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1

Reinelt, Gerhard. "TSPLIB—A Traveling Salesman Problem Library." ORSA Journal on Computing 3, no. 4 (1991): 376–84. http://dx.doi.org/10.1287/ijoc.3.4.376.

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Yun, Ho-Yoeng, Suk-Jae Jeong, and Kyung-Sup Kim. "Advanced Harmony Search with Ant Colony Optimization for Solving the Traveling Salesman Problem." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/123738.

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We propose a novel heuristic algorithm based on the methods of advanced Harmony Search and Ant Colony Optimization (AHS-ACO) to effectively solve the Traveling Salesman Problem (TSP). The TSP, in general, is well known as an NP-complete problem, whose computational complexity increases exponentially by increasing the number of cities. In our algorithm, Ant Colony Optimization (ACO) is used to search the local optimum in the solution space, followed by the use of the Harmony Search to escape the local optimum determined by the ACO and to move towards a global optimum. Experiments were performed
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3

Karagul, Kenan, Erdal Aydemir, and Sezai Tokat. "Using 2-Opt based evolution strategy for travelling salesman problem." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6, no. 2 (2016): 103–13. http://dx.doi.org/10.11121/ijocta.01.2016.00268.

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Harmony search algorithm that matches the (µ+1) evolution strategy, is a heuristic method simulated by the process of music improvisation. In this paper, a harmony search algorithm is directly used for the travelling salesman problem. Instead of conventional selection operators such as roulette wheel, the transformation of real number values of harmony search algorithm to order index of vertex representation and improvement of solutions are obtained by using the 2-Opt local search algorithm. Then, the obtained algorithm is tested on two different parameter groups of TSPLIB. The proposed method
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Veeresh, M., T. Jayanth Kumar, and M. Thangaraj. "Solving the single depot open close multiple travelling salesman problem through a multi-chromosome based genetic algorithm." Decision Science Letters 13, no. 2 (2024): 401–14. http://dx.doi.org/10.5267/j.dsl.2024.1.006.

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The multiple travelling salesman problem (MTSP) extends the classical travelling salesman problem (TSP) by involving multiple salesman in the solution. MTSP has found widespread applications in various domains, such as transportation, robotics, and networking. Despite extensive research on MTSP and its variants, there has been limited attention given to the open close multiple travelling salesman problem (OCMTSP) and its variants in the literature. To the best of the author's knowledge, only one study has addressed OCMTSP, introducing an exact algorithm designed for optimal solutions. However,
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Ahmed, Zakir Hussain. "The Ordered Clustered Travelling Salesman Problem: A Hybrid Genetic Algorithm." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/258207.

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The ordered clustered travelling salesman problem is a variation of the usual travelling salesman problem in which a set of vertices (except the starting vertex) of the network is divided into some prespecified clusters. The objective is to find the least cost Hamiltonian tour in which vertices of any cluster are visited contiguously and the clusters are visited in the prespecified order. The problem is NP-hard, and it arises in practical transportation and sequencing problems. This paper develops a hybrid genetic algorithm using sequential constructive crossover, 2-opt search, and a local sea
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6

Zhang, Jing Min, and Cong Cong Wu. "Improved Shuffled Frog-Leaping Algorithm and its Application." Applied Mechanics and Materials 155-156 (February 2012): 92–96. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.92.

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This paper proposes an improved shuffled frog-leaping algorithm, the algorithm improves the subpopulation frog individual optimization way which is not just the worst individual optimization. "Guide optimal" probability and "guide suboptimal" probability are put forward. The experiments results of multiple problems of the TSPLIB show that the algorithm is feasible and effective.
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Thirugnanasambandam, Kalaipriyan, Raghav R.S, Saravanan D, Prabu U, and Rajeswari M. "Experimental Analysis of Ant System on Travelling Salesman Problem Dataset TSPLIB." EAI Endorsed Transactions on Pervasive Health and Technology 5, no. 19 (2019): 163092. http://dx.doi.org/10.4108/eai.13-7-2018.163092.

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8

Ismail, A. H., N. Hartono, S. Zeybek, and D. T. Pham. "Using the Bees Algorithm to solve combinatorial optimisation problems for TSPLIB." IOP Conference Series: Materials Science and Engineering 847 (May 28, 2020): 012027. http://dx.doi.org/10.1088/1757-899x/847/1/012027.

