Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

Optimization Problems ◽

Minimum Cost ◽

Pso Algorithm ◽

Traveling Salesman ◽

Local Search Algorithms ◽

Engineering Sciences ◽

The traveling salesman problem (TSP) is one of the most important issues in combinatorial optimization problems that are used in many engineering sciences and has attracted the attention of many scientists and researchers. In this issue, a salesman starts to move from a desired node called warehouse and returns to the starting place after meeting n customers provided that each customer is only met once. The aim of this issue is to determine a cycle with a minimum cost for this salesman. One of the major weaknesses of the PSO algorithm in the classical version is that it gets stuck in local optimizations. Therefore, in the proposed algorithm, called MPSO, the best solution in the current iteration is also used in the movement step. In addition, a variety of local search algorithms are provided that are used when better answers are generated than before. Also, a new method for moving the particle towards the best particle is presented, which, in addition to probably increasing the quality of the new answer, prevents the premature convergence of the algorithm due to consideration of the concept of random. The results evaluated with the results of several metaheuristic algorithms in the literature show the efficiency of the MPSO algorithm because it has been able to achieve excellent solutions in most of these instances.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

International Journal of Strategic Decision Sciences ◽

10.4018/jsds.2010040104 ◽

2010 ◽

Vol 1 (2) ◽

pp. 82-92 ◽

Cited By ~ 2

Author(s):

Gilbert Laporte

Keyword(s):

Vehicle Routing ◽

Vehicle Routing Problem ◽

Heuristic Algorithms ◽

Optimization Problems ◽

Traveling Salesman ◽

Routing Problem ◽

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

Microcanonical Optimization Applied to the Traveling Salesman Problem

International Journal of Modern Physics C ◽

10.1142/s012918319800011x ◽

1998 ◽

Vol 09 (01) ◽

pp. 133-146 ◽

Cited By ~ 8

Author(s):

Alexandre Linhares ◽

José R. A. Torreão

Keyword(s):

Simulated Annealing ◽

Optimization Problems ◽

Search Algorithm ◽

New Physics ◽

Traveling Salesman ◽

Tabu Search Algorithm ◽

Microcanonical Annealing ◽

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms μO as a competitive approach for the solution of general combinatorial optimization problems.

Research on MPI-Based Parallel Max-Min Ant System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.198-199.1321 ◽

2012 ◽

Vol 198-199 ◽

pp. 1321-1326 ◽

Cited By ~ 1

Author(s):

Yu Liu ◽

Guo Dong Wu

Keyword(s):

Numerical Experiments ◽

Large Scale ◽

Optimization Problems ◽

Computation Time ◽

Traveling Salesman ◽

Ant System ◽

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

An exact -constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits

European Journal of Operational Research ◽

10.1016/j.ejor.2007.12.014 ◽

2009 ◽

Vol 194 (1) ◽

pp. 39-50 ◽

Cited By ~ 193

Author(s):

Jean-François Bérubé ◽

Michel Gendreau ◽

Jean-Yves Potvin

Keyword(s):

Optimization Problems ◽

Traveling Salesman ◽

The Traveling Salesman Problem ◽

Exact Constraint ◽

Constraint Method

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

Mathematics ◽

10.3390/math8101650 ◽

2020 ◽

Vol 8 (10) ◽

pp. 1650

Author(s):

Zhaojun Zhang ◽

Zhaoxiong Xu ◽

Shengyang Luan ◽

Xuanyu Li ◽

Yifei Sun

Keyword(s):

Ant Colony Optimization ◽

Optimization Algorithm ◽

Optimization Problems ◽

Traveling Salesman ◽

Ant Colony ◽

Ant Colony Optimization Algorithm ◽

Opposition Based Learning ◽

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.

