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

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.

scholarly journals On the Classical Version of the Branch and Bound Method

2021 ◽  
pp. 21-44
Author(s):  
Boris Melnikov ◽  
◽  
Elena Melnikova ◽  
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Branch And Bound Method ◽  
Main Subject ◽  
Classical Version ◽  
The Traveling Salesman Problem ◽  
Discrete Optimization Problems

In the computer literature, a lot of problems are described that can be called discrete optimization problems: from encrypting information on the Internet (including creating programs for digital cryptocurrencies) before searching for “interests” groups in social networks. Often, these problems are very difficult to solve on a computer, hence they are called “intractable”. More precisely, the possible approaches to quickly solving these problems are difficult to solve (to describe algorithms, to program); the brute force solution, as a rule, is programmed simply, but the corresponding program works much slower. Almost every one of these intractable problems can be called a mathematical model. At the same time, both the model itself and the algorithms designed to solve it are often created for one subject area, but they can also be used in many other areas. An example of such a model is the traveling salesman problem. The peculiarity of the problem is that, given the relative simplicity of its formulation, finding the optimal solution (the optimal route). This problem is very difficult and belongs to the so-called class of NP-complete problems. Moreover, according to the existing classification, the traveling salesman problem is an example of an optimization problem that is an example of the most complex subclass of this class. However, the main subject of the paper is not the problem, but the method of its soluti- on, i.e. the branch and bound method. It consists of several related heuristics, and in the monographs, such a multi-heuristic branch and bound method was apparently not previously noted: the developers of algorithms and programs should have understood this themselves. At the same time, the method itself can be applied (with minor changes) to many other discrete optimization problems. So, the classical version of branch and bound method is the main subject of this paper, but also important is the second subject, i.e. the traveling salesman problem, also in the classical formulation. The paper deals with the application of the branch and bound method in solving the traveling salesman problem, and about this application, we can also use the word “classical”. However, in addition to the classic version of this implementation, we consider some new heuristics, related to the need to develop real-time algorithms.

scholarly journals Comparison of the Sub-Tour Elimination Methods for the Asymmetric Traveling Salesman Problem Applying the SECA Method

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Ramin Bazrafshan ◽  
Sarfaraz Hashemkhani Hashemkhani Zolfani ◽  
S. Mohammad J. Mirzapour Al-e-hashem
Keyword(s):  
Traveling Salesman Problem ◽  
Mathematical Problem ◽  
Multiple Criteria Decision Making ◽  
Traveling Salesman ◽  
Mathematical Problem Solving ◽  
Web Based ◽  
Asymmetric Traveling Salesman Problem ◽  
Simultaneous Evaluation ◽  
Mcdm Method ◽  
The Traveling Salesman Problem

There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results.

Implementing Parallel Branch-and-Bound with Extended Sisal 2.0

1998 ◽  
Vol 08 (01) ◽  
pp. 41-50
Author(s):  
Yung-Syau Chen ◽  
Jean-Luc Gaudiot
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Optimization Technique ◽  
Traveling Salesman ◽  
Functional Language ◽  
Global Variables ◽  
Parallel Version ◽  
Parallel Branch And Bound ◽  
Hard Problems ◽  
The Traveling Salesman Problem

Parallel branch-and-bound is an optimization technique which renders more efficient the solution of some hard problems such as the puzzle of colored blocks and the traveling-salesman problem. In a functional language such as Sisal 2.0, it is difficult for the programmer to describe a parallel version of this technique due to the lack of imperative features in the language. In this paper, we propose a version of Sisal 2.0 extended with user-declared mutable global variables in order to enable Sisal programmers to apply the parallel branch-and-bound technique. In a simple example (the puzzle of colored blocks), we show that this approach yields better performance than either conventional functional programs or imperative programs. It is easy to see that the same strategy can be used to solve a number of hard problems such as the traveling-salesman problem.

An exact algorithm for the Traveling Salesman Problem with Deliveries and Collections

Networks ◽  
2003 ◽  
Vol 42 (1) ◽  
pp. 26-41 ◽  
Author(s):  
R. Baldacci ◽  
E. Hadjiconstantinou ◽  
A. Mingozzi
Keyword(s):  
Traveling Salesman Problem ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem
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