Improved Mean Variance Mapping Optimization for the Travelling Salesman Problem

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 31)

Abstract

This paper presents an improved Mean Variance Mapping Optimization to address and solve the NP-hard combinatorial problem, the travelling salesman problem. MVMO, conceived and developed by István Erlich is a recent addition to the large set of heuristic optimization algorithms with a strategic novel feature of mapping function used for mutation on basis of the mean and variance of the population set initialized. Also, a new crossover scheme has been proposed which is a collective of two crossover techniques to produce fitter offsprings. The mutation technique adopted is only used if it converges towards more economic traversal. Also, the change in control parameters of the algorithm doesn’t affect the result thus making it a fine algorithm for combinatorial as well as continuous problems as is evident from the experimental results and the comparisons with other algorithms which has been tested against the set of benchmarks from the TSPLIB library.

Keywords

Mean variance mapping optimization Travelling salesman problem Combinatorial optimization 

References

  1. 1.
    Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM 45(5), 753–782 (1998)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    Teodorovic, D., Lucic, P., Markovic, G., Orco, M.D.: Bee colony optimization: principles and applications. In: 8th Seminar on neural network applications in electrical engineering, pp. 151–156. IEEE (2006)Google Scholar
  3. 3.
    Yang, X.S., Deb, S.: Cuckoo search via levy flights. In: World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), pp. 210–214. IEEE (2009)Google Scholar
  4. 4.
    Yang, X.S.: Firefly algorithms for multimodal optimization. In: Stochastic Algorithms: Foundations and Application (SAGA 2009). Lecture notes in computer sciences, vol. 5792, pp. 169–178 (2009)Google Scholar
  5. 5.
    Mucherino, A., Seref, O.: Monkey search: a novel metaheuristic search for global optimization. In: Data mining, systems analysis, and optimization in biomedicine (AIP conference proceedings), vol. 953, pp. 162–173. American Institute of Physics, Melville, USA (2007)Google Scholar
  6. 6.
    Dorigo, M., Gambardella, L.M., et al.: Ant colonies for the travelling salesman problem. BioSystems 43(2), 73–82 (1997)CrossRefGoogle Scholar
  7. 7.
    Ouaarab, A., Ahiod, B., Yang X.S.: Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput. Appl. (2013) Google Scholar
  8. 8.
    Erlich, I, Venayagamoorthy, G.K., Nakawiro, W: A mean-variance optimization algorithm. In: Proceedings of 2010 IEEE World Congress on Computational Intelligence, pp. 1–6, Barcelona, Spain (2010)Google Scholar
  9. 9.
    Ahmed, Z.H.: Genetic algorithm for the travelling salesman problem using sequential constructive crossover. IJBB 3(6) (2010)Google Scholar
  10. 10.
    Oliver, I., et al.: A study of permutation crossover operators on the travelling salesman problem. In: Proceedings of the Second International Conference on Genetic Algorithms, pp. 224–230 (1987)Google Scholar
  11. 11.
    Hlaing, Z., Khine, M.: Solving travelling salesman problem by using improved ant colony optimization algorithm. Int. J. Inf. Educ. Technol. 1(5), 404–409 (2011)CrossRefGoogle Scholar
  12. 12.
    Chen, W., et al.: A novel set-based particle swarm optimization method for discrete optimization problems. IEEE Trans. Evol. Comput. 14(2), 278–300 (2010)CrossRefGoogle Scholar
  13. 13.
    Chen, S.M., Chien, C.Y.: Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst. Appl. 38(12), 14439–14450 (2010)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringVeer Surendra Sai University of TechnologyBurlaIndia
  2. 2.Department of Electrical Engineering and Information TechnologiesUniversity of DuisburgEssenGermany

Personalised recommendations