A New Heuristic for Traveling Salesman Problem Based on LCO

2012 ◽  
Author(s):  
Soichiro Yokoyama ◽  
Ikuo Suzuki ◽  
Masahito Yamamoto ◽  
Masashi Furukawa
Keyword(s):  
Traveling Salesman Problem ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Accurate Solution ◽  
Traveling Salesman ◽  
Wide Range ◽  
Benchmark Instances ◽  
Clustering Optimization ◽  
The Traveling Salesman Problem ◽  
Random Insertion

The Traveling Salesman Problem (TSP) is one of the most well known combinatorial optimization problem and has wide range of application. Since the TSP is NP-hard, many heuristics for the TSP have been developed. This study proposes a new heuristic for the TSP based on one of these heuristics named Local Clustering Optimization (LCO). LCO is a metaheuristic proposed by Furukawa at el. to give an accurate solution for large scale problems in a reasonable time. However, conventional LCO-based heuristics for the TSP is not suited to solving asymmetric instances. The proposed method iteratively adopts tour construction heuristics such as nearest neighbor and random insertion to get an accurate solution more efficiently for the both asymmetric and symmetric TSP. The proposed method and other heuristics are applied to benchmark instances from TSPLIB and randomly generated instances. The experiment shows the proposed method is superior to conventional LCO in terms of accuracy of the solution. However, the proposed method is inefficient for instances which are not close to Euclidean due to the same property of insertion heuristic.

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.

Local Clustering Organization (LCO) Solving a Large-Scale TSP

2005 ◽  
Vol 17 (5) ◽  
pp. 560-567 ◽  
Author(s):  
Masashi Furukawa ◽  
◽  
Michiko Watanabe ◽  
Yusuke Matsumura ◽  
◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Numerical Experiments ◽  
Large Scale ◽  
The Self ◽  
Traveling Salesman ◽  
Self Organizing Map ◽  
Two Cities ◽  
Local Clustering ◽  
Different Types ◽  
The Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most difficult problems that occur in different types of industrial scheduling situations. We propose a solution, involving local clustering organization (LCO), for a large-scale TSP based on the principle of the self-organizing map (SOM). Although the SOM can solve TSPs, it is not applicable to practical TSPs because the SOM references city coordinates and assigns synapses to coordinates. LCO indirectly uses the SOM principle and, instead of city coordinates, references costs between two cities, to determine the sequence of cities. We apply LCO to a large-scale TSP to determine its efficiency in numerical experiments. Results demonstrate that LCO obtains the desired solutions.

Artificial Bee Colony Algorithm for Traveling Salesman Problem

2011 ◽  
Vol 314-316 ◽  
pp. 2191-2196 ◽  
Author(s):  
Wei Hua Li ◽  
Wei Jia Li ◽  
Yuan Yang ◽  
Hai Qiang Liao ◽  
Ji Long Li ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Nearest Neighbor ◽  
Traveling Salesman ◽  
Comparison Study ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Benchmark Instances ◽  
Bee Colony Optimization

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.

scholarly journals An Improved Ant Colