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Development of a Modification of the Particle Collision Algorithm (PCA), Providing an Approximate Solution to the Traveling Salesman Problem

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Abstract—

This work is devoted to the development of a modification of the particle collision algorithm (PCA), which provides an approximate solution to the traveling salesman problem. The resulting modification was tested on a number of well-known tasks and demonstrated greater accuracy and efficiency than its analogues.

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REFERENCES

  1. Makarkin, S.B., Mel’nikov, B.F., and Trenina, M.A., Approach to solving pseudo-geometric version of the travelling salesman problem, Izv. Vyssh. Uchebn. Zaved., Povolzhskii Region, Fiziko-Mat. Nauki, 2015, no. 2, pp. 135–147.

  2. Makarkin, S.B. and Mel’nikov, B.F., Suitability of the mathematical models on example of the travelling salesman problem, Filosofskie Probl. Inf. Tekhnol. Kiberprostranstva, 2013, no. 2, pp. 4–17.

  3. Kureichik, V.M. and Logunova, J.A., The hybrid approach for the travelling salesman problem solving using cloud computing in the Internet, Izv. Yuzhnogo Fed. Univ., Tekh. Nauki, 2019, no. 5, pp. 25–33. https://doi.org/10.23683/2311-3103-2019-5-25-33

  4. Ramazanova, R.R., Filippova, A.S., and Kartak, V.M., Analysis of practical use of one algorithm for solving the problem of transport logistics in information system, Sbornik trudov mezhdunarodnoi nauchno-tekhnicheskoi konferentsii Perspektivnye informatsionnye tekhnologii PIT-2013 (Proc. Int. Sci.-Tech. Conf. on Perspective Information Technologies), Samara, 2013, Prokhorov, S.A., Ed., Samara: Izd-vo Samarskogo Nauchnogo Tsentra Ross. Akad. Nauk, 2013, pp. 221–224.

  5. Mel’nikov, B.F., Aksenova, E.A., Anokhina, T.V., Korneeva, S.A., Zotova, M.A., Naumov, V.V., Smirnova, T.G., Sokurova, A.M., and Yuldashev, A.V., Heuristic algorithms for solving the problems of combinatorial optimization, Mire Nauchnykh Otkrytii, 2012, nos. 12–1, pp. 86–114.

  6. Betin, V.N., Ivashchenko, V.A., and Suprun, A.P., Eliciting and the use of information concerning regular structures in the formalism of functional neural networks in decision-support systems, Autom. Doc. Math. Linguist., 2022, vol. 56, no. 4, pp. 179–186. https://doi.org/10.3103/s0005105522040021

    Article  Google Scholar 

  7. Betin, V.N., Luk’yanov, S.E., and Suprun, A.P., A mechanism for a solution search within the formalism of functional neural networks, Autom. Doc. Math. Linguist., 2020, vol. 54, pp. 124–129. https://doi.org/10.3103/S0005105520030024

    Article  Google Scholar 

  8. Kolesnikov, A.V., Kirikov, I.A., Listopad, S.V., Rumovskaya, S.B., and Domanitskii, A.A., Reshenie slozhnykh zadach kommivoyazhera metodami funktsional’nykh gibridnykh intellektual’nykh sistem (Solving Complicated Travelling Salesman Problems by the Methods of Functional Hybrid Intelligent Systems), Kolesnikov, A.V., Ed., Moscow: Inst. Problem Informatiki Ross. Akad. Nauk, 2011.

    Google Scholar 

  9. Sacco, W.F. and De Oliveira, C.R.E., A new stochastic optimization algorithm based on particle collisions, Proc. 2005 ANS Annu. Meeting. Transactions of the American Nuclear Society, San Diego, Calif.: American Nuclear Society, 2005, pp. 657–659.

  10. Da Luz, E.F.P. and Beccener, J.C., A new multi-particle collision algorithm for optimization in a high performance environment, J. Comput. Interdiscip. Sci., 2008, vol. 1, no. 1, pp. 3–10.

