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Journal articles on the topic 'Salesman problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Liao, Shuran. "The Solutions to Traveling Salesman Problem." Highlights in Science, Engineering and Technology 47 (May 11, 2023): 136–43. http://dx.doi.org/10.54097/hset.v47i.8182.

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This paper presents solutions to symmetric, asymmetric, and multiple traveling salesman problems. In the symmetric traveling salesman problem, one salesperson must go to five cities, making precisely one stop at each location. A matrix with the distances between each city is provided. Using the branch and bound algorithm and expressing it in Python, the final result is obtained. The formulations of the asymmetric traveling salesman problem and the multiple traveling salesman problem are demonstrated in the paper. The asymmetric problem in the paper is solved by transforming the asymmetric trav

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Essani, Furqan, and Sajjad Haider. "An Algorithm for Mapping the Asymmetric Multiple Traveling Salesman Problem onto Colored Petri Nets." Algorithms 11, no. 10 (2018): 143. http://dx.doi.org/10.3390/a11100143.

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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 map

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Mzili, Ilyass, Toufik Mzili, and Mohammed Essaid Riffi. "Efficient routing optimization with discrete penguins search algorithm for MTSP." Decision Making: Applications in Management and Engineering 6, no. 1 (2023): 730–43. http://dx.doi.org/10.31181/dmame04092023m.

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The Travelling Salesman Problem (TSP) is a well-known combinatorial optimization problem that belongs to a class of problems known as NP-hard, which is an exceptional case of travelling salesman problem (TSP), which determines a set of routes enabling multiple salesmen to start at and return to home cities (depots). The penguins search optimization algorithm (PeSOA) is a new metaheuristic optimization algorithm. In this paper, we present a discrete penguins search optimization algorithm (PeSOA) for solving the multiple travelling salesman problem (MTSP). The PeSOA evaluated by a set of benchma

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Al-Furhud, Maha Ata, and Zakir Hussain Ahmed. "Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem." Mathematical Problems in Engineering 2020 (October 27, 2020): 1–13. http://dx.doi.org/10.1155/2020/3431420.

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The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex

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Chris, Jojo Obi, Qiang Xiong, and Martinson Yeboah Appiah. "Using genetic algorithm to solve multiple traveling salesman problem and considering Carbon emissions." Indian Journal of Science and Technology 13, no. 36 (2020): 3707–15. https://doi.org/10.17485/IJST/v13i36.1316.

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Abstract <strong>Objectives:</strong> The Multiple Travelling Salesman problem is a complex combinatorial optimization problem which is a variance of the Traveling Salesman Problem,where a lot of salesmen are utilized in the solution. In this work a cold chain logistics and route optimization model with minimum transport cost, carbon cost and Refrigeration cost are constructed. <strong>Methods:</strong> A genetic algorithm is then proposed to solve for the Multiple Travelling Salesman Problem with time windows while transport cost, carbon emission cost and refrigeration cost is

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Iriani, Rahma Try, Sapti Wahyuningsih, and Darmawan Satyananda. "TWO PHASE HEURISTIC ALGORITHM (TPHA) PADA MULTIPLE TRAVELLING SALESMAN PROBLEM (MTSP) DAN IMPLEMENTASI PROGRAMNYA." Jurnal Kajian Matematika dan Aplikasinya (JKMA) 1, no. 1 (2020): 10. http://dx.doi.org/10.17977/um055v1i12020p10-17.

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Multiple Traveling Salesman Problem (MTSP) is one variant of Traveling Salesman Problem (TSP) which involves several salesmen in making a trip to visit several customers. In this article, the Two-Phase Heuristic Algorithm (TPHA) is used to solve MTSP problems. The algorithm classifies customers into several regions using the K-Means algorithm, which will then find a route solution for each region using a genetic algorithm. The MTSP problems that were resolved using TPHA were implemented into the Borland Delphi 7.0 programming language. Application testing was conducted using 21, 32, and 46 poi

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Obi, Chris Jojo. "Using genetic algorithm to solve multiple traveling salesman problem and considering Carbon emissions." Indian Journal of Science and Technology 13, no. 36 (2020): 3707–15. http://dx.doi.org/10.17485/ijst/v13i36.1316.