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9

Liu, Ping, and Yue Guang Li. "An Improve Firefly Algorithm and its Application." Applied Mechanics and Materials 404 (September 2013): 533–37. http://dx.doi.org/10.4028/www.scientific.net/amm.404.533.

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In this paper, according to the characteristics of TSP. A Novel Firefly Algorithm was used to solve the TSP, the algorithm was experimented and the experimental results show that the new algorithm to be successful in locating multiple solutions and better accuracy. The experimental result demonstrates that the Improve firefly algorithm can get better solutions to some Traveling Salesman Problems (TSP) than the solutions given in TSPLIB.
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Nanda Ginting, Subhan Hafiz, and Mayang Mughnyanti. "The Utilization Of The Simple Multi Attribute Rating Exploiting Ranks Can Enhance The Performance Of The Aco Algorithm." Jurnal Minfo Polgan 12, no. 1 (2023): 1325–29. http://dx.doi.org/10.33395/jmp.v12i1.12743.

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In a comparative study, the performance of the ACO algorithm and a modified genetic algorithm (MGA) were evaluated for solving the multiple salesman traveling problem (MTSP) using various datasets from TSPLIB. The results revealed that although the proposed algorithm did not achieve the best solution, it exhibited improved time efficiency as the dataset size increased. The objective of this study is to improve the performance of the ACO algorithm by integrating the SMARTER algorithm, which aims to find the optimal route and minimize travel time. The combination of these algorithms offers alter
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11

Zhou, Shipei, Yuandong Ding, Chi Zhang, Zhiguang Cao, and Yan Jin. "DualOpt: A Dual Divide-and-Optimize Algorithm for the Large-scale Traveling Salesman Problem." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 25 (2025): 27178–86. https://doi.org/10.1609/aaai.v39i25.34926.

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This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency. The first strategy is a grid-based divide-and-conquer procedure that partitions the TSP into smaller sub-problems, solving them in parallel and iteratively refining the solution by merging nodes and partial routes. The process continues until only one grid remains, yielding a high-quality initial solution. The second strategy involves a path-based divide-and-o
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12

Zeybek, Sultan, Asrul Harun Ismail, Natalia Hartono, Mario Caterino, and Kaiwen Jiang. "An Improved Vantage Point Bees Algorithm to Solve Combinatorial Optimization Problems from TSPLIB." Macromolecular Symposia 396, no. 1 (2021): 2000299. http://dx.doi.org/10.1002/masy.202000299.

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13

El Afia, Abdellatif, Safae Bouzbita, and Rdouan Faizi. "The Effect of Updating the Local Pheromone on ACS Performance using Fuzzy Logic." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 4 (2017): 2161. http://dx.doi.org/10.11591/ijece.v7i4.pp2161-2168.

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Fuzzy Logic Controller (FLC) has become one of the most frequently utilised algorithms to adapt the metaheuristics parameters as an artificial intelligence technique. In this paper, the 𝜉 parameter of Ant Colony System (ACS) algorithm is adapted by the use of FLC, and its behaviour is studied during this adaptation. The proposed approach is compared with the standard ACS algorithm. Computational results are done based on a library of sample instances for the Traveling Salesman Problem (TSPLIB).
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Abdellatif, El Afia, Bouzbita Safae, and Faizi Rdouan. "The Effect of Updating the Local Pheromone on ACS Performance using Fuzzy Logic." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 4 (2017): 2161–68. https://doi.org/10.11591/ijece.v7i4.pp2161-2168.

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Fuzzy Logic Controller (FLC) has become one of the most frequently utilised algorithms to adapt the metaheuristics parameters as an artificial intelligence technique. In this paper, the 𝜉 parameter of Ant Colony System (ACS) algorithm is adapted by the use of FLC, and its behaviour is studied during this adaptation. The proposed approach is compared with the standard ACS algorithm. Computational results are done based on a library of sample instances for the Traveling Salesman Problem (TSPLIB).
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15

Li, Wei Hua, Wei Jia Li, Yuan Yang, Hai Qiang Liao, Ji Long Li, and Xi Peng Zheng. "Artificial Bee Colony Algorithm for Traveling Salesman Problem." Advanced Materials Research 314-316 (August 2011): 2191–96. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.2191.

