+7 (3412) 91 60 92

## Archive of Issues

Russia Yekaterinburg
Year
2017
Volume
27
Issue
4
Pages
540-557
 Section Mathematics Title On one routing problem modeling movement in radiation fields Author(-s) Chentsov A.G.ab, Chentsov A.A.a, Grigoryev A.M.a Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb Abstract We consider a routing problem with constraints and complicated cost functions. The visited objects are assumed to be clusters, or megalopolises (nonempty finite sets), and the visit to each of them entails certain tasks, which we call interior jobs. The order of visits is subject to precedence constraints. The costs of movements depend on the set of pending tasks (not yet complete at the time of the movement), which is also referred to as “sequence dependence”, “position dependence”, and “state dependence”. Such a dependence arises, in particular, in routing problems concerning emergencies at nuclear power plants, similar to the Chernobyl and Fukushima Daiichi incidents. For example, one could consider a disaster recovery problem concerned with sequential dismantlement of radiation sources; in this case, the crew conducting the dismantlement is exposed to radiation from the sources that have not yet been dealt with. This gives rise to dependence on pending tasks in the cost functions that measure the crew's radiation exposure. The latter dependence reflects the “shutdown” operations for the corresponding radiation sources. This paper sets forth an approach to a parallel solution for this problem, which was implemented and run on the URAN supercomputer. Keywords dynamic programming, route, precedence constraints, parallel computation UDC 519.6 MSC 49L20, 90C39 DOI 10.20537/vm170405 Received 21 August 2017 Language Russian Citation Chentsov A.G., Chentsov A.A., Grigoryev A.M. On one routing problem modeling movement in radiation fields, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 4, pp. 540-557. References Garey M.R., Johnson D.S. Computers and intractability: A guide to the theory of $NP$-completeness, New York: W.H. Freeman, 1979, 338 p. Gutin G., Punnen A.P. The traveling salesman problem and its variations, New York: Springer US, 2007. DOI: 10.1007/b101971 Cook W.J. In pursuit of the traveling salesman. Mathematics at the limits of computation, New Jersey: Princeton University Press, 2012, 248 p. Melamed I.I., Sergeev S.I., Sigal I.Kh. The traveling salesman problem. I: Theoretical issues, Automation and Remote Control, 1989, vol. 50, no. 9, pp. 1147-1173. Melamed I.I., Sergeev S.I., Sigal I.Kh. The traveling salesman problem. II: Exact methods, Automation and Remote Control, 1989, vol. 50, no. 10, pp. 1303-1324. Melamed I.I., Sergeev S.I., Sigal I.Kh. The traveling salesman problem. Approximate algorithms, Automation and Remote Control, 1989, vol. 50, no. 11, pp. 1459-1479. Little J.D.C., Murty K.G., Sweeney D.W., Karel C. An algorithm for the traveling salesman problem, Operations Research, 1963, vol. 11, issue 6, pp. 972-989. DOI: 10.1287/opre.11.6.972 Bellman R. Dynamic programming treatment of the travelling salesman problem, J. ACM, 1962, vol. 9, issue 1, pp. 61-63. DOI: 10.1145/321105.321111 Held M., Karp R.M. A dynamic programming approach to sequencing problems, Journal of the Society for Industrial and Applied Mathematics, 1962, vol. 10, no. 1, pp. 196-210. DOI: 10.1137/0110015 Gimadi E.Kh., Khachai M.Yu. Ekstremal'nye zadachi na mnozhestvakh perestanovok (Extremal problems on sets of permutations), Yekaterinburg: UMC UPI, 2016, 220 p. Leon V.J., Peters B.A. Replanning and analysis of partial setup strategies in printed circuit board assembly systems, International Journal of Flexible Manufacturing Systems, 1996, vol. 8, issue 4, pp. 389-411. DOI: 10.1007/BF00170019 Alkaya A.F., Duman E. A new generalization of the traveling salesman problem, Appl. Comput. Math., 2010, vol. 9, no. 2, pp. 162-175. Kinable J., Cire A.A., van Hoeve W.