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Some approaches to solving the NP-hard Mixed Chinese Postman Problem
P. 272–290.
The routing problems are important for logistic and transport sphere. Basically, the routing problems related to determining the optimal set of routes in the multigraph. The Chinese postman problem (CPP) is a special case of the routing problem, which has many potential applications. We propose to solve the MCPP (special NP-hard case of CPP, which defined on mixed multigraph) using the reduction of the original problem into General Travelling Salesman Problem (GTSP). The variants of CPP are pointed out. The mathematical formulations of some problems are presented. The algorithm for reduction the MCPP in multigraph into GTSP is shown. The experimental results of solving MCPP in multigraph through the reduction into GTSP are presented.
Keywords: задача коммивояжераTraveling Salesman Problemheuristic algorithmMixed Chinese Postman ProblemArc Routing ProblemСмешанная задача китайского почтальонаЗадача маршрутизации дугGeneral Routing ProblemVehicle Routing ProblemAsymmetric Traveling Salesman ProblemGeneralized Traveling Salesman Problem
In book
Pozin B. Vol. 1989: CEUR Workshop Proceedings. , M.: HSE, 2017.
Fomichev M., Информационные технологии моделирования и управления 2018 Т. 109 № 1 С. 47–54
В современном мире промедление в секунду, или даже долю секунды, может стоить миллионы рублей. Заинтересованному лицу важно получить точный ответ на вопрос в кратчайшие сроки. Но, к сожалению, даже при ны- нешних вычислительных мощностях, многие задачи не могут быть решены точно за приемлемое время. ...
Added: March 22, 2020
Головешкин В. А., Zhukova G., Ulyanov M. et al., Системы компьютерной математики и их приложения 2017 № 18 С. 136–138
В докладе рассматривается статистическая зависимость числа
порожденных вершин дерева решений и физического времени работы
программной реализации метода ветвей и границ для задачи
коммивояжера (TSP). На основе результатов вычислительного
эксперимента получено приближенное соотношение между числом
порожденных вершин (сложность индивидуальной TSP) и физическим
временем. Предлагается использовать это эмпирическое соотношение
для прогнозирования времени работы программы, решающей TSP с
числом «городов» больше 40. ...
Added: March 22, 2020
Ulyanov M., Fomichev M., Информационные технологии 2019 Т. 25 № 10 С. 590–595
The algorithm that implements the Branch and Bound method for solving the Traveling Salesman Problem is one of the common exact algorithms for solving it. Metaheuristic algorithms for solving this problem do not guarantee obtaining an exact solution, however they work "quickly". In order to reduce the nodes number of the generated decision tree in ...
Added: February 16, 2020
Zhukova G., Ulyanov M., Fomichev M., Automation and Remote Control 2019 Vol. 80 No. 11 P. 2054–2067
We present the results of a comparative statistical analysis of the time for solving the asymmetric traveling salesman problem (ATSP) with the branch-and-bound method (without precalculation of the tour) and with a hybrid method. The hybrid method consists of the Lin–Kernighan–Helsgaun approximate algorithm used to calculate the initial tour and the branch-and-bound method. We show ...
Added: November 24, 2019
Zhukova G., Ulyanov M., Fomichev M., Автоматика и телемеханика 2019 № 11 С. 155–172
We present the results of a comparative statistical analysis of the time for solving the asymmetric traveling salesman problem (ATSP) with the branch-and-bound method (without precalculation of the tour) and with a hybrid method. The hybrid method consists of the Lin-Kernighan-Helsgaun approximate algorithm used to calculate the initial tour and the branch-and-bound method. We show ...
Added: November 10, 2019
Baklanov A., Ченцов П. А., , in: CEUR Workshop Proceedings 48. Сер. "SoProMat 2017 - Proceedings of the 48th International Youth School Conference "Modern Problems in Mathematics and its Applications"".: CEUR Workshop Proceedings, 2017. P. 203–208.
We consider a version of the traveling salesperson problem for a doubleintegrator : given a set of stationary points, find the fastest tour overthis set of points. Control constraints are defined in terms of a convexcompact set, velocity is constrained only at the points. To obtainan upper bound for the minimum travel time, we propose ...
Added: July 22, 2019
Aleksander V. Belov, Загуменнов Ф. Д., , in: Proceedings of the 2018 IEEE International Conference "Quality Management, Transport and Information Security, Information Technologies" (IT&QM&IS).: IEEE, 2018. P. 308–311.
