The Traveling Salesman Problem

1996 ◽  
pp. 209-237 ◽  
Author(s):  
Zbigniew Michalewicz
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

A New Heuristic Procedure To Solve The Traveling Salesman Problem

2007 ◽  
Vol 5 (1) ◽  
pp. 1-9
Author(s):  
Paulo Henrique Siqueira ◽  
Sérgio Scheer ◽  
Maria Teresinha Arns Steiner
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Heuristic Procedure ◽  
The Traveling Salesman Problem

scholarly journals An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 48
Author(s):  
Jin Zhang ◽  
Li Hong ◽  
Qing Liu
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Relevant Literature ◽  
Population Diversity ◽  
Traveling Salesman ◽  
Whale Optimization Algorithm ◽  
Neighborhood Search ◽  
Whale Optimization ◽  
The Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

scholarly journals An Optimal Algorithm for the Traveling Salesman Problem with Time Windows

1995 ◽  
Vol 43 (2) ◽  
pp. 367-371 ◽  
Author(s):  
Yvan Dumas ◽  
Jacques Desrosiers ◽  
Eric Gelinas ◽  
Marius M. Solomon
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Algorithm ◽  
Time Windows ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Christoph Hansknecht ◽  
Imke Joormann ◽  
Sebastian Stiller
Keyword(s):  
Column Generation ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Valid Inequalities ◽  
Shortest Paths ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Full Generality ◽  
Branching Rule ◽  
The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

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.

GENI Ants for the Traveling Salesman Problem

2004 ◽  
Vol 131 (1-4) ◽  
pp. 187-201 ◽  
Author(s):  
François-Xavier Le Louarn ◽  
Michel Gendreau ◽  
Jean-Yves Potvin
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem
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