-J. Hybrid optimization methods for time-dependent sequencing problems, European Journal of Operational Research, vol. 259, issue 3, pp. 887-897. DOI: 10.1016/j.ejor.2016.11.035 Chentsov A.G. Ekstremal'nye zadachi marshrutizatsii i raspredeleniya zadanii: voprosy teorii (Extreme problems of routing and tasks distribution), Moscow-Izhevsk: Regular and Chaotic Dynamics, 2008, 240 p. Korobkin V.V., Sesekin A.N., Tashlykov O.L., Chentsov A.G. Metody marshrutizatsii i ikh prilozheniya v zadachakh povysheniya bezopasnosti i effektivnosti ekspluatatsii atomnykh stantsii (Routing methods and their applications in problems of improving the safety and efficiency of operation of nuclear power plants), Moscow: Novye Tekhnologii, 2012, 234 p. Tashlykov O.L. Dozovye zatraty personala v atomnoi energetike. Analiz. Puti snizheniya. Optimizatsiya (Personnel dose costs in the nuclear industry. Analysis. Ways to decrease. Optimization), Lambert Academic Publishing, 2011. Petunin A.A. About some strategies of the programming of tool route by developing of control programs for thermal cutting machines, Vestnik Ufimskogo Gosudarstvennogo Aviatsionnogo Tekhnicheskogo Universiteta. Seriya: Upravlenie, Vychislitel'naya Tekhnika i Informatika, 2009, vol. 13, no. 2 (35), pp. 280-286 (in Russian). Petunin A.A., Chentsov A.G., Chentsov P.A. On routing tool motion on the sheet cutting NPC machines, St. Petersburg State Polytechnical University Journal. Computer Science. Telecommunication and Control Systems, 2013, issue 2 (169), pp. 103-111 (in Russian). Frolovskii V.D. Computer-aided design of the control programs for thermal metal cutting on NPC machines, Informatsionnye Tekhnologii v Proektirovanii i Proizvodstve, 2005, no. 4, pp. 63-66 (in Russian). Wang G.G., Xie S.Q. Optimal process planning for a combined punch-and-laser cutting machine using ant colony optimization, International Journal of Production Research, 2005, vol. 43, issue 11, pp. 2195-2216. DOI: 10.1080/00207540500070376 Dewil R., Vansteenwegen P., Cattrysse D. Construction heuristics for generating tool paths for laser cutters, International Journal of Production Research, 2014, vol. 52, issue 20, pp. 5965-5984. DOI: 10.1080/00207543.2014.895064 Chentsov A.G. To question of routing of works complexes, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 59-82. DOI: 10.20537/vm130107 Chentsov A.G. On a parallel procedure for constructing the Bellman function in the generalized problem of courier with internal jobs, Automation and Remote Control, 2012, vol. 73, no. 3, pp. 532-546. DOI: 10.1134/S0005117912030113 Chentsov A.G. A parallel procedure of constructing Bellman function in the generalized courier problem with interior works, Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2012, issue 12, pp. 53-76. Chentsov A.G., Grigoryev A.M. Dynamic programming method in a routing problem: a scheme of independent computations, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 12, pp. 834-846 (in Russian). DOI: 10.17587/mau.17.834-846 Dieudonné J. Foundations of modern analysis, New York: Academic Press Inc., 1960. 361 p. Cormen T.H., Leizerson C.E., Rivest R.L. Introduction to algorithms, Cambridge: MIT Press, 1990. Chentsov A.G., Chentsov A.A. Route problem with constraints depending on a list of tasks, Doklady Mathematics, 2015, vol. 92, no. 3, pp. 685-688. DOI: 10.1134/S1064562415060083 Chentsov A.G., Chentsov P.A. Routing under constraints: Problem of visit to megalopolises, Autom. Remote Control, 2016, vol. 77, no. 11, pp. 1957-1974. DOI: 10.1134/S0005117916110060 Chentsov A.G., Chentsov, A.A. On the question of finding the value of routing problem with constraints, Journal of Automation and Information Sciences, 2016, vol. 48, issue 2, pp. 11-27. DOI: 10.1615/JAutomatInfScien.v48.i2.30 Schmidt G., Ströhlein T. Relations and graphs. Discrete mathematics for computer scientists, Springer-Verlag Berlin Heidelberg, 1993, IX+301 p. DOI: 10.1007/978-3-642-77968-8 Steiner G. On the complexity of dynamic programming for sequencing problems with precedence constraints, Annals of Operations Research, 1990, vol. 26, issue 1, pp. 103-123. DOI: 10.1007/BF02248587 Full text