Time-dependent asymmetric traveling salesman problem with time windows: Properties and an exact algorithm

This paper proposes a method of rapidly finding a feasible solution to the asymmetric traveling salesman problem with time windows (ATSP-TW). ATSP-TW is a problem that involves determining the route with the minimum travel cost for visiting n cities one time each with time window constraints (the period of time in which the city must be visited is constrained). “Asymmetrical” denotes a difference between the cost of outbound and return trips. For such a combinatorial optimization problem with constraints, we propose a method that combines a pre-process based on the insertion method with metaheuristics called “the compressed annealing approach.” In an experiment using a 3-GHz computer, our method derives a feasible solution that satisfies the time window constraints for all of up to about 300 cities at an average of about 1/7 the computing time of existing methods, an average computing time of 0.57 seconds, and a maximum computing time of 9.40 seconds.

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Dynamic Discretization Discovery for Solving the Time-Dependent Traveling Salesman Problem with Time Windows

Transportation Science ◽

10.1287/trsc.2019.0911 ◽

2020 ◽

Vol 54 (3) ◽

pp. 703-720 ◽

Cited By ~ 8

Author(s):

Duc Minh Vu ◽

Mike Hewitt ◽

Natashia Boland ◽

Martin Savelsbergh

Keyword(s):

Integer Programming ◽

Traveling Salesman Problem ◽

Time Windows ◽

Traveling Salesman ◽

Time Dependent ◽

Programming Formulation ◽

Solution Approach ◽

Integer Programming Formulation ◽

Time Dependencies ◽

Time Expanded Network

We present a new solution approach for the time-dependent traveling salesman problem with time windows. This problem considers a salesman who departs from his home, has to visit a number of cities within a predetermined period of time, and then, returns home. The problem allows for travel times that can depend on the time of departure. We consider two objectives for the problem: (1) a makespan objective that seeks to return the salesman to his home as early as possible and (2) a duration objective that seeks to minimize the amount of time that he is away from his home. The solution approach is based on an integer programming formulation of the problem on a time-expanded network, because doing so enables time dependencies to be embedded in the definition of the network. However, because such a time-expanded network (and thus, the integer programming formulation) can rapidly become prohibitively large, the solution approach uses a dynamic discretization discovery framework, which has been effective in other contexts. Our computational results indicate that the solution approach outperforms the best-known methods on benchmark instances and is robust with respect to instance parameters.

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A polyhedral study of the asymmetric traveling salesman problem with time windows

Networks ◽

10.1002/1097-0037(200009)36:2<69::aid-net1>3.0.co;2-q ◽

2000 ◽

Vol 36 (2) ◽

pp. 69-79 ◽

Cited By ~ 67

Author(s):

Norbert Ascheuer ◽

Matteo Fischetti ◽

Martin Gr�tschel

Keyword(s):

Traveling Salesman Problem ◽

Time Windows ◽

Traveling Salesman ◽

Asymmetric Traveling Salesman Problem ◽

Polyhedral Study

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An integer programming approach for the time-dependent traveling salesman problem with time windows

Computers & Operations Research ◽

10.1016/j.cor.2017.06.026 ◽

2017 ◽

Vol 88 ◽

pp. 280-289 ◽

Cited By ~ 26

Author(s):

Agustín Montero ◽

Isabel Méndez-Díaz ◽

Juan José Miranda-Bront

Keyword(s):

Integer Programming ◽

Traveling Salesman Problem ◽

Time Windows ◽

Traveling Salesman ◽

Time Dependent ◽

Programming Approach

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Research of Features of the Combined Algorithm for Solving the Asymmetric Traveling Salesman Problem

INFORMACIONNYE TEHNOLOGII ◽

10.17587/it.27.3-8 ◽

2021 ◽

Vol 27 (1) ◽

pp. 3-8

Author(s):

M. V. Ulyanov ◽

◽

M. I. Fomichev ◽

◽

...

Keyword(s):

Decision Tree ◽

Traveling Salesman Problem ◽

Branch And Bound ◽

Exact Algorithm ◽

Traveling Salesman ◽

Branch And Bound Method ◽

Asymmetric Traveling Salesman Problem ◽

The Individual ◽

The Traveling Salesman Problem ◽

Combined Algorithm

The exact algorithm that implements the Branch and Boimd method with precomputed tour which is calculated by Lin-Kernighan-Helsgaun metaheuristic algorithm for solving the Traveling Salesman Problem is concerned here. Reducing the number of decision tree nodes, which are created by the Branches and Bound method, due to a "good" precomputed tour leads to the classical balancing dilemma of time costs. A tour that is close to optimal one takes time, even when the Lin-Kernighan-Helsgaun algorithm is used, however it reduces the working time of the Branch and Bound method. The problem of determining the scope of such a combined algorithm arises. In this article it is solved by using a special characteristic of the individual Traveling Salesman Problem — the number of changes tracing direction in the search decision tree generated by the Branch and Bound Method. The use of this characteristic allowed to divide individual tasks into three categories, for which, based on experimental data, recommendations of the combined algorithm usage are formulated. Based on the data obtained in a computational experiment (in range from 30 to 45), it is recommended to use a combined algorithm for category III problems starting with n = 36, and for category II problems starting with n = 42.

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