    Google Scholar 

  11. Sulimov, V. and Shkapov, P., Application of hybrid global optimization algorithms to extremum problems in hydro-mechanical systems, Nauka Obraz., 2013, vol. 13, no. 11, pp. 141–158.

    Google Scholar 

  12. Sulimov, V.D., Shkapov, P.M., and Nosachev, S.K., Hooke–Jeeves method-used local search in a hybrid global optimization algorithm, Nauka Obraz., 2014, vol. 14, no. 6, pp. 107–123.

    Google Scholar 

  13. Syedin, D.Yu., On hybridization of stochastic global optimization algorithms taking into account the features of their architecture, Informatizatsiya Svyaz’, 2021, no. 1, pp. 113–117. https://doi.org/10.34219/2078-8320-2021-12-1-113-117

  14. Zakharov, V.V. and Mugaiskikh, A.V., Dynamic adaptation of genetic algorithm for the large-scale routing problems, Upr. Bol’shimi Sist., 2018, vol. 73, pp. 108–133. https://doi.org/10.25728/ubs.2018.73.6

    Article  Google Scholar 

  15. Andrianova, E.G., Raev, V.K., and Filgus, D.I., Determination of the shortest Hamiltonian paths in an arbitrary graph of distributed databases, Ross. Tekhnol. Zh., 2019, vol. 7, no. 4, pp. 7–20. https://doi.org/10.32362/2500-316x-2019-7-4-7-20

    Article  Google Scholar 

  16. El Krari, M., Ahiod, B., and El Benani, B., Breakout local search for the travelling salesman problem, Comput. Inf., 2018, vol. 37, no. 3, pp. 656–672. https://doi.org/10.4149/cai_2018_3_656

    Article  MathSciNet  Google Scholar 

  17. Sengupta, L., Mariescu-Istodor, R., and Fränti, P., Which local search operator works best for the open-loop TSP?, Appl. Sci., 2019, vol. 9, no. 19, p. 3985. https://doi.org/10.3390/app9193985

    Article  Google Scholar 

  18. Croes, G.A., A method for solving traveling-salesman problems, Oper. Res., 1958, vol. 6, no. 6, pp. 791–812. https://doi.org/10.1287/opre.6.6.791

    Article  MathSciNet  Google Scholar 

  19. Flood, M.M., The traveling-salesman problem, Oper. Res., 1956, vol. 4, no. 1, pp. 61–75. https://doi.org/10.1287/opre.4.1.61

    Article  Google Scholar 

  20. Martin, O., Otto, S.W., and Felten, E.W., Large-step Markov chains for the TSP incorporating local search heuristics, Oper. Res. Lett., 1992, vol. 11, no. 4, pp. 219–224. https://doi.org/10.1016/0167-6377(92)90028-2

    Article  MathSciNet  Google Scholar 

  21. Bjelić, N. and Popović, D., Two-phase algorithm for solving heterogeneous travelling repairmen problem with time windows, Int. J. Traffic Transp. Eng., 2015, vol. 5, no. 1, pp. 64–73. https://doi.org/10.7708/ijtte.2015.5(1).08

    Article  Google Scholar 

  22. Hoos, H. and Stützle, T., Stochastic Local Search: Foundations and Applications, San Francisco: Morgan Kaufmann, 2005.

    Google Scholar 

  23. Holland, J.H., Adaptation in Natural and Artificial Systems, Ann Arbor, Mich.: Univ. of Michigan Press, 1975.

  24. Kennedy, J. and Eberhart, R. Particle swarm optimization, Proc. ICNN'95 Int. Conf. on Neural Networks, Perth, Australia, 1995, vol. 4, pp. 1942–1948.https://doi.org/10.1109/ICNN.1995.488968

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Correspondence to D. Yu. Syedin.

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Syedin, D.Y. Development of a Modification of the Particle Collision Algorithm (PCA), Providing an Approximate Solution to the Traveling Salesman Problem. Autom. Doc. Math. Linguist. 58, 1–9 (2024). https://doi.org/10.3103/S0005105524010047

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