The development of methods and algorithms for solving a routing problem is being implemented over the years, but it is still a topical problem. This is, primarily, due to the fact that this problem is NP-complete, and to develop a universal algorithm for finding an exact optimal solution during a reasonable time is difficult. In this regard, in order to reduce the algorithm time complexity (ATC), the development of sequential and parallel bionic algorithms for solving the transportation problems based on the evolutionary strategies is prospective. The bionic algorithms (BA) have proved their efficiency at the solution of the time-consuming tasks of optimization, approximation, and intellectual data processing. Benefits include the possibility to perform the genetic and evolutionary search, as well as the fact that BA consist in parallel generation of the quasioptimal alternative decision sets with possible "migration" of decisions between these sets. Schemes that differ from the known ones in the outlining structure and recording the parameter variation are proposed for the bionic search simulation. The investigation of the developed bionic algorithms for solving transportation problems show the advantage in the solution quality compared to the known methods. The developed algorithms allow obtaining a set of alternative quasioptimal results with the polynomial time complexity. The transformation of the population size during the transition from one iteration to another in the process of the bionic algorithm operation is presented.
transportation problem, methods, adaptation, efficiency, bionic search, genetic operator, algorithm
Введение. При решении задач об экстремальных путях эффективно используют стратегии, концепции, методы и
механизмы эволюционного моделирования на основе различных стратегий адаптации. Основные цели адаптации
связаны с экстремальными требованиями, предъявляемыми к объекту адаптации в виде максимизации эффективности
его функционирования.
1. Poluyan, А.Y. Parallel´nyy bionicheskiy poisk dlya resheniya zadach optimizatsii [Parallel bionic search for solving optimization problems.] Bezopasnost´ zhiznedeyatel´nosti. Okhrana truda i okruzhayushchey sredy: mezhvuz. sb. nauch. tr. [Life Safety. Labour and environmental protection: interuniversity coll. of sci.papers.] Rostov-on-Don, 2009, pp. 53-54 (in Russian).
2. Luger, G. Artificial Intelligence: Structures and Strategies for Complex Problem Solving. Fourth Edition. Addison-Wesley Publishing Company, 2002, p.928
3. Poluyan, А.Y. Evolyutsionnyy podkhod k resheniyu zadach o nakhozhdenii kratchayshego puti v grafe. [Evolutionary approach to the problem of finding the shortest path in the graph.] Informatsionnye tekhnologii v professional´noy deyatel´nosti i nauchnoy rabote : sb. materialov Vseros. nauch.-prakt. konf. s mezhdunar. uchastiem. [Information technologies in professional activities and research: Proc. Sci.-Pract. Conf. with int. participation.] Yoshkar-Ola, 2008, vol. 2, pp. 143-147 (in Russian).
4. Kureychik, V.М. Sovmestnye metody kvantovogo i bionicheskogo poiska. [Shared methods of quantum and bionic search.] IEEE AIS’04, CAD-2004: Proc. Conf. Moscow, 2004, pp. 12-19 (in Russian).
5. Kureychik, V.М., Mishchenko, M.N. Bionicheskiy metod opredeleniya putey optimal´noy dliny v grafovykh modelyakh. [Bionic method for determining optimum length paths in graph models.] Integrirovannye modeli i myagkie vychisleniya v iskusstvennom intellekte : sb. trudov III-go mezhdunar. nauchno-prakt. seminara. [Integrated models and soft computing in Artificial Intelligence: Proc.III Int.Sci.-Pract. Seminar.] Moscow, 2005, pp. 261-266 (in Russian).
6. Kureychik, V.М., Lebedev, B.K., Lebedev, O.B. Poiskovaya adaptatsiya: teoriya i praktika. [Search adaptation theory and practice.] Moscow: Fizmatlit, 2006, 272 p. (in Russian).
7. Kureychik, V.М., Lebedev, B.K., Lebedev, O.B. Adaptatsiya v zadachakh proektirovaniya topologii. [Adaption in the problems of layout design.] Problemy razrabotki perspektivnykh mikro- i nanoelektronnykh sistem - 2010: sb. nauch. trudov. [Problems of development of advanced micro- and nanoelectronic systems - 2010: Coll. Sci. Papers.] Moscow, 2010, pp. 170-177 (in Russian).
