for solving graph bandwidth minimization problem, in
*Proceedings of the second Joint Congress on Fuzzy and Intelligent Systems, Tehran, Iran*(2008)Google Scholar - 22.A.S. Mamaghani, M.R. Meybodi, A learning automaton based approach to solve the graph bandwidth minimization problem, in
*International Conference on Application of Information and Communication Technologies (AICT)*(2011), pp. 1–5Google Scholar - 23.A. Isazadeh, H. Izadkhah, A. Mokarram, A learning based evolutionary approach for minimization of matrix bandwidth problem. Appl. Math.
**6**, 51–57 (2012)MathSciNetGoogle Scholar - 24.A.S. Mamaghani, M.R. Meybodi, Clustering of software systems using new hybrid algorithms, in
*Ninth IEEE International Conference on Computer and Information Technology*(2009), pp. 20–25Google Scholar - 25.A. Safari Mamaghani, M.R. Meybodi, Hybrid evolutionary algorithms for solving software clustering problem, in
*Proceedings of the second Joint Congress on Fuzzy and Intelligent Systems, Tehran, Iran*(2008)Google Scholar - 26.K. Asghari, M.R. Meybodi, Solving single machine total weighted tardiness scheduling problem using learning automata and genetic algorithm, in
*Proceedings of the 3rd Iran Data Mining Conference(IDMC’09), Tehran Iran*(2009)Google Scholar - 27.A.S. Mamaghani, M. Mahi, M.R. Meybodi, A learning automaton based approach for data fragments allocation in distributed database systems, in
*IEEE 10th International Conference on Computer and Information Technology (CIT)*(2010), pp. 8–12Google Scholar - 28.A.S. Mamaghani, M. Mahi, M.R. Meybodi, M.H. Moghaddam, A novel evolutionary algorithm for solving static data allocation problem in distributed database systems, in
*Second International Conference on Network Applications Protocols and Services (NETAPPS)*(2010), pp. 14–19Google Scholar - 29.V. Majid Nezhad, H. Motee Gader, E. Efimov, A novel hybrid algorithm for task graph scheduling. Int. J. Comput. Sci. Issues
**8**, 32–38 (2011)Google Scholar - 30.A. Bansal, R. Kaur, Task graph scheduling on multiprocessor system using genetic algorithm. Int. J. Eng. Res. Technol.
**1**, 1–5 (2012)Google Scholar - 31.W. Yuan-Kai, F. Kuo-Chin, H. Jorng-Tzong, Genetic-based search for error-correcting graph isomorphism. IEEE Trans. Syst. Man Cybern. B Cybern.
**27**, 588–597 (1997)CrossRefGoogle Scholar - 32.P. Foggia, C. Sansone, M. Vento, A database of graphs for isomorphism and sub-graph isomorphism benchmarking, in
*Proceedings of the 3rd IAPR TC*-*15 International Workshop on Graph*-*based Representations*(2001), pp. 176–187Google Scholar - 33.J.R. Ullmann, An algorithm for subgraph isomorphism. J. ACM
**23**, 31–42 (1976)MathSciNetCrossRefGoogle Scholar - 34.L.P. Cordella, P. Foggia, C. Sansone, M. Vento, A (sub) graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell.
**26**, 1367–1372 (2004)CrossRefGoogle Scholar