Skip to main content

Advertisement

SpringerLink
Log in

A random-permutation based GA for generalized traveling salesman problem in imprecise environments

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

A random-permutation technique and the features of the genetic algorithm (GA) are combined together to develop a novel heuristic for solving generalized travelling salesman problem. Here, the random-permutation technique is used to find the sequence of clusters of a probable solution in which a complete tour to be commenced. The features of GA are used to select the cities from different clusters of the sequence. The algorithm has the ability to solve the problems in both the crisp as well as in the imprecise environments. A fuzzy membership-based selection process is proposed to select a solution for the mating pool. A general comparison rule of the solutions is proposed to rank the potential solutions of the population in imprecise environments. In the crisp environment, the efficiency of the proposed approach is tested against a set of different benchmark test problems from GTSPLIB having sizes up to 226 cities with 26 clusters. It is observed from the experimental results that the algorithm produces 100% accurate results for all the benchmark test problems under consideration. Imprecise test problems are generated from different benchmark crisp test problems of TSPLIB and are used to test the algorithm in the imprecise environments. It is also observed from the experimental results that the proposed approach finds multiple optimal paths (i.e, more than one path), if exists, for the problems in the crisp as well as in the imprecise environments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Ardalan Z, Karimi S, Poursabzi O, Naderi B (2015) A novel imperialist competitive algorithm for generalized traveling salesman problems. Appl Soft Comput 26:546–555

    Article  Google Scholar 

  2. Bontouxa B, Artigues C, Feilletc D (2010) A memetic algorithm with a large neighborhood crossover operator for the generalized traveling salesman problem. Comput Oper Res 37:1844–1852

    Article  Google Scholar 

  3. Changdar C, Maiti MK, Maiti M (2013) A constrained solid TSP in fuzzy environment: two heuristic approaches. Iran J Fuzzy Syst 10(1):1–28

    MATH  Google Scholar 

  4. Changdar C, Mahapatra GS, Pal R (2014) An efficient genetic algorithm for multi-objective solid traveling salesman problem under fuzziness. Swarm Evol Comput 15:27–37

    Article  Google Scholar 

  5. Dimitrijević V, Šarić Z (1997) An efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphs. Inf Sci 102:1–4

    Article  MATH  Google Scholar 

  6. Fischetti M, Salazar JJ, Toth P (1997) A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper Res 45:378–394

    Article  MATH  Google Scholar 

  7. Goldberg DE (1989) Genetic algorithms: search, optimization and machine learning. Addison Wesley, Reading

    MATH  Google Scholar 

  8. Guchhait P, Maiti MK, Maitia M (2013) Inventory model of a deteriorating item with price and credit linked fuzzy demand: a fuzzy differential equation approach. Opsearch 51(3):321–353

    Article  MATH  Google Scholar 

  9. Gutin G, Karapetyan D (2010) A memetic algorithm for the generalized traveling salesman problem. Nat Comput 9:47–60

    Article  MATH  Google Scholar 

  10. Helsgaun K (2015) Solving the equality generalized traveling salesman problem using the Lin–Kernighan–Helsgaun algorithm. Math Program Comput 7(3):269–287

    Article  MATH  Google Scholar 

  11. Henry-Labordere AL (1969) The record balancing problem: a dynamic programming solution of a generalized traveling salesman problem. RAIRO Oper Res B2:43–49

    MATH  Google Scholar 

  12. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor

    Google Scholar 

  13. Khanra A, Maiti MK, Maiti M (2015) Profit maximization of TSP with uncertain parameters through a hybrid algorithm. In: Proceedings of the 4th international conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA), advances in intelligent systems and computing. Springer, p 404

  14. Khanra A, Maiti MK, Maiti M (2016) A hybrid heuristic algorithm for single and multi-objective imprecise traveling salesman problems. J Intell Fuzzy Syst 30:1987–2001

    Article  MATH  Google Scholar 

  15. Khan I, Maiti MK (2018) A novel hybrid algorithm for generalized traveling salesman problems in different environments. Vietnam J Comput Sci 1(5):27–43

    Article  Google Scholar 

  16. Laporte G, Nobert Y (1983) Generalized traveling salesman through n sets of nodes: an integer programming approach. INFOR 21:61–75

    MATH  Google Scholar 

  17. Laporte G, Asef-Vaziri A, Sriskandarajah C (1996) Some applications of the generalized traveling salesman problem. J Oper Res Soc 47:1461–1467