8. Yemelyanov, V.V., Afonin, V.P. Modeli iskusstvennoy zhizni v optimizatsionnykh zadachakh. [Models of artificial life in optimization problems.] Intellektual´nye sistemy (AIS’04). Intellektual´nye SAPR (CAD’-2004): sb. trudov mezhdunar. nauch.- tekhn. konf. [Intelligent Systems (AIS´04). Intelligent CAD (CAD´-2004): Proc. Int.Sci.-Tech. Conf.] Moscow, 2004, pp. 39-47 (in Russian).
9. Kureychik, V.М., Lebedev, B.K., Lebedev, O.B., Chernyshev, Y.O. Adaptatsiya na osnove samoobucheniya. [Adaptation on the basis of self-learning.] Rostov-on-Don: izd-vo RGASKhM, 2004, 142 p. (in Russian).
10. Rejngold, E., Nivergelt, J., Deo, N. Kombinatornye algoritmy. Teoriya i praktika. [Combinatorial algorithms. Theory and practice.] Moscow: Mir, 1980, 476 p. (in Russian).
11. Tsoy, Y.R., Spitsyn, V.G. K vyboru razmera populyatsii. [On the choice of the population size.] Intellektual´nye sistemy (IEEAIS’04). Intellektual´nye SAPR (CAD-2004): tr. mezhdunar. nauch.- tekhn. konf. [Intelligent Systems (IEEAIS´04). Intelligent CAD (CAD-2004): Proc. Int. Sci.-Tech. Conf.] Moscow, 2004, pp. 90-96 (in Russian).
12. Chernyshev, Y.O., Basova, A.V., Ventsov, N.N., Poluyan, A.Y. Razvitie teorii evolyutsionnogo modelirovaniya na osnove geneticheskikh metodov poiskovoy adaptatsii pri reshenii optimal´nykh zadach proektirovaniya, sverkhbol´shikh integral´nykh skhem (SBIS): otchet o NIR , RGASKhM. [Development of the theory of evolution simulation based on genetic search adaptation methods for solving optimum design problems, very large scale integration (VLSI): research report, RGASKhM.] Rostov-on-Don, 2009, 119 p. (in Russian).
13. Chernyshev, Y.O., Basova, A.V., Poluyan, A.Y. Reshenie zadach transportnogo tipa geneticheskimi algoritmami. [Solution of transport-type genetic algorithms.] Rostov-on-Don: izd-vo YuFU, 2008, 73 p. (in Russian).
14. Chernyshev, Y.O., Belyavskiy, P.G., Poluyan, A.Y. Evolyutsionnyy podkhod k resheniyu zadachi o naznachenii cherez opredelenie kratchayshego puti. [Evolution approach to the solution of the problem about setting through the shortest path determination.] Izvestiya SFedU. Engineering Sciences. 2008, no. 9, pp. 18-24 (in Russian).
15. Kremer, N.Sh. Teoriya veroyatnostey i matematicheskaya statistika. [Probability theory and mathematical statistics.] Moscow: YuNITI-DANA, 2004, 565 p. (in Russian).
16. Poluyan, A.Y. Adaptivnyy geneticheskiy algoritm dlya resheniya zadachi optimizatsii na osnove strategii elitizma. [Adaptive algorithm for the decision of the problems of optimization on the basis of strategy of elitism.] Izvestiya SFedU. Engineering Sciences. 2008, no. 9, pp. 36-39 (in Russian).
17. Holland, John H. Adaptation in natural and artificial systems. The MIT Press edition, Massachusetts, London, England, 1992, 210 р.
18. Kureychik, V.М., Gladkov, L.A., Kureychik, V.V., Sorokoletov, P.V. Bioinspirirovannye metody v optimizatsii. [Bioinspired methods in optimization.] Moscow: Fizmatlit, 2009, 384 p. (in Russian).
19. Kling, R.M., Banerjee, P. Placement by Simulated Evolution. IEEE Trans. on CAD, 1989, vol.8, no.3 pp. 245-255.