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Objectives: The Multiple Travelling Salesman problem is a complex combinatorial optimization problem which is a variance of the Traveling Salesman Problem,where a lot of salesmen are utilized in the solution. In this work a cold chain logistics and route optimization model with minimum transport cost, carbon cost and Refrigeration cost are constructed. Methods: A genetic algorithm is then proposed to solve for the Multiple Travelling Salesman Problem with time windows while transport cost, carbon emission cost and refrigeration cost is minimized. Findings: It was observed that the algorithm ev

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8

Singamsetty, Purusotham, and Jayanth Kumar Thenepalle. "An efficient genetic algorithm for solving open multiple travelling salesman problem with load balancing constraint." Decision Science Letters 10, no. 4 (2021): 525–34. http://dx.doi.org/10.5267/j.dsl.2021.5.003.

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The multiple travelling salesman problem (MTSP) is one of the widely studied combinatorial optimization problems with various theoretical and practical applications. However, most of the studies intended to deal with classical MTSP, very limited attention has been given to an open multiple travelling salesman problem and its variants. In this paper, an open multiple travelling salesman problem with load balancing constraint (OMTSPLB) is addressed. The OMTSPLB differs from the conventional MTSP, in which all the salesmen start from the central depot and need not come back to it after visiting t

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YOGA DWI WAHYU NUGRAHA, HENDRAWAN ARMANTO, and YOSI KRISTIAN. "Single Objective Mayfly Algorithm with Balancing Parameter for Multiple Traveling Salesman Problem." Journal of Electronics, Electromedical Engineering, and Medical Informatics 5, no. 3 (2023): 193–204. http://dx.doi.org/10.35882/jeemi.v5i3.299.

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The Multiple Travelling Salesman Problem (MTSP) is a challenging combinatorial problem that involves multiple salesman visiting a set of cities, each exactly once, starting and ending at the same depot. The aim is to determine the optimal route with minimal cost and node cuts for each salesman while ensuring that at least one salesman visits each city. As the problem is NP-Hard, a single-objective metaheuristic algorithm, called the Mayfly Algorithm, inspired by the collective behavior of mayflies, is employed to solve the problem using the TSPlib95 test data. Since the Mayfly Algorithm employ

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Meng, Xianghu, Jun Li, and MengChu Zhou. "A Colored Traveling Salesman Problem with Varying City Colors." Discrete Dynamics in Nature and Society 2021 (December 9, 2021): 1–14. http://dx.doi.org/10.1155/2021/4533483.

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A colored traveling salesman problem (CTSP) is a path optimization problem in which colors are used to characterize diverse matching relationship between cities and salesmen. Namely, each salesman has a single color while every city has one to multiple salesmen’s colors, thus allowing salesmen to visit exactly once the cities of their colors. It is noteworthy that cities’ accessibilities to salesmen may change over time, which usually takes place in the multiwarehouse distribution of online retailers. This work presents a new CTSP with dynamically varying city colors for describing and modelin

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Terzi, Dmitri. "A Natural Approach to Solving the Traveling Salesman Problem." Cybernetics and Computer Technologies, no. 4 (December 4, 2023): 43–52. http://dx.doi.org/10.34229/2707-451x.23.4.6.

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Introduction. The traveling salesman problem is a transport-type problem. It is natural to use a method based on the technology for solving transport problems to solve it. The cyclicity and degeneracy of the solution to the traveling salesman problem requires significant modification of the corresponding stages of solving the transport problem (drawing up an initial feasible solution; checking the plan for optimality; obtaining a new feasible solution). Purpose. Development of a natural approach to solving the traveling salesman problem. Description of the structure of a set of traveling sales

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Harrath, Youssef. "Three-Step Metaheuristic for the Multiple Objective Multiple Traveling Salesmen Problem." International Journal of Applied Metaheuristic Computing 11, no. 4 (2020): 130–48. http://dx.doi.org/10.4018/ijamc.2020100107.