    Article  MATH  Google Scholar 

  18. Liu B (2002) Theory and practice of uncertain programming. Physica, Heidelberg

    Book  MATH  Google Scholar 

  19. Maity AK (2011) One machine multiple-product problem with production-inventory system under fuzzy inequality constraint. Appl Soft Comput 11:1549–1555

    Article  Google Scholar 

  20. Maiti AK, Maiti MK, Maiti M (2009) Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Appl Math Model 33:2433–2443

    Article  MATH  Google Scholar 

  21. Michalewicz Z (1992) Genetic algorithms + data structure = evolution programs. Springer, Berlin

    Book  MATH  Google Scholar 

  22. Mondal M, Maity AK, Maiti MK, Maiti M (2013) A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money. Appl Math Model 37:3200–3215

    Article  MATH  Google Scholar 

  23. Mohon C (2000) Optimization in fuzzy-stochastic environment and its importance in present day industrial scenario. In: Proceedings on mathematics and its application in industry and business. Narosa Publishing House, India

  24. Noon CE, Bean JC (1991) A Lagrangian based approach for the asymmetric generalized traveling salesman problem. Oper Res 39:623–632

    Article  MATH  Google Scholar 

  25. Noon CE, Bean JC (1993) An efficient transformation of the generalized traveling salesman problem. INFOR Inf Syst Oper Res 31(1):39–44

    MATH  Google Scholar 

  26. Pramanik P, Maiti MK, Maiti M (2017) Three level partial trade credit with promotional cost sharing. Appl Soft Comput 58:553–575

    Article  Google Scholar 

  27. Reinelt G (1991) TSPLIB—a traveling salesman problem library. ORSA J Comput 3:376–84

    Article  MATH  Google Scholar 

  28. Renaud J, Boctor FF (1998) An efficient composite heuristic for the symmetric generalized traveling salesman problem. Eur J Oper Res 108(3):571–584

    Article  MATH  Google Scholar 

  29. Ren X, Wang X, Wang Z, Wu T (2020) Parallel DNA algorithms of generalized traveling salesman problem-based bioinspired computing model. Int J Comput Intell Syst 14:228–237

    Article  Google Scholar 

  30. Smith SL, Imeson F (2017) GLNS: an effective large neighborhood search heuristic for the generalized traveling salesman problem. Comput Oper Res 87:1–19

    Article  MATH  Google Scholar 

  31. Saskena JP (1970) Mathematical model of scheduling clients through welfare agencies. J Can Oper Res Soc 8:185–200

    Google Scholar 

  32. Shi XH, Lianga YC, Leeb HP, Lub C, Wanga QX (2007) Particle swarm optimization-based algorithms for TSP and generalized TSP. Inf Process Lett 103:69–176

    Article  Google Scholar 

  33. Srivastava SS, Kumar S, Garg RC, Sen P (1969) Generalized traveling salesman problem through n sets of nodes. CORS J 7:97–101

    MATH  Google Scholar 

  34. Snyder LV, Daskin MS (2006) A random-key genetic algorithm for the generalized traveling salesman problem. Eur J Oper Res 174:38–53

    Article  MATH  Google Scholar 

  35. Wu CG, Liang YC, Lee HP, Lu C (2004) A generalized chromosome genetic algorithm for generalized traveling salesman problems and its applications for machining. Phys Rev E 70:016701

    Article  Google Scholar 

  36. Yang J, Shi X, Marchese M, Liang Y (2008) An ant colony optimization method for generalized TSP problem. Prog Nat Sci 18:1417–1422

    Article  Google Scholar 

  37. Zadeh L (1965) Fuzzy sets. Inf Control 8:338–356

    Article  MATH  Google Scholar 

  38. Zhao X, Zhu XP (2010) Innovative genetic algorithm for solving GTSP. In: Second international conference on modeling, simulation and visualization methods. College of Computer Science and Engineering, Guangdong Institute of Science and Technology

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Chandrakon Vidyasagar Mahavidyalaya, Paschim-Medinipur, West Bengal, 721201, India

    Indadul Khan

  2. Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur, West Bengal, 721628, India

    Manas Kumar Maiti

  3. Department of Computer Science, West Bengal State University, Barasat, Kolkata, West Bengal, 700126, India

    Krishnendu Basuli

Authors
  1. Indadul Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manas Kumar Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Krishnendu Basuli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Indadul Khan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, I., Maiti, M.K. & Basuli, K. A random-permutation based GA for generalized traveling salesman problem in imprecise environments. Evol. Intel. 16, 229–245 (2023). https://doi.org/10.1007/s12065-021-00651-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-021-00651-5

Keywords

Search

Navigation