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.

scholarly journals Comparative Solutions of Exact and Approximate Methods for Traveling Salesman Problem

Lámpsakos ◽  
2021 ◽  
pp. 3804
Author(s):  
Agung Chandra ◽  
Christine Natalia ◽  
Aulia Naro
Keyword(s):  
Approximate Method ◽  
Traveling Salesman Problem ◽  
Fruit Fly ◽  
Optimization Methods ◽  
Traveling Salesman ◽  
Exact Method ◽  
Fruit Fly Optimization Algorithm ◽  
Approximate Methods ◽  
Fruit Fly Optimization ◽  
Exact And Approximate Methods

There are two major optimization methods: Exact and Approximate methods. A well known exact method, Branch and Bound algorithm (B&B) and approximate methods, Elimination-based Fruit Fly Optimization Algorithm (EFOA) and Artificial Atom Algorithm (A3) are used for solving the Traveling Salesman Problem (TSP). For 56 destinations, the results of total distance, processing time, and the deviation between exact and approximate method will be compared where the distance between two destinations is a Euclidean distance and this study shows that the distance of B&B is 270 , EFOA is 270 and A3 is 288.38 which deviates 6.81%. For time processing aspect, B&B needs 12.5 days to process, EFOA needs 36.59 seconds, A3 needs 35.34 seconds. But for 29 destinations, exact method is more powerful than approximate method.

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.

scholarly journals Solving the Traveling Salesman Problem on the D-Wave Quantum Computer

2021 ◽  
Vol 9 ◽  
Author(s):  
Siddharth Jain
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Quantum Computer ◽  
Traveling Salesman ◽  
Hard Problem ◽  
Problem Size ◽  
Quadratic Unconstrained Binary Optimization ◽  
Np Hard Problem ◽  
The Traveling Salesman Problem ◽  
D Wave

The traveling salesman problem is a well-known NP-hard problem in combinatorial optimization. This paper shows how to solve it on an Ising Hamiltonian based quantum annealer by casting it as a quadratic unconstrained binary optimization (QUBO) problem. Results of practical experiments are also presented using D-Wave’s 5,000 qubit Advantage 1.1 quantum annealer and the performance is compared to a classical solver. It is found the quantum annealer can only handle a problem size of 8 or less nodes and its performance is subpar compared to the classical solver both in terms of time and accuracy.

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 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.

BEE COLONY OPTIMIZATION WITH LOCAL SEARCH FOR TRAVELING SALESMAN PROBLEM

2010 ◽  
Vol 19 (03) ◽  
pp. 305-334 ◽  
Author(s):  
LI-PEI WONG ◽  
MALCOLM YOKE HEAN LOW ◽  
CHIN SOON CHONG
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Path ◽  
Industrial Applications ◽  
Traveling Salesman ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Routing Problem ◽  
Bee Colony ◽  
Pruning Strategy ◽  
Bee Colony Optimization

Many real world industrial applications involve the Traveling Salesman Problem (TSP), which is a problem that finds a Hamiltonian path with minimum cost. Examples of problems that belong to this category are transportation routing problem, scan chain optimization and drilling problem in integrated circuit testing and production. This paper presents a Bee Colony Optimization (BCO) algorithm for symmetrical TSP. The BCO model is constructed algorithmically based on the collective intelligence shown in bee foraging behaviour. The algorithm is integrated with a fixed-radius near neighbour 2-opt (FRNN 2-opt) heuristic to further improve prior solutions generated by the BCO model. To limit the overhead incurred by the FRNN 2-opt, a frequency-based pruning strategy is proposed. The pruning strategy allows only a subset of the promising solutions to undergo local optimization. Experimental results comparing the proposed BCO algorithm with existing approaches on a set of benchmark problems are presented. For 84 benchmark problems, the BCO algorithm is able to obtain an overall average solution quality of 0.31% from known optimum. The results also show that it is comparable to other algorithms such as Ant Colony Optimization and Particle Swarm Optimization.

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