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In this article, the multiple objective multiple Traveling Salesman Problem is considered. m salesmen have to visit n cities to perform some tasks each taking a given processing time. Two objectives are considered: balance the working loads of different salesmen and minimize their total traveled distance. To solve this NP-hard problem, a 3-phase metaheuristic was developed. In the first 2 phases, the principle of center of mass and a neighborhood search technique are used to assign the n cities to the m salesmen. In the third phase, a TSP solver was used to generate an optimal tour to every sa

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Latheef, Mohamed Ghaisan. "Solving Symmetrical Travelling Salesman Problem." Journal of Advanced Research in Dynamical and Control Systems 12, SP7 (2020): 2629–35. http://dx.doi.org/10.5373/jardcs/v12sp7/20202399.

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Zhafira, Noufal, Feri Afrinaldi, and Taufik Taufik. "An Application of Genetic Algorithm in Determining Salesmen’s Routes: A Case Study." Jurnal Optimasi Sistem Industri 17, no. 1 (2018): 26. http://dx.doi.org/10.25077/josi.v17.n1.p26-34.2018.

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This paper presents a case study of determining vehicles’ routes. The case is taken from a pharmaceutical products distribution problem faced by a distribution company located in the city of Padang, Indonesia. The objective of this paper is to reduce the total distribution time required by the salesmen of the company. Since the company uses more than one salesman, then the problem is modeled as a multi traveling salesman problem (m-TSP). The problem is solved by employing genetic algorithm (GA) and a Matlab® based computer program is developed to run the algorithm. It is found that, by employi

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Tadios, Kiros Kenea. "Solving Shortest Route Using Dynamic Programming Problem." Indian Journal of Science and Technology 15, no. 31 (2022): 1527–31. https://doi.org/10.17485/IJST/v15i31.1342.

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Abstract <strong>Objective:</strong>- To determine the shortest distance in salesman of dynamic programming problem. <strong>Method:-</strong> Recursive equation and arrow drawing methods are used to determine the shortest distance in salesman of dynamic programming problem. An implementation of the traveling salesman problem using dynamic programming is presented in this study which generates optimal answer.<strong> Findings:-</strong> Forward and backward recursive methods take time and complex to find optimal solution (shortest distance) but arrow drawing method is usefu

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SUZUKI, Hisatoshi, Masato TSUJI, and Ryuichi HIRABAYASHI. "WATER SALESMAN PROBLEM." Journal of the Operations Research Society of Japan 30, no. 4 (1987): 472–92. http://dx.doi.org/10.15807/jorsj.30.472.

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Sulistia, Nadya, Irwansyah Irwansyah, and Marwan Marwan. "Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem." International Journal of Computing Science and Applied Mathematics 11, no. 1 (2025): 9. https://doi.org/10.12962/j24775401.v11i1.20259.

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18

Demiral, Mehmet Fatih, and Halil Şen. "Integer Programming Model for Two-Centered Double Traveling Salesman Problem." European Journal of Economics and Business Studies 5, no. 1 (2016): 80. http://dx.doi.org/10.26417/ejes.v5i1.p80-86.

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Traveling Salesman Problem (TSP) is among the most popular combinatorial problems and has been widely studied with many extensions in the literature. There have been integer programming formulations and solution approaches for TSP and its variations. One of the most popular topics is the multiple TSP (m-TSP). It has been started to work on the last decades. Generally, m-TSP has a single depot and more than one tour. However, some types have more than one depot. Besides, if seeking, many encounter with double traveling salesman problem (d-TSP). As inferred from the literature, d-TSP is a variat

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Pacheco-Valencia, Víctor Hugo, Nodari Vakhania, Frank Ángel Hernández-Mira, and José Alberto Hernández-Aguilar. "A Multi-Phase Method for Euclidean Traveling Salesman Problems." Axioms 11, no. 9 (2022): 439. http://dx.doi.org/10.3390/axioms11090439.

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The Traveling Salesman Problem (TSP) aims to find the shortest tour for a salesman who starts and ends in the same city and visits the remaining n−1 cities exactly once. There are a number of common generalizations of the problem including the Multiple Traveling Salesman Problem (MTSP), where instead of one salesman, there are k salesmen and the same amount of individual tours are to be constructed. We consider the Euclidean version of the problem where the distances between the cities are calculated in two-dimensional Euclidean space. Both general the TSP and its Euclidean version are strongl

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Маций, Ольга Борисовна. "ОГЛЯД ЗАВДАНЬ МАРШРУТИЗАЦІЇ, ЩО ЗВОДЯТЬСЯ ДО ЗАДАЧІ КОМІВОЯЖЕРА". Open Information and Computer Integrated Technologies, № 86 (14 лютого 2020): 152–59. http://dx.doi.org/10.32620/oikit.2019.86.11.

