scholarly journals Computer tools for solving the traveling salesman problem

2020 ◽  
Vol 18 (1) ◽  
pp. 25-39
Author(s):  
Juraj Pekár ◽  
Ivan Brezina ◽  
Jaroslav Kultan ◽  
Iryna Ushakova ◽  
Oleksandr Dorokhov
Keyword(s):  
Mathematical Programming ◽  
Traveling Salesman Problem ◽  
Software Package ◽  
Nearest Neighbor ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Exact Methods ◽  
Computational Point ◽  
The Traveling Salesman Problem

The task of the traveling salesman, which is to find the shortest or least costly circular route, is one of the most common optimization problems that need to be solved in various fields of practice. The article analyzes and demonstrates various methods for solving this problem using a specific example: heuristic (the nearest neighbor method, the most profitable neighbor method), metaheuristic (evolutionary algorithm), methods of mathematical programming. In addition to classic exact methods (which are difficult to use for large-scale tasks based on existing software) and heuristic methods, the article suggests using the innovative features of the commercially available MS Excel software using a meta-heuristic base. To find the optimal solution using exact methods, the Excel (Solver) software package was used, as well as the specialized GAMS software package. Comparison of different approaches to solving the traveling salesman problem using a practical example showed that the use of traditional heuristic approaches (the nearest neighbor method or the most profitable neighbor method) is not difficult from a computational point of view, but does not provide solutions that would be acceptable in modern conditions. The use of MS Excel for solving the problem using the methods of mathematical programming and metaheuristics enabled us to obtain an optimal solution, which led to the conclusion that modern tools are an appropriate addition to solving the traveling salesman problem while maintaining the quality of the solution.

Comparison of Heuristics for Resolving the Traveling Salesman Problem with Information Technology

2014 ◽  
Vol 886 ◽  
pp. 593-597 ◽  
Author(s):  
Wei Gong ◽  
Mei Li
Keyword(s):  
Information Technology ◽  
Traveling Salesman Problem ◽  
Spanning Tree ◽  
Nearest Neighbor ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Problem Class ◽  
The Traveling Salesman Problem ◽  
Random Insertion

Traveling Salesman Problem (Min TSP) is contained in the problem class NPO. It is NP-hard, means there is no efficient way to solve it. People have tried many kinds of algorithms with information technology. Thus in this paper we compare four heuristics, they are nearest neighbor, random insertion, minimum spanning tree and heuristics of Christofides. We dont try to find an optimal solution. We try to find approximated short trips via these heuristics and compare them.

Tree Physiology Optimization in Benchmark Function and Traveling Salesman Problem

2017 ◽  
Vol 28 (5) ◽  
pp. 849-871 ◽  
Author(s):  
A. Hanif Halim ◽  
I. Ismail
Keyword(s):  
Plant Growth ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Optimization Approach ◽  
Metaheuristic Algorithm ◽  
Tree Physiology ◽  
Growth System ◽  
The Traveling Salesman Problem

Abstract Nature has the ability of sustainability and improvisation for better survival. This unique characteristic reflects a pattern of optimization that inspires the computational intelligence toward different scopes of optimization: a nondeterministic optimization approach or a nature-inspired metaheuristic algorithm. To date, there are many metaheuristic algorithms introduced with good promising results and also becoming a powerful method for solving numerous optimization problems. In this paper, a new metaheuristic algorithm inspired from a plant growth system is proposed, which is defined as tree physiology optimization (TPO). A plant growth consists of two main counterparts: plant shoots and roots. Shoots extend to find better sunlight for the photosynthesis process that converts light and water supplied from the roots into energy for plant growth; at the same time, roots elongate in the opposite way in search for water and nutrients for shoot survival. The collaboration from both systems ensures plant sustainability. This idea is transformed into an optimization algorithm: shoots with defined branches find the potential solution with the help of roots variable. The shoots-branches extension enhances the search diversity and the root system amplifying the search via evaluated fitness. To demonstrate its effectiveness, two different classes of problem are evaluated: (1) a continuous benchmark test function compared to particle swarm optimization (PSO) and genetic algorithm (GA) and (2) an NP-hard problem with the traveling salesman problem (TSP) compared to GA and nearest-neighbor (NN) algorithm. The simulation results show that TPO outperforms PSO and GA in all problem characteristics (flat surface and steep-drop with a combination of many local minima and plateau). In the TSP, TPO has a comparable result to GA.

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.

