A Collaborative Neurodynamic Optimization Algorithm Based on Boltzmann Machines for Solving the Traveling Salesman Problem

2021 ◽  
Author(s):  
Hongzong Li ◽  
Jun Wang
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Traveling Salesman ◽  
Boltzmann Machines ◽  
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.

Hierarchical Solution of the Traveling Salesman Problem with Random Dyadic Tilings

2018 ◽  
Vol 17 (01) ◽  
pp. 1850003
Author(s):  
Tamás Kalmár-Nagy ◽  
Bendegúz Dezső Bak
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Numerical Experiments ◽  
Heuristic Approach ◽  
Traveling Salesman ◽  
Benchmark Problem ◽  
Unit Square ◽  
The Traveling Salesman Problem ◽  
American Cities ◽  
Independent Identically Distributed

We propose a hierarchical heuristic approach for solving the Traveling Salesman Problem (TSP) in the unit square. The points are partitioned with a random dyadic tiling and clusters are formed by the points located in the same tile. Each cluster is represented by its geometrical barycenter and a “coarse” TSP solution is calculated for these barycenters. Midpoints are placed at the middle of each edge in the coarse solution. Near-optimal (or optimal) minimum tours are computed for each cluster. The tours are concatenated using the midpoints yielding a solution for the original TSP. The method is tested on random TSPs (independent, identically distributed points in the unit square) up to 10,000 points as well as on a popular benchmark problem (att532 — coordinates of 532 American cities). Our solutions are 8–13% longer than the optimal ones. We also present an optimization algorithm for the partitioning to improve our solutions. This algorithm further reduces the solution errors (by several percent using 1000 iteration steps). The numerical experiments demonstrate the viability of the approach.

scholarly journals Solving Multiple Traveling Salesman Problem by Meerkat Swarm Optimization Algorithm

2019 ◽  
Vol 54 (3) ◽  
Author(s):  
Belal Al-Khateeb ◽  
Mohammed Yousif
Keyword(s):  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Optimization Algorithm ◽  
Real Life ◽  
Traveling Salesman ◽  
Swarm Optimization ◽  
Total Cost ◽  
Life Problems ◽  
Multiple Traveling Salesman Problem ◽  
The Traveling Salesman Problem

Multiple Traveling Salesman Problem (MTSP) is one of various real-life applications, MTSP is the extension of the Traveling Salesman Problem (TSP). TSP focuses on searching of minimum or shortest path (traveling distance) to visit all cities by salesman, while the primary goal of MTSP is to find shortest path for m paths by n salesmen with minimized total cost. Wherever, total cost means the sum of distances of all salesmen. In this work, we proposed metaheuristic algorithm is called Meerkat Swarm Optimization (MSO) algorithm for solving MTSP and guarantee good quality solution in reasonable time for real-life problems. MSO is a metaheuristic optimization algorithm that is derived from the behavior of Meerkat in finding the shortest path. The implementation is done using many dataset from TSPLIB95. The results demonstrate that MSO in most results is better than another results that compared in average cost that means the MSO superior to other results of MTSP.

scholarly journals Opposition-Based Ant Colony Optimization Algorithm for the Traveling Salesman Problem

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1650
Author(s):  
Zhaojun Zhang ◽  
Zhaoxiong Xu ◽  
Shengyang Luan ◽  
Xuanyu Li ◽  
Yifei Sun
Keyword(s):  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Combinatorial Optimization Problems ◽  
Opposition Based Learning ◽  
The Traveling Salesman Problem

Opposition-based learning (OBL) has been widely used to improve many swarm intelligent optimization (SI) algorithms for continuous problems during the past few decades. When the SI optimization algorithms apply OBL to solve discrete problems, the construction and utilization of the opposite solution is the key issue. Ant colony optimization (ACO) generally used to solve combinatorial optimization problems is a kind of classical SI optimization algorithm. Opposition-based ACO which is combined in OBL is proposed to solve the symmetric traveling salesman problem (TSP) in this paper. Two strategies for constructing opposite path by OBL based on solution characteristics of TSP are also proposed. Then, in order to use information of opposite path to improve the performance of ACO, three different strategies, direction, indirection, and random methods, mentioned for pheromone update rules are discussed individually. According to the construction of the inverse solution and the way of using it in pheromone updating, three kinds of improved ant colony algorithms are proposed. To verify the feasibility and effectiveness of strategies, two kinds of ACO algorithms are employed to solve TSP instances. The results demonstrate that the performance of opposition-based ACO is better than that of ACO without OBL.

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