Abstract
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.
Highlights
The traveling salesman problem (TSP) is one of the most well-known combinational optimization problems studied in the operation research literature
Solving the TSP problem is crucial because it belongs to the class of non-polynomial (NP)-complete
DFJ relaxation gets the best answer from others because it has one type of variable
Summary
The traveling salesman problem (TSP) is one of the most well-known combinational optimization problems studied in the operation research literature. Solving the TSP problem is crucial because it belongs to the class of non-polynomial (NP)-complete. In this class of problems, no polynomial–time algorithm has been discovered. If someone finds an efficient TSP algorithm, it can be extended to other NP-complete class issues. The TSP is divided into two categories, symmetric and asymmetric, based on the distance between any two nodes. The TSP consists of determining a minimum-distance circuit passing through each vertex once and only once. Such a circuit is known as a tour or Hamiltonian circuit (or cycle) [2]
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