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The solution to the problem of improving the management of the transport process depends not only on the level of modernization of vehicles and the degree of use of modern information technologies, but also on the choice of routes that reduce the cost of transporting goods and passengers. Actual working conditions of vehicles in road networks put forward a number of tasks for optimizing closed routes, which are based on the classic routing problem (VRP - Vehicle Routing Problem).VRP is one of the generalizations of the hard-to-solve traveling salesman problem. The traveling salesman task is NP

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Ulyanov, M. V., and M. I. Fomichev. "Combined Algorithm for Solving the Asymmetric Traveling Salesman Problem as Applied to Transport Logistics Problems." Informacionnye Tehnologii 28, no. 3 (2022): 141–47. http://dx.doi.org/10.17587/it.28.141-147.

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The traveling salesman problem is to find a Hamiltonian cycle with the minimum sum of the weights of arcs in a complete oriented asymmetric graph. Despite its simple formulation, the traveling salesman problem is NP-hard. The Branch and Bound method is the basis of the most time efficient algorithm for solving the traveling salesman problem, delivering the exact solution. However, for a number of applied problems, the time to obtain a solution using this algorithm is practically unacceptable. Despite the majority of heuristic algorithms developed for the traveling salesman problem, for some ap

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Gavrilova, Anastasiya V., and Yaroslavna B. Pankratova. "About Construction of Realizability Arias of Salesman Strategies in Dynamic Salesmen Problem." Contributions to Game Theory and Management 14 (2021): 113–21. http://dx.doi.org/10.21638/11701/spbu31.2021.10.

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The dynamic travelling salesman problem, where we assume that all objects can move with constant velocity, is considered. To solve this NPhard problem we use a game-theoretic approach and well-known solution concepts of pursuit games. We identify the realizability areas of salesman strategies depending on the initial positions of customers and their velocities. We present different cases of realizability areas of salesman strategies constructing in Python program with several numbers of customers.

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Purusotham, S., T. Jayanth Kumar, T. Vimala, and K. J. Ghanshyam. "An efficient hybrid genetic algorithm for solving truncated travelling salesman problem." Decision Science Letters 11, no. 4 (2022): 473–84. http://dx.doi.org/10.5267/j.dsl.2022.6.003.

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This paper considers a practical truncated traveling salesman problem (TTSP), in which the salesman is only required to cover a subset of out of given cities (rather than covering all the given cities as in conventional travelling salesman problem (TSP)) with minimal traversal distance. Thus, every feasible solution tour contains exactly cities including the starting city. However, extensive research on TSP has been received and various efficient solution techniques including exact, heuristic, and metaheuristic algorithms are devoted, a very limited attention has been given to TTSP models beca

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Patterson, Mike, and Daniel Friesen. "Variants of the Traveling Salesman Problem." Studies in Business and Economics 14, no. 1 (2019): 208–20. http://dx.doi.org/10.2478/sbe-2019-0016.

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AbstractThis paper includes an introduction to the concept of spreadsheet optimization and modeling as it specifically applies to combinatorial problems. One of the best known of the classic combinatorial problems is the “Traveling Salesman Problem” (TSP). The classic Traveling Salesman Problem has the objective of minimizing some value, usually distance, while defining a sequence of locations where each is visited once. An additional requirement is that the tour ends in the same location where the tour started. Variants of the classic Traveling Salesman Problem are developed including the Bot

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Kalaiarasi, S., and P. Sriramya. "Seed based plant propagation algorithm for multiple travelling salesman problem." International Journal of Engineering & Technology 7, no. 3.3 (2018): 515. http://dx.doi.org/10.14419/ijet.v7i2.33.14823.

