scholarly journals A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Zakir Hussain Ahmed
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Computational Time ◽  
Cost Matrix ◽  
Asymmetric Traveling Salesman Problem ◽  
Path Representation ◽  
Random Instances ◽  
Representation Method ◽  
The Cost

A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem (ATSP) is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisearch algorithm is applied. It is shown that this minor preprocessing of the data before the simple lexisearch algorithm is applied improves the computational time substantially. The efficiency of our algorithms to the problem against two existing algorithms has been examined for some TSPLIB and random instances of various sizes. The results show remarkably better performance of our algorithms, especially our data-guided algorithm.

scholarly journals An Algorithm for Mapping the Asymmetric Multiple Traveling Salesman Problem onto Colored Petri Nets

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 143 ◽  
Author(s):  
Furqan Essani ◽  
Sajjad Haider
Keyword(s):  
Petri Nets ◽  
Traveling Salesman Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Colored Petri Nets ◽  
Cost Matrix ◽  
Multiple Traveling Salesman Problem ◽  
Hard Problems ◽  
The Cost

The Multiple Traveling Salesman Problem is an extension of the famous Traveling Salesman Problem. Finding an optimal solution to the Multiple Traveling Salesman Problem (mTSP) is a difficult task as it belongs to the class of NP-hard problems. The problem becomes more complicated when the cost matrix is not symmetric. In such cases, finding even a feasible solution to the problem becomes a challenging task. In this paper, an algorithm is presented that uses Colored Petri Nets (CPN)—a mathematical modeling language—to represent the Multiple Traveling Salesman Problem. The proposed algorithm maps any given mTSP onto a CPN. The transformed model in CPN guarantees a feasible solution to the mTSP with asymmetric cost matrix. The model is simulated in CPNTools to measure two optimization objectives: the maximum time a salesman takes in a feasible solution and the collective time taken by all salesmen. The transformed model is also formally verified through reachability analysis to ensure that it is correct and is terminating.

A Compressed Annealing Approach with Pre-Process for the Asymmetric Traveling Salesman Problem with Time Windows

2011 ◽  
Vol 5 (5) ◽  
pp. 669-678
Author(s):  
Tadanobu Mizogaki ◽  
◽  
Masao Sugi ◽  
Masashi Yamamoto ◽  
Hidetoshi Nagai ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Feasible Solution ◽  
Time Window ◽  
Time Windows ◽  
Computing Time ◽  
Traveling Salesman ◽  
Asymmetric Traveling Salesman Problem ◽  
Insertion Method ◽  
Time Window Constraints ◽  
The Cost

This paper proposes a method of rapidly finding a feasible solution to the asymmetric traveling salesman problem with time windows (ATSP-TW). ATSP-TW is a problem that involves determining the route with the minimum travel cost for visiting n cities one time each with time window constraints (the period of time in which the city must be visited is constrained). “Asymmetrical” denotes a difference between the cost of outbound and return trips. For such a combinatorial optimization problem with constraints, we propose a method that combines a pre-process based on the insertion method with metaheuristics called “the compressed annealing approach.” In an experiment using a 3-GHz computer, our method derives a feasible solution that satisfies the time window constraints for all of up to about 300 cities at an average of about 1/7 the computing time of existing methods, an average computing time of 0.57 seconds, and a maximum computing time of 9.40 seconds.

scholarly journals On Tightly Bounding the Dubins Traveling Salesman's Optimum

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
Sivakumar Rathinam
Keyword(s):  
Lower Bound ◽  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Motion Constraints ◽  
Euclidean Traveling Salesman Problem ◽  
Problem Instances ◽  
Feasible Solutions ◽  
The Cost ◽  
Dubins Traveling Salesman Problem

The Dubins traveling salesman problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. This problem requires finding a curvature constrained shortest path for a vehicle visiting a set of target locations. Currently, there is no algorithm that can find an optimal solution to the DTSP. In addition, relaxing the motion constraints and solving the resulting Euclidean traveling salesman problem (ETSP) provide the only lower bound available for the DTSP. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This paper addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.

scholarly journals A generalization of the convex-hull-and-line traveling salesman problem

1998 ◽  
Vol 2 (2) ◽  
pp. 177-191 ◽  
Author(s):  
Md. Fazle Baki ◽  
S. N. Kabadi
Keyword(s):  
Convex Hull ◽  
Traveling Salesman Problem ◽  
Equivalence Relation ◽  
General Class ◽  
Traveling Salesman ◽  
Cost Matrix ◽  
Solvable Case ◽  
Special Cases ◽  
The Traveling Salesman Problem ◽  
The Cost

Two instances of the traveling salesman problem, on the same node set {1,2,…,n} but with different cost matrices C and C′ , are equivalent iff there exist {ai,bi: i=1,…, n} such that for any 1≤i, j≤n,i≠j,C′(i,j)=C(i,j)+ai+bj [7]. One of the well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP.

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.

scholarly journals ON SAMPLING BASED METHODS FOR THE DUBINS TRAVELING SALESMAN PROBLEM WITH NEIGHBORHOODS

2015 ◽  
Vol 2 (2) ◽  
pp. 57-61
Author(s):  
Petr Váňa ◽  
Jan Faigl
Keyword(s):  
Path Planning ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Computational Time ◽  
Solution Quality ◽  
Goal Region ◽  
Dubins Vehicle ◽  
Proposed Modification ◽  
Dubins Traveling Salesman Problem

In this paper, we address the problem of path planning to visit a set of regions by Dubins vehicle, which is also known as the Dubins Traveling Salesman Problem Neighborhoods (DTSPN). We propose a modification of the existing sampling-based approach to determine increasing number of samples per goal region and thus improve the solution quality if a more computational time is available. The proposed modification of the sampling-based algorithm has been compared with performance of existing approaches for the DTSPN and results of the quality of the found solutions and the required computational time are presented in the paper.

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