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By combining the modified nearest neighbor approach and the improved inver-over operation, an Artificial Bee Colony (ABC) Algorithm for Traveling Salesman Problem (TSP) is proposed in this paper. The heuristic approach was tested in some benchmark instances selected from TSPLIB. In addition, a comparison study between the proposed algorithm and the Bee Colony Optimization (BCO) model is presented. Experimental results show that the presented algorithm outperforms the BCO method and can efficiently tackle the small and medium scale TSP instances.
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16

Sawik, T. "A note on the Miller-Tucker-Zemlin model for the asymmetric traveling salesman problem." Bulletin of the Polish Academy of Sciences Technical Sciences 64, no. 3 (2016): 517–20. http://dx.doi.org/10.1515/bpasts-2016-0057.

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Abstract An enhancement of the Miller-Tucker-Zemlin (MTZ) model for the asymmetric traveling salesman problem is presented by introducing additional constraints to the initial formulation. The constraints account for ordering of boundary nodes as well as all successive nodes in the salesman tour. The enhanced MTZ subtour elimination constraints are computationally compared with the basic MTZ constraints and the version of MTZ lifted by Desrochers and Laporte. The proposed enhancement shows improved performance on a number of asymmetric TSPLIB instances.
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17

Zheng, Jiongzhi, Kun He, Jianrong Zhou, Yan Jin, and Chu-Min Li. "Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 14 (2021): 12445–52. http://dx.doi.org/10.1609/aaai.v35i14.17476.

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We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent per
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18

Cui, Fang Song, Wei Feng, Da Zhi Pan, Guo Zhong Cheng, and Shuang Yang. "An Improved and Realized Volatility Strategy of the Ant Colony Optimization Algorithm." Applied Mechanics and Materials 389 (August 2013): 849–53. http://dx.doi.org/10.4028/www.scientific.net/amm.389.849.

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In order to overcome the shortcomings of precocity and stagnation in ant colony optimization algorithm, an improved algorithm is presented. Considering the impact that the distance between cities on volatility coefficient, this study presents an model of adjusting volatility coefficient called Volatility Model based on ant colony optimization (ACO) and Max-Min ant system. There are simulation experiments about TSP cases in TSPLIB, the results show that the improved algorithm effectively overcomes the shortcoming of easily getting an local optimal solution, and the average solutions are superio
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19

Nababan, Erna Budhiarti, Opim Salim Sitompul, and Yuni Cancer. "Genetic Algorithms Dynamic Population Size with Cloning in Solving Traveling Salesman Problem." Data Science: Journal of Computing and Applied Informatics 2, no. 2 (2018): 87–100. http://dx.doi.org/10.32734/jocai.v2.i2-326.

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Population size of classical genetic algorithm is determined constantly. Its size remains constant over the run. For more complex problems, larger population sizes need to be avoided from early convergence to produce local optimum. Objective of this research is to evaluate population resizing i.e. dynamic population sizing for Genetic Algorithm (GA) using cloning strategy. We compare performance of proposed method and traditional GA employed to Travelling Salesman Problem (TSP) of A280.tsp taken from TSPLIB. Result shown that GA with dynamic population size exceed computational time of traditi
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20

Zakharov, Aleksey O., and Yulia V. Zakharova. "On Investigation of Crisp Bi-Objective Formulations for Fuzzy Traveling Salesman Problem and Fuzzy p-Median Problem." Journal of Physics: Conference Series 2182, no. 1 (2022): 012043. http://dx.doi.org/10.1088/1742-6596/2182/1/012043.

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Abstract We consider two classic problems: the Traveling Salesman Problem and the p-Median Problem. In both problems the total traveling cost (in some sense) is minimized, assuming that all traveling times are known. In most real-word applications the input data are uncertain, and this fact should be taken into account when a solution is constructed. In this paper we investigate bi-objective versions of the problems, where the total cost and fuzzy uncertainty associated with the traveling times (membership function) are optimized. A greedy approximation algorithm is proposed and experimentally
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21

Alaidi, A. H., C. Soong Der, and Y. Weng Leong. "Increased Efficiency of the Artificial Bee Colony Algorithm Using the Pheromone Technique." Engineering, Technology & Applied Science Research 12, no. 6 (2022): 9732–36. http://dx.doi.org/10.48084/etasr.5305.