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Multiple Travelling Salesman Problem is a complex problem in which route for a salesman is assigned to visit a city that has various hurdles such as congested road, damaged road, etc. In recent years biologically inspired algorithms are most widely used to solve many optimization problems. Here seed based plant propagation algorithm is applied for the multiple travelling salesman problem that is also a optimization problem, and the result is compared with a short-cut routing algorithm. The result shows that Seed based Propagation Algorithm is easy to implement since it has few parameters to be

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Cuevas, Azcarie Manuel Cabrera, Jania Astrid Saucedo Martínez, and José Antonio Marmolejo Saucedo. "A Two Stage Method for the Multiple Traveling Salesman Problem." International Journal of Applied Metaheuristic Computing 11, no. 3 (2020): 79–91. http://dx.doi.org/10.4018/ijamc.2020070104.

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The variation of the traveling salesman problem (TSP) with multiple salesmen (m-TSP) has been studied for many years resulting in diverse solution methods, both exact and heuristic. However, the high difficulty level on finding optimal (or acceptable) solutions has opposed the many efforts of doing so. The proposed method regards a two stage procedure which implies a modified version of the p-Median Problem (PMP) alongside the TSP, making a partition of the nodes into subsets that will be assigned to each salesman, solving it with Branch & Cut (B&C), in the first stage. This is followe

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Silalahi, Bib Paruhum, Nurul Fathiah, and Prapto Tri Supriyo. "Use of Ant Colony Optimization Algorithm for Determining Traveling Salesman Problem Routes." Jurnal Matematika "MANTIK" 5, no. 2 (2019): 100–111. http://dx.doi.org/10.15642/mantik.2019.5.2.100-111.

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Ant Colony Optimization is one of the meta-heuristic methods used to solve combinatorial optimization problems that are quite difficult. Ant Colony Optimization algorithm is inspired by ant behavior in the real world to build the shortest path between food sources and their nests. Traveling Salesman Problem is a problem in optimization. Traveling Salesman Problem is a problem to find the minimum distance from the initial node to the whole node with each node must be visited exactly once and must return to the initial node. Traveling Salesman Problem is a non-deterministic polynomial-time compl

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Sutapa, I. Nyoman, I. Gede Agus Widyadana, and Christine Christine. "STUDI TENTANG TRAVELLING SALESMAN DAN VEHICLE ROUTING PROBLEM DENGAN TIME WINDOWS." Jurnal Teknik Industri 5, no. 2 (2004): 81–89. http://dx.doi.org/10.9744/jti.5.2.81-89.

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The article shows the study of model development of travelling salesman problem. Three models are studied, i.e. travelling salesman problem with time windows, vehicle routing problem, and vehicle routing problem with time windows.   Abstract in Bahasa Indonesia :   Dalam artikel ini dipaparkan kajian mengenai pengembangan model travelling salesman problem. Ada tiga model yang dikaji yaitu travelling salesman problem dengan time windows, vehicle routing problem, serta vehicle routing problem dengan time windows.   Kata-kunci: travelling salesman problem

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Aswandi, Sugiarto Cokrowibowo, and Arnita Irianti. "Model Penentuan Rute Terpendek Penjemputan Sampah Menggunakan Metode MTSP dan Algoritma Genetika." Journal of Applied Computer Science and Technology 2, no. 1 (2021): 43–48. http://dx.doi.org/10.52158/jacost.v2i1.168.

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Garbage pick-ups performed by two or more people must have a route in their pickup. However, it is not easy to model the route of the pickup that each point must be passed and each point is only passed once. Now, the method to create a route has been done a lot, one of the most commonly used methods is the creation of routes using the Traveling Salesman Problem method. Traveling Salesman Problem is a method to determine the route of a series of cities where each city is only traversed once. In this study, the shortest route modeling was conducted using Multiple Traveling Salesman Problem and G

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Terzi, Dmitri. "Algorithm for Constructing the Traveling Salesman Problem with a Given Optimal Solution." Intellectus, no. 1 (July 2023): 171–78. http://dx.doi.org/10.56329/1810-7087.23.1.17.