The objective of this research is to develop a software algorithm for evaluating the effectiveness of using the Financial Message Transfer System for Remote Banking Systems. The study considers hardware system that provide two types of interactions between the legal entity and the bank: ≪Direct Banking≫ and ≪Internet Banking≫. During the work were identified and ...
Added: November 27, 2018
Alexey Nikolaev, Mikhail Batsyn, , in: Combinatorial Algorithms. 29th International Workshop, IWOCA 2018, Singapore, July 16–19, 2018. Lecture Notes in Computer ScienceVol. 10979.: Springer, 2018. P. 311–322.
In this paper a branch-and-bound algorithm for the Symmetric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new branching strategy is suggested in which the algorithm branches on the 1-tree edge belonging to the vertex with maximum degree in the 1-tree and having the maximum tolerance. This ...
Added: October 23, 2018
Zhukova G., Ulyanov M., Fomichev M., Business Informatics 2018 Vol. 45 No. 3 P. 20–28
For practical, important tasks in the fi elds of economics and logistics, as well as in a number of
technical applications, it becomes necessary to solve the traveling salesman problem (TSP). Quite
often, the features of these problems lead to the traveling salesman problem in asymmetric formulation
(asymmetric traveling salesman problem, ATSP). Moreover, in some practical applications it ...
Added: October 18, 2018
Gordenko M., Avdoshin S. M., Proceedings of the Institute for System Programming of the RAS 2018 Vol. 30 No. 3 P. 221–232
In this article, the routing problems are described. It is shown, that almost all routing problem can be transformed into each other. An example of the Mixed Chinese Postman problem is discussed. The article gives an overview of various variants of Chinese Postman Problem. For all problems the mathematical formulation is given. Moreover, the useful ...
Added: September 2, 2018
Voloshinov V., Smirnov S., Sukhoroslov O. V., Procedia Computer Science 2017 Vol. 108 P. 1532–1541
This paper examines the coarse-grained approach to parallelization of the branch-and-bound (B&B) algorithm in a distributed computing environment. This approach is based on preliminary decomposition of a feasible domain of mixed-integer programming problem into a set of subproblems. The produced subproblems are solved in parallel by a distributed pool of standalone B&B solvers. The incumbent ...
Added: August 30, 2018
Ulyanov M., Zhukova G., Fomichev M. et al., Автоматика и телемеханика 2018 № 7 С. 149–166
We show the results of a statistical study of the complexity of the asymmetric traveling salesman problem (ATSP) obtained by processing a specially generated pool of matrices. We show that the normal distribution can serve as an approximation to the distribution of the logarithm of complexity for a fixed problem dimension. We construct a family ...
Added: July 16, 2018
G. N. Zhukova, M. V. Ulyanov, M. I. Fomichev et al., Automation and Remote Control 2018 Vol. 79 No. 7 P. 1296–1310
We show the results of a statistical study of the complexity of the asymmetric traveling salesman problem (ATSP) obtained by processing a specially generated pool of matrices. We show that the normal distribution can serve as an approximation to the distribution of the logarithm of complexity for a fixed problem dimension. We construct a family ...
Added: July 16, 2018
Beresneva E., Gordenko M., Открытые системы. СУБД 2018 № 01 С. 40–42
Едва научившись ходить, человек начал строить маршруты и сегодня задача прокладки оптимальных трасс актуальна для всех логистических предприятий, хотя ее точного решения до сих пор нет, а есть проблема выбора эвристического алгоритма. ...
Added: June 22, 2018
Gordenko M., Коротков Д. А., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: МИЭМ НИУ ВШЭ, 2018. С. 42–44.
В работе рассмотрен меметический алгоритм, являющий-ся комбинацией генетического алгоритма и алгоритмов ло-кального поиска решения ассиметричной задачи коммивоя-жера (A TSP). Приведена математическая постановка задачиA TSP . Кратко описан принцип работы меметического алгорит-ма. Проведено экспериментальное исследование временных и точностных характеристик меметического алгоритма на откры-той базе данных TSPLIB в зависимости от входных параметров с целью выявления оптимальных настроек алгоритма. ...
Added: June 5, 2018
Gordenko M., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: МИЭМ НИУ ВШЭ, 2018. С. 20–21.
В данной работе рассмотрены алгоритмы ближайшего соседа решения обобщенной задачи коммивояжера в качестве начальной инициализации для алгоритма LKH. Проведено экспериментальное исследование алгоритма LKH с целью сравнительной оценки рациональности полученных решений при различных начальных инициализациях. ...
Added: June 5, 2018