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Artificial Bee Colony (ABC) is a powerful metaheuristic algorithm inspired by the behavior of a honey bee swarm. ABC suffers from poor exploitation and, in some cases, poor exploration. Ant Colony Optimization (ACO) is another metaheuristic algorithm that uses pheromones as a guide for an ant to find its way. This study used a pheromone technique from ACO on ABC to enhance its exploration and exploitation. The performance of the proposed method was verified through twenty instances from TSPLIB. The results were compared with the original ABC method and showed that the proposed method leverages
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22

Alaidi, A. H., S. D. Chen, and Υ. Weng Leong. "Artificial Bee Colony with Crossover Operations for Discrete Problems." Engineering, Technology & Applied Science Research 12, no. 6 (2022): 9510–14. http://dx.doi.org/10.48084/etasr.5250.

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The Artificial Bee Colony (ABC) is an algorithm designed to solve continuous problems. ABC has been proven to be more effective than other biological-inspired algorithms. However, it is needed to modify its functionality in order to solve a discrete problem. In this work, a natural modification to the original ABC is made to make it able to solve discrete problems. Six neighborhood operators are proposed to simulate the original behavior of ABC. Moreover, several Traveling Salesman Problem Library (TSPLIB) problems were used to examine the proposed method. The results of the proposed method ar
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Akhmet-Sultan, Alatau, Ayan Aksha, Abzal Myrzash, Nazerke Raimberdiyeva, Nazerke Kazhdenbekova, and Gulnur Ibragim. "BRIEF REVIEW OF 20TH CENTURY IN DEVELOPMENT AND ACCESSIBILITY OF TRAVELLING SALESMAN PROBLEM AND TSPLIB." Theoretical & Applied Science 120, no. 04 (2023): 130–36. http://dx.doi.org/10.15863/tas.2023.04.120.23.

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Huo, Li, Bo Jiang, and Tao Ning. "A New Algorithm for Solving TSP and its Applications." Applied Mechanics and Materials 713-715 (January 2015): 1504–8. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1504.

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A new algorithm for TSP which is an improved ACO combined with MMAS and CSDT is proposed. MMAS can prevent the search from local optimum and search stagnation. We use candidate set strategy based on the Delaunay triangle (CSDT) in order to reduce serch space and accelerate the speed of the algorithm. Additionally, pheromone update and parameter optimization are detailed in this paper. The comparison analysis of the new algorithm, basic ant colony algorithm and MMAS algorithm is also given by using TSPLIB experimental data. Finally, we give an actual TSP case and compute the optimum solution by
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Twaróg, Sebastian, Jacek Szołtysek, Krzysztof Szwarc, and Urszula Boryczka. "Probabilistic Traveling Salesman Problem and Harmony Search Algorithms in Pharmacy Supply Optimization." Acta Universitatis Lodziensis. Folia Oeconomica 6, no. 345 (2019): 111–25. http://dx.doi.org/10.18778/0208-6018.345.06.

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This paper demonstrates the utilitarian significance of the Probabilistic Traveling Salesman Problem (PTSP) in planning travel routes by companies which provide distribution services for pharmacies, with a particular consideration of variable customer demand. The optimization problem was solved using the Harmony Search (HS) algorithm, thus verifying its utility based on one real instance of PTSP (representing the problem of pharmacy supply reliability) and three tasks from the public TSPLIB library (adjusted to PTSP). As a result of the conducted research, significant utility of the hybrid app
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Bian, Jinhua, and Xiaoxia Zhang. "A Hill-Climbing Differential Evolutionary Algorithm for solving Multiple Travelling Salesman Problem." Frontiers in Computing and Intelligent Systems 9, no. 2 (2024): 4–7. http://dx.doi.org/10.54097/fm6hta13.

