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

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.

A Critical Analysis of a Tourist Trip Design Problem with Time-Dependent Recommendation Factors and Waiting Times

“…In order to solve the problems (27 instances), CPLEX 20.1.0 [22] software was used, with a maximum computational time of one hour per instance. CPLEX has been successfully used to optimally solve and to compare different formulations of routing problems, such as TSP [23]. Variants of TTDP were solved using this solver as well [7,9,14,16,21].…”

Solving TSP Problems with Integer Programming

“…𝑥 , ∈ 0,1 , ∀𝑖, 𝑗 ∈ 𝑉 where x i,j =1 means going from city i to city j; x i,j = 0 means otherwise. We introduce the decision variable μ i , ∀i∈V, μ i ≥ 0 and add the following MTZ constraints [4]:…”

Application of Fuzzy-TOPSIS Method in Supporting Supplier Selection with Focus on HSE Criteria: A Case Study in the Oil and Gas Industry

“…Among the different MCDM techniques employed to solve the supplier selection problem, some of the most applied are the analytic hierarchy process (AHP), the analytic network process (ANP), the technique for order of preference by similarity to ideal solution (TOPSIS), the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), preference ranking organization method for enrichment evaluations (PROMOTHEE), the decision-making trial and evaluation laboratory (DEMATEL), and the best-worst method (BWM) [4,11,16,21,[29][30][31][32][33]. A new generation of MCDM techniques has been developed in recent decades and has also been successfully applied to solve supplier selection problems, such as the simultaneous evaluation of criteria and alternatives (SECA) [34], the weighted aggregated sum product assessment (WASPAS) [35,36], the evaluation based on distance from average solution (EDAS) [37,38], the pivot pairwise relative criteria importance assessment (PIPRECIA) [39], the additive ratio assessment (ARAS) [40,41], the weighted implementation of suboptimal paths (WISP) [42] and the MULTIMOOSRAL method [43]. Some authors have also proposed the application of hybrid models, which are combined MCDM techniques, to mitigate the weaknesses presented by them when used in isolation, such as AHP and VIKOR [26], ANP and TOPSIS [44], AHP and TOPSIS [45], and AHP and DEA [46].…”