Improved Ant Colony Algorithm for Optimal Solution TSP

2013 ◽  
Vol 765-767 ◽  
pp. 699-702
Author(s):  
Tian Yuan Zhou
Keyword(s):  
Traveling Salesman Problem ◽  
Ant Colony Algorithm ◽  
Search Strategy ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Algorithm Analysis ◽  
Simulation Testing ◽  
The Traveling Salesman Problem ◽  
Improved Ant Colony Algorithm

Based on the ant colony algorithm analysis and research, this paper proposed an improved ant colony algorithm. Through updating pheromone and optimal search strategy, then applied to the Traveling Salesman Problem (TSP), effectively improved the searching capability of the algorithm. Finally through the simulation testing and analysis, verified that the improved ant colony algorithm is effective, and has good performance.

scholarly journals Unconventional GVNS for Solving the Garbage Collection Problem with Time Windows

Technologies ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 61 ◽  
Author(s):  
Christos Papalitsas ◽  
Theodore Andronikos
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Time Windows ◽  
Experimental Information ◽  
Traveling Salesman ◽  
Neighborhood Search ◽  
Np Hard ◽  
The Novel ◽  
Global Positioning ◽  
The Traveling Salesman Problem

GVNS, which stands for General Variable Neighborhood Search, is an established and commonly used metaheuristic for the expeditious solution of optimization problems that belong to the NP-hard class. This paper introduces an expansion of the standard GVNS that borrows principles from quantum computing during the shaking stage. The Traveling Salesman Problem with Time Windows (TSP-TW) is a characteristic NP-hard variation in the standard Traveling Salesman Problem. One can utilize TSP-TW as the basis of Global Positioning System (GPS) modeling and routing. The focus of this work is the study of the possible advantages that the proposed unconventional GVNS may offer to the case of garbage collector trucks GPS. We provide an in-depth presentation of our method accompanied with comprehensive experimental results. The experimental information gathered on a multitude of TSP-TW cases, which are contained in a series of tables, enable us to deduce that the novel GVNS approached introduced here can serve as an effective solution for this sort of geographical problems.

scholarly journals Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming

Information ◽  
2018 ◽  
Vol 10 (1) ◽  
pp. 7 ◽  
Author(s):  
Ai-Hua Zhou ◽  
Li-Peng Zhu ◽  
Bin Hu ◽  
Song Deng ◽  
Yan Song ◽  
...  
Keyword(s):  
Gene Expression ◽  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Heuristic Algorithms ◽  
Gene Expression Programming ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Np Hard Problem ◽  
Convergence Performance ◽  
The Traveling Salesman Problem

The traveling-salesman problem can be regarded as an NP-hard problem. To better solve the best solution, many heuristic algorithms, such as simulated annealing, ant-colony optimization, tabu search, and genetic algorithm, were used. However, these algorithms either are easy to fall into local optimization or have low or poor convergence performance. This paper proposes a new algorithm based on simulated annealing and gene-expression programming to better solve the problem. In the algorithm, we use simulated annealing to increase the diversity of the Gene Expression Programming (GEP) population and improve the ability of global search. The comparative experiments results, using six benchmark instances, show that the proposed algorithm outperforms other well-known heuristic algorithms in terms of the best solution, the worst solution, the running time of the algorithm, the rate of difference between the best solution and the known optimal solution, and the convergent speed of algorithms.

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

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman 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.

scholarly journals PERFORMANCE ANALYSIS OF OPTIMIZATION METHODS FOR SOLVING TRAVELING SALESMAN PROBLEM

2021 ◽  
pp. 69-75
Author(s):  
Chandra Agung ◽  
Natalia Christine
Keyword(s):  
Approximate Method ◽  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Traveling Salesman ◽  
Exact Method ◽  
Problem Size ◽  
Exact Methods ◽  
Approximate Methods ◽  
Bee Colony

The subject of this research is distance and time of several city tour problems which known as traveling salesman problem (tsp). The goal is to find out the gaps of distance and time between two types of optimization methods in traveling salesman problem: exact and approximate. Exact method yields optimal solution but spends more time when the number of cities is increasing and approximate method yields near optimal solution even optimal but spends less time than exact methods. The task in this study is to identify and formulate each algorithm for each method, then to run each algorithm with the same input and to get the research output: total distance, and the last to compare both methods: advantage and limitation.  Methods used are Brute Force (BF) and Branch and Bound (B&B) algorithms which are categorized as exact methods are compared with Artificial Bee Colony (ABC), Tabu Search (TS) and Simulated Annealing (SA) algorithms which are categorized as approximate methods or known as a heuristics method. These three approximate methods are chosen because they are effective algorithms, easy to implement and provide good solutions for combinatorial optimization problems. Exact and approximate algorithms are tested in several sizes of city tour problems: 6, 9, 10, 16, 17, 25, 42, and 58 cities. 17, 42 and 58 cities are derived from tsplib: a library of sample instances for tsp; and others are taken from big cities in Java (West, Central, East) island. All of the algorithms are run by MATLAB program. The results show that exact method is better in time performance for problem size less than 25 cities and both exact and approximate methods yield optimal solution. For problem sizes that have more than 25 cities, approximate method – Artificial Bee Colony (ABC) yields better time which is approximately 37% less than exact and deviates 0.0197% for distance from exact method. The conclusion is to apply exact method for problem size that is less than 25 cities and approximate method for problem size that is more than 25 cities. The gap of time will be increasing between two methods when sample size becomes larger.

Microcanonical Optimization Applied to the Traveling Salesman Problem

1998 ◽  
Vol 09 (01) ◽  
pp. 133-146 ◽  
Author(s):  
Alexandre Linhares ◽  
José R. A. Torreão
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Physics ◽  
Traveling Salesman ◽  
Tabu Search Algorithm ◽  
Combinatorial Optimization Problems ◽  
Microcanonical Annealing ◽  
The Traveling Salesman Problem

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.

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