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The Multiple Travelling Salesman Problem (MTSP) is a basic deformation of the Travelling Salesman Problem (TSP), which is a typical NP-Hard problem. For combinatorial optimization problems shaped like MTSP, researchers often use intelligent optimization algorithms such as genetic algorithms, differential evolutionary algorithms, simulated annealing algorithms and other intelligent optimization algorithms to approximate the solution. However, typical intelligent optimization algorithms have the disadvantage of being prone to local convergence and failing to produce theoretically optimal solutio
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Hao, Tan, Wu Yingnian, Zhang Jiaxing, and Zhang Jing. "Study on a hybrid algorithm combining enhanced ant colony optimization and double improved simulated annealing via clustering in the Traveling Salesman Problem (TSP)." PeerJ Computer Science 9 (October 2, 2023): e1609. http://dx.doi.org/10.7717/peerj-cs.1609.

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In the process of solving the Traveling Salesman Problem (TSP), both Ant Colony Optimization and simulated annealing exhibit different limitations depending on the dataset. This article aims to address these limitations by improving and combining these two algorithms using the clustering method. The problems tackled include Ant Colony Optimization’s susceptibility to stagnation, slow convergence, excessive computations, and local optima, as well as simulated annealing’s slow convergence and limited local search capability. By conducting tests on various TSPLIB datasets, the algorithm proposed
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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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Akshay, Vyas *1 Dashmeet Kaur Chawla 2. Anuj Bhai Mehta3 Abhishek Chelawat4 Dr. Urjita Thakar5. "GENETIC ALGORITHM FOR SOLVING THE TRAVELING SALESMAN PROBLEM USING NEIGHBOR-BASED CONSTRUCTIVE CROSSOVER OPERATOR." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 4 (2018): 101–10. https://doi.org/10.5281/zenodo.1401725.

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In this paper, a new crossover operator named Neighbor-based Constructive Crossover (NCX) is evolved for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The proposed crossover operator uses the better edges present in parents’ structure by comparing the neighboring nodes of a node in order to generate off-springs. The efficacy of the proposed crossover operator, NCX is set against two other crossover operators, single point crossover (SPCX) [19] and sequential constructive crossover (SCX) [1] for several standard TSPLIB instances [2]. Em
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ASMAA, HEKAL OMAR, and AHMED NAIM AMANY. "NEW CROSSOVER VIA HYBRID ANT COLONY SYSTEM WITH GENETIC ALGORITHM AND MAKING STUDY OF DIFFERENT CROSSOVER FOR TSP." Journal of Theoretical and Applied Information Technology 99, no. 20 (2021): 4824–36. https://doi.org/10.5281/zenodo.6870621.

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The traveling salesman problem (TSP) is a very famous NP-hard problem in computer science and operations research. In this study, proposed a new hybrid crossover (SPMX) combining the shuffle crossover and partially mapping crossover which served to develop Genetic algorithm (GA) to solve this problem since crossover is the main component of GA. And, apply the proposed SPMX on hybrid ant colony system with GA with Ant colony system (ACS), which called by (ACSGA) to solve TSP. Experimental results on some well-known TSPLIB instances of different types and sizes. The obtained comparative study cl
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Zhang, Jin, Li Hong, and Qing Liu. "An Improved Whale Optimization Algorithm for the Traveling Salesman Problem." Symmetry 13, no. 1 (2020): 48. http://dx.doi.org/10.3390/sym13010048.

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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
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Ahmed, Zakir Hussain. "A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem." Mathematical Problems in Engineering 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/750968.

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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 alg
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Li, Juan, and Ting Zhang. "The Kalman Filter Cuckoo Search Algorithm to Solve the TSP Problem." Applied Mechanics and Materials 733 (February 2015): 918–21. http://dx.doi.org/10.4028/www.scientific.net/amm.733.918.

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TSP problem optimization is a combinatorial optimization model studied which is NP hard, and it has been solved by a lot of algorithms. A new improved cuckoo optimization algorithm (KF-CS) has been put forward to solve the routing optimization problem of logistics distribution vehicle. Kalman Filter Cuckoo search (KF-CS) is a new intelligent algorithm which used to estimate the state of a stochastic phenomenon which has Gaussian distribution. The problem of travelling salesman was experimented. To demonstrate the effectiveness and efficiency of the proposed algorithm, the benchmark problems fr
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Hartono, Natalia, Hamid Furkan Suluova, Fatih Mehmet Eker, Sultan Zeybek, and Mario Caterino. "Comparative Study of Reduced Parameter Versions of the Bees Algorithm for Traveling Salesman Problem." Journal of Integrated System 7, no. 1 (2024): 1–12. http://dx.doi.org/10.28932/jis.v7i1.8602.

