scholarly journals A note on the Miller-Tucker-Zemlin model for the asymmetric traveling salesman problem

2016 ◽  
Vol 64 (3) ◽  
pp. 517-520 ◽  
Author(s):  
T. Sawik
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Asymmetric Traveling Salesman Problem ◽  
Subtour Elimination ◽  
Improved Performance ◽  
Additional Constraints

Abstract An enhancement of the Miller-Tucker-Zemlin (MTZ) model for the asymmetric traveling salesman problem is presented by introducing additional constraints to the initial formulation. The constraints account for ordering of boundary nodes as well as all successive nodes in the salesman tour. The enhanced MTZ subtour elimination constraints are computationally compared with the basic MTZ constraints and the version of MTZ lifted by Desrochers and Laporte. The proposed enhancement shows improved performance on a number of asymmetric TSPLIB instances.

scholarly journals A relax and cut approach using the multi-commodity flow formulation for the traveling salesman problem

DYNA ◽  
2015 ◽  
Vol 82 (191) ◽  
pp. 42-50 ◽  
Author(s):  
Makswell Seyiti Kawashima ◽  
Socorro Rangel ◽  
Igor Litvinchev ◽  
Luis Infante
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Computational Study ◽  
Traveling Salesman ◽  
Commodity Flow ◽  
Asymmetric Traveling Salesman Problem ◽  
Subtour Elimination ◽  
The Traveling Salesman Problem ◽  
Dual Bounds

<p class="ADYNAAbstrac"><span lang="EN-US">In this paper we explore the multi-commodity flow formulation for the Asymmetric Traveling Salesman Problem (ATSP) to obtain dual bounds. The procedure employed is a variant of a relax and cut procedure proposed in the literature that computes the Lagrangean multipliers associated to the subtour elimination constraints preserving the optimality of the multipliers associated to the assignment constraints. The results obtained by the computational study are encouraging and show that the proposed algorithm generated good dual bounds for the ATSP with a low execution time.</span></p>

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.

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