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Issues related to the solution of the traveling salesman problem are considered. An algorithm for constructing the traveling salesman problem with a predetermined optimal cyclic solution has been developed. The algorithm can be used to evaluate the effectiveness of methods for solving the traveling salesman problem, to determine the optimality of a feasible solution found in some way, and also to understand the structure of problems with a given cyclic optimal solution.

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Pap, Gyula, and József Varnyú. "Synchronized Traveling Salesman Problem." Journal of Graph Algorithms and Applications 25, no. 1 (2021): 437–59. http://dx.doi.org/10.7155/jgaa.00566.

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Oberlin, Paul, Sivakumar Rathinam, and Swaroop Darbha. "Today's Traveling Salesman Problem." IEEE Robotics & Automation Magazine 17, no. 4 (2010): 70–77. http://dx.doi.org/10.1109/mra.2010.938844.

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Current, John R., and David A. Schilling. "The Covering Salesman Problem." Transportation Science 23, no. 3 (1989): 208–13. http://dx.doi.org/10.1287/trsc.23.3.208.

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Gutin, Gregory, and Abraham Punnen. "The traveling salesman problem." Discrete Optimization 3, no. 1 (2006): 1. http://dx.doi.org/10.1016/j.disopt.2005.12.001.

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Fazle Baki, Md, and Santosh N. Kabadi. "Pyramidal traveling salesman problem." Computers & Operations Research 26, no. 4 (1999): 353–69. http://dx.doi.org/10.1016/s0305-0548(98)00067-7.

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Papadakos, Nikolaos, George Tzallas-Regas, Berç Rustem, and Joanne Thoms. "Risky traveling salesman problem." European Journal of Operational Research 212, no. 1 (2011): 69–73. http://dx.doi.org/10.1016/j.ejor.2011.01.025.

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Kotov, Vladimir, and Michail Kovalev. "Maximum travelling salesman problem." Mathematical Methods of Operations Research 43, no. 2 (1996): 169–81. http://dx.doi.org/10.1007/bf01680370.

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Li, Jun, MengChu Zhou, Qirui Sun, Xianzhong Dai, and Xiaolong Yu. "Colored Traveling Salesman Problem." IEEE Transactions on Cybernetics 45, no. 11 (2015): 2390–401. http://dx.doi.org/10.1109/tcyb.2014.2371918.

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Chakrabarti, B. K. "Directed travelling salesman problem." Journal of Physics A: Mathematical and General 19, no. 7 (1986): 1273–75. http://dx.doi.org/10.1088/0305-4470/19/7/028.

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Zhang, Huili, and Yinfeng Xu. "Online covering salesman problem." Journal of Combinatorial Optimization 35, no. 3 (2018): 941–54. http://dx.doi.org/10.1007/s10878-017-0227-9.

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Dror, Moshe. "The travelling salesman problem." European Journal of Operational Research 25, no. 1 (1986): 142–44. http://dx.doi.org/10.1016/0377-2217(86)90125-6.

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Zia, Mohammed, Ziyadin Cakir, and Dursun Seker. "Spatial Transformation of Equality – Generalized Travelling Salesman Problem to Travelling Salesman Problem." ISPRS International Journal of Geo-Information 7, no. 3 (2018): 115. http://dx.doi.org/10.3390/ijgi7030115.

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Skybytskyi, N. M., and K. I. Denysov. "COMPUTATIONAL EQUIVALENCE OF ONE-DIMENSIONAL QUOTA TSP VARIANT AND (MIN, +) CONVOLUTION." Journal of Numerical and Applied Mathematics, no. 2 (2024): 62–67. https://doi.org/10.17721/2706-9699.2024.2.04.

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The paper considers a variant of the one-dimensional quota traveling salesman problem and its connection to the (min, +) convolution problem. We propose fine-grained reductions between these problems, resulting in a conditional lower bound on the computational complexity of the quota traveling salesman problem variant. We highlight the role of convexity in both problems and its connection to the proposed reductions.

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E, Іvohin, Gavrylenko V, and Іvohina K. "One Approach to Solving the Fuzzy Traveling Salesman Problem Based on a Multicriteria Approach." Artificial Intelligence 30, AI.2025.30(2) (2025): 84–94. https://doi.org/10.15407/jai2025.02.084.