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Metaheuristics have shown dominance over exact methods with their capability to find near-optimal solutions to complex problems in a shorter time. Among these metaheuristics, the Bees Algorithm (BA) has proven its performance in various applications. However, fine-tuning the parameters of the BA is challenging due to its numerous parameters. There have been few studies aiming to reduce the number of parameters while maintaining or improving performance, such as the ternary BA, two-parameter BA, and Fibonacci BA. This paper reviews these variants for combinatorial problems using 13 datasets fro
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Tsai, Cheng-Hsiung, Yu-Da Lin, Cheng-Hong Yang, Chien-Kun Wang, Li-Chun Chiang, and Po-Jui Chiang. "A Biogeography-Based Optimization with a Greedy Randomized Adaptive Search Procedure and the 2-Opt Algorithm for the Traveling Salesman Problem." Sustainability 15, no. 6 (2023): 5111. http://dx.doi.org/10.3390/su15065111.

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We develop a novel method to improve biogeography-based optimization (BBO) for solving the traveling salesman problem (TSP). The improved method is comprised of a greedy randomized adaptive search procedure, the 2-opt algorithm, and G2BBO. The G2BBO formulation is derived and the process flowchart is shown in this article. For solving TSP, G2BBO effectively avoids the local minimum problem and accelerates convergence by optimizing the initial values. To demonstrate, we adopt three public datasets (eil51, eil76, and kroa100) from TSPLIB and compare them with various well-known algorithms. The r
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Jiang, Yuan, Yaoxin Wu, Zhiguang Cao, and Jie Zhang. "Learning to Solve Routing Problems via Distributionally Robust Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (2022): 9786–94. http://dx.doi.org/10.1609/aaai.v36i9.21214.

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Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust optimization (group DRO) to tackle this issue, where we jointly optimize the weights for different groups of distributions and the parameters for the deep model in an interleaved manner during training. We also design a module based on convolutional neural network, which allows the deep model to learn more informative latent pattern among the nodes. We evaluate t
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Mzili, Toufik, Ilyass Mzili, and Mohammed Essaid Riffi. "Artificial rat optimization with decision-making: A bio-inspired metaheuristic algorithm for solving the traveling salesman problem." Decision Making: Applications in Management and Engineering 6, no. 2 (2023): 150–76. http://dx.doi.org/10.31181/dmame622023644.

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In this paper, we present the Rat Swarm Optimization with Decision Making (HDRSO), a hybrid metaheuristic algorithm inspired by the hunting behavior of rats, for solving the Traveling Salesman Problem (TSP). The TSP is a well-known NP-hard combinatorial optimization problem with important applications in transportation, logistics, and manufacturing systems. To improve the search process and avoid getting stuck in local minima, we added a natural mechanism to HDRSO through the incorporation of crossover and selection operators. In addition, we applied 2-opt and 3-opt heuristics to the best solu
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Fayçal, Chebihi, Essaid Riffi Mohammed, Agharghor Amine, Cherif Bourki Semlali Soukaina, and Haily Abdelfattah. "Improved Chicken Swarm Optimization Algorithm to Solve the Travelling Salesman Problem." Indonesian Journal of Electrical Engineering and Computer Science 12, no. 3 (2018): 1054–62. https://doi.org/10.11591/ijeecs.v12.i3.pp1054-1062.

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This paper proposes a novel discrete bio-inspired chicken swarm optimization algorithm (CSO) to solve the problem of the traveling salesman problem (TSP) which is one of the most known problems used to evaluate the performance of the new metaheuristics. This problem is solved by applying a local search method 2-opt in order to improve the quality of the solutions. The DCSO as a swarm system of the algorithm increases the level of diversification, in the same way the hierarchical order of the chicken swarm and the behaviors of chickens increase the level of intensification. In this contribution
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39

Wei, Bo, Ying Xing, Xuewen Xia, and Ling Gui. "A Novel Particle Swarm Optimization With Genetic Operator and Its Application to TSP." International Journal of Cognitive Informatics and Natural Intelligence 15, no. 4 (2021): 1–17. http://dx.doi.org/10.4018/ijcini.20211001.oa31.