Reinforcement learning for the traveling salesman problem with refueling

Complex & Intelligent Systems ◽

10.1007/s40747-021-00444-4 ◽

2021 ◽

Author(s):

André L. C. Ottoni ◽

Erivelton G. Nepomuceno ◽

Marcos S. de Oliveira ◽

Daniela C. R. de Oliveira

Keyword(s):

Reinforcement Learning ◽

Optimization Problems ◽

Autonomous Vehicle ◽

Route Planning ◽

Potential Method ◽

Traveling Salesman ◽

Q Learning ◽

AbstractThe traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Many methods derived from TSP have been applied to study autonomous vehicle route planning with fuel constraints. Nevertheless, less attention has been paid to reinforcement learning (RL) as a potential method to solve refueling problems. This paper employs RL to solve the traveling salesman problem With refueling (TSPWR). The technique proposes a model (actions, states, reinforcements) and RL-TSPWR algorithm. Focus is given on the analysis of RL parameters and on the refueling influence in route learning optimization of fuel cost. Two RL algorithms: Q-learning and SARSA are compared. In addition, RL parameter estimation is performed by Response Surface Methodology, Analysis of Variance and Tukey Test. The proposed method achieves the best solution in 15 out of 16 case studies.

Branch and Bound Algorithm for the Traveling Salesman Problem is not a Direct Type Algorithm

Modeling and Analysis of Information Systems ◽

10.18255/1818-1015-2020-1-72-85 ◽

2020 ◽

Vol 27 (1) ◽

pp. 72-85

Author(s):

Aleksandr N. Maksimenko

Keyword(s):

Branch And Bound ◽

Optimization Problems ◽

Clique Number ◽

Traveling Salesman ◽

Branch And Bound Algorithm ◽

Type Algorithm ◽

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. us, the class of direct type algorithms is not so wide as previously assumed.

PARALLEL TEMPERING FOR THE TRAVELING SALESMAN PROBLEM

International Journal of Modern Physics C ◽

10.1142/s0129183109013893 ◽

2009 ◽

Vol 20 (04) ◽

pp. 539-556 ◽

Cited By ~ 7

Author(s):

CHIAMING WANG ◽

JEFFREY D. HYMAN ◽

ALLON PERCUS ◽

RUSSEL CAFLISCH

Keyword(s):

Simulated Annealing ◽

Minimum Distance ◽

Optimization Problems ◽

Optimization Method ◽

Traveling Salesman ◽

Parallel Tempering ◽

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.

Orthogonal Genetic Algorithm and its Application in Traveling Salesman Problem

Advanced Engineering Forum ◽

10.4028/www.scientific.net/aef.6-7.290 ◽

2012 ◽

Vol 6-7 ◽

pp. 290-293

Author(s):

Han Min Liu ◽

Qing Hua Wu ◽

Xue Song Yan

Keyword(s):

Genetic Algorithm ◽

Local Minimum ◽

Optimization Problems ◽

Orthogonal Test ◽

Traveling Salesman ◽

Crossover Operator ◽

Great Efficiency ◽

The traveling salesman problem (TSP) is one of the most widely studied NP-hard combinatorial optimization problems. Its statement is deceptively simple, and yet it remains one of the most challenging problems and traditional genetic algorithm trapped into the local minimum easily for solving this problem. Therefore, based on a simple genetic algorithm and combine the base ideology of orthogonal test then applied it to the population initialization, crossover operator, as well as the introduction of adaptive orthogonal local search to prevent local convergence to form a new orthogonal genetic algorithm. The new algorithm shows great efficiency in solving TSP with the problem scale under 300 under the experiment results analyze.

An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽

10.3390/sym13010048 ◽

2020 ◽

Vol 13 (1) ◽

pp. 48

Author(s):

Jin Zhang ◽

Li Hong ◽

Qing Liu

Keyword(s):

Optimization Algorithm ◽

Optimization Problems ◽

Relevant Literature ◽

Population Diversity ◽

Traveling Salesman ◽

Whale Optimization Algorithm ◽

Neighborhood Search ◽

Whale Optimization ◽

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.