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The aim of this work is to develop methods for solving fuzzy traveling salesman problems based on a multi-criteria approach. The paper considers options for solving multi-criteria traveling salesman problems, methods for reducing the problem to a single-criteria problem, and approaches to forming a compromise route using Prim's algorithm. The paper considers methods for solving a fuzzy problem of finding the fastest route with fuzzy specified values of travel time on a transport system. Fuzzy triangular numbers are used to represent the duration. The fuzzy traveling salesman problem is conside

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Akschat, Arya1, Perumal2 Boominathan, and Krishnan3 Santhi. "Parallelized solution to the asymmetric travelling salesman problem using central processing unit acceleration." Indonesian Journal of Electrical Engineering and Computer Science 25, no. 3 (2022): 1795–802. https://doi.org/10.11591/ijeecs.v25.i3.pp1795-1802.

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Travelling salesman problem is a well researched problem in computer science and has many practical applications. It is classified as a NP-hard problem as its exact solution can only be obtained in exponential time unless P = NP. There are different variants of the travelling salesman problem (TSP) and in this paper, asymmetric travelling salesman problem is addressed since this variant is quite often observed in real world scenarios. There are a number of heuristic approaches to this problem which provides approximate solutions in polynomial time, however this paper proposes an exact optimal

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El Hassani, Hicham, Said Benkachcha, and Jamal Benhra. "New Genetic Operator (Jump Crossover) for the Traveling Salesman Problem." International Journal of Applied Metaheuristic Computing 6, no. 2 (2015): 33–44. http://dx.doi.org/10.4018/ijamc.2015040103.

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Inspired by nature, genetic algorithms (GA) are among the greatest meta-heuristics optimization methods that have proved their effectiveness to conventional NP-hard problems, especially the traveling salesman problem (TSP) which is one of the most studied supply chain management problems. This paper proposes a new crossover operator called Jump Crossover (JMPX) for solving the travelling salesmen problem using a genetic algorithm (GA) for near-optimal solutions, to conclude on its efficiency compared to solutions quality given by other conventional operators to the same problem, namely, Partia

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Lu, Yongliang, Jin-Kao Hao, and Qinghua Wu. "Solving the clustered traveling salesman problem via traveling salesman problem methods." PeerJ Computer Science 8 (June 13, 2022): e972. http://dx.doi.org/10.7717/peerj-cs.972.

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The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by converting it to the well-studied TSP. For this purpose, we first investigate a technique to convert a CTSP instance to a TSP and then apply powerful TSP solvers (including exact and heuristic solvers) to solve the resulting TSP instance. We want to answer the following questions: How do state-of-the-art TSP solvers perform on clustered instances converted from the

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Lien, Y. "Transformation of the generalized traveling-salesman problem into the standard traveling-salesman problem." Information Sciences 74, no. 1-2 (1993): 177–89. http://dx.doi.org/10.1016/0020-0255(93)90133-7.

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Zerovnik, Janez, and Niko Herakovic. "A new application of the generalized traveling salesman problem in industry 4.0 and 5.0." Multiple Criteria Decision Making 16 (2021): 153–63. http://dx.doi.org/10.22367/mcdm.2021.16.09.

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A novel application of the generalized traveling salesman is pro- posed. The practical problem considered is optimization of different optimization criteria in various models of a mixed assembly worksta- tion. Several models that give rise to interesting optimization problems are discussed. Keywords: generalized traveling salesman problem, flexible assembly workstation.

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Arya, Akschat, Boominathan Perumal, and Santhi Krishnan. "Parallelized solution to the asymmetric travelling salesman problem using central processing unit acceleration." Indonesian Journal of Electrical Engineering and Computer Science 25, no. 3 (2022): 1795. http://dx.doi.org/10.11591/ijeecs.v25.i3.pp1795-1802.

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<p><span>Travelling salesman problem is a well researched problem in computer science and has many practical applications. It is classified as a NP-hard problem as its exact solution can only be obtained in exponential time unless P = NP. There are different variants of the travelling salesman problem (TSP) and in this paper, asymmetric travelling salesman problem is addressed since this variant is quite often observed in real world scenarios. There are a number of heuristic approaches to this problem which provides approximate solutions in polynomial time, however this paper propo

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