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To solve some problems of particle swarm optimization, such as the premature convergence and falling into a sub-optimal solution easily, we introduce the probability initialization strategy and genetic operator into the particle swarm optimization algorithm. Based on the hybrid strategies, we propose a improved hybrid particle swarm optimization, namely IHPSO, for solving the traveling salesman problem. In the IHPSO algorithm, the probability strategy is utilized into population initialization. It can save much more computing resources during the iteration procedure of the algorithm. Furthermo
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40

Lancia, Giuseppe, and Marcello Dalpasso. "Finding the Best 3-OPT Move in Subcubic Time." Algorithms 13, no. 11 (2020): 306. http://dx.doi.org/10.3390/a13110306.

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Given a Traveling Salesman Problem solution, the best 3-OPT move requires us to remove three edges and replace them with three new ones so as to shorten the tour as much as possible. No worst-case algorithm better than the Θ(n3) enumeration of all triples is likely to exist for this problem, but algorithms with average case O(n3−ϵ) are not ruled out. In this paper we describe a strategy for 3-OPT optimization which can find the best move by looking only at a fraction of all possible moves. We extend our approach also to some other types of cubic moves, such as some special 6-OPT and 5-OPT move
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41

Wang, Yong. "A quick method to compute sparse graphs for traveling salesman problem using random frequency quadrilaterals." Filomat 32, no. 5 (2018): 1697–702. http://dx.doi.org/10.2298/fil1805697w.

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Traveling salesman problem (TSP) is extensively studied in combinatorial optimization and computer science. This paper gives a quick method to compute the sparse graphs for TSP based on the random frequency quadrilaterals so as to reduce the TSP on the complete graph to the TSP on the sparse graphs. When we choose N frequency quadrilaterals containing an edge e to compute its total frequency, the frequency of e in the optimal Hamiltonian cycle will be bigger than that of most of the other edges. We fix N to compute the frequency of each edge and the computation time of the quick method is O(n2
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42

Deng, Yong, Yang Liu, and Deyun Zhou. "An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/212794.

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A new initial population strategy has been developed to improve the genetic algorithm for solving the well-known combinatorial optimization problem, traveling salesman problem. Based on thek-means algorithm, we propose a strategy to restructure the traveling route by reconnecting each cluster. The clusters, which randomly disconnect a link to connect its neighbors, have been ranked in advance according to the distance among cluster centers, so that the initial population can be composed of the random traveling routes. This process isk-means initial population strategy. To test the performance
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43

Hussain, Abid, Yousaf Shad Muhammad, M. Nauman Sajid, Ijaz Hussain, Alaa Mohamd Shoukry, and Showkat Gani. "Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator." Computational Intelligence and Neuroscience 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/7430125.

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Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we
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44

Chebihi, Fayçal, Mohammed essaid Riffi, Amine Agharghor, Soukaina Cherif Bourki Semlali, and Abdelfattah Haily. "Improved Chicken Swarm Optimization Algorithm to Solve the Travelling Salesman Problem." Indonesian Journal of Electrical Engineering and Computer Science 12, no. 3 (2018): 1054. http://dx.doi.org/10.11591/ijeecs.v12.i3.pp1054-1062.

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<p>This paper proposes a novel discrete bio-inspired chicken swarm optimization algorithm (CSO) to solve the problem of the traveling salesman problem (TSP) which is one of the most known problems used to evaluate the performance of the new metaheuristics. This problem is solved by applying a local search method 2-opt in order to improve the quality of the solutions. The DCSO as a swarm system of the algorithm increases the level of diversification, in the same way the hierarchical order of the chicken swarm and the behaviors of chickens increase the level of intensification. In this con
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45

Weise, Thomas, Yan Jiang, Qi Qi, and Weichen Liu. "A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem." International Journal of Cognitive Informatics and Natural Intelligence 13, no. 3 (2019): 1–18. http://dx.doi.org/10.4018/ijcini.2019070101.

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In this article, the new crossover operator BBX for Evolutionary Algorithms (EAs) for traveling salesman problems (TSPs) is introduced. It uses branch-and-bound to find the optimal combination of the (directed) edges present in the parent solutions. The offspring solutions created are at least as good as their parents and are only composed of parental building blocks. The operator is closer to the ideal concept of crossover in EAs than existing operators. This article provides the most extensive study on crossover operators on the TSP, comparing BBX to ten other operators on the 110 instances
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46

LÓPEZ, ERASMO, and ENRIQUE VÍLCHEZ. "MÉTODO DE BÚSQUEDA TABÚ PARA OPTIMIZACIÓN COMBINATORIA APOYADO CON EL SOFTWARE WOLFRAM MATHEMATICA." Revista de Matemática: Teoría y Aplicaciones 26, no. 1 (2019): 99–114. http://dx.doi.org/10.15517/rmta.v26i1.36225.

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En este trabajo se presentan los resultados obtenidos de un algoritmo basado en la Búsqueda Tabú que fue programado utilizando el software comercial Wolfram Mathematica. En Wolfram Language se realizaron distintas implementaciones de instancias aleatorias y otras disponibles en la biblioteca TSPLIB, comparándolas posteriormente con los resultados provistos del mismo algoritmo en el ambiente de programación Visual Basic 6.0. Las mejoras que se obtuvieron obedecen a la estructuración de funciones prediseñadas que permitieron analizar específicamente dos aspectos: la optimización de la solución y
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47

Fosin, Juraj, Davor Davidović, and Tonči Carić. "A GPU Implementation of Local Search Operators for Symmetric Travelling Salesman Problem." PROMET - Traffic&Transportation 25, no. 3 (2013): 225–34. http://dx.doi.org/10.7307/ptt.v25i3.300.

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The Travelling Salesman Problem (TSP) is one of the most studied combinatorial optimization problem which is significant in many practical applications in transportation problems. The TSP problem is NP-hard problem and requires large computation power to be solved by the exact algorithms. In the past few years, fast development of general-purpose Graphics Processing Units (GPUs) has brought huge improvement in decreasing the applications’ execution time. In this paper, we implement 2-opt and 3-opt local search operators for solving the TSP on the GPU using CUDA. The novelty presented in this p
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48

Saud, Suhair, Halife Kodaz, and İsmail Babaoğlu. "Solving Travelling Salesman Problem by Using Optimization Algorithms." KnE Social Sciences 3, no. 1 (2018): 17. http://dx.doi.org/10.18502/kss.v3i1.1394.

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This paper presents the performances of different types of optimization techniques used in artificial intelligence (AI), these are Ant Colony Optimization (ACO), Improved Particle Swarm Optimization with a new operator (IPSO), Shuffled Frog Leaping Algorithms (SFLA) and modified shuffled frog leaping algorithm by using a crossover and mutation operators. They were used to solve the traveling salesman problem (TSP) which is one of the popular and classical route planning problems of research and it is considered as one of the widely known of combinatorial optimization. Combinatorial optimizatio
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Eldem, Hüseyin, and Erkan Ülker. "A Hierarchical Approach Based on ACO and PSO by Neighborhood Operators for TSPs Solution." International Journal of Pattern Recognition and Artificial Intelligence 34, no. 11 (2020): 2059039. http://dx.doi.org/10.1142/s0218001420590399.

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It is known that some of the algorithms in optimization field have originated from inspiration from animal behaviors in nature. Natural phenomena such as searching behavior of ants for food in a collective way, movements of birds and fish groups as swarms provided the inspiration for solutions of optimization problems. Traveling Salesman Problem (TSP), a classical problem of combinatorial optimization, has implementations in planning, scheduling and various scientific and engineering fields. Ant colony optimization (ACO) and Particle swarm optimization (PSO) techniques have been commonly used
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50

Sakiyama, Tomoko, and Ikuo Arizono. "Can the Agent with Limited Information Solve Travelling Salesman Problem?" Complexity 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/9562125.

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Here, we develop new heuristic algorithm for solving TSP (Travelling Salesman Problem). In our proposed algorithm, the agent cannot estimate tour lengths but detect only a few neighbor sites. Under the circumstances, the agent occasionally ignores the NN method (choosing the nearest site from current site) and chooses the other site far from current site. It is dependent on relative distances between the nearest site and the other site. Our algorithm performs well in symmetric TSP and asymmetric TSP (time-dependent TSP) conditions compared with the NN algorithm using some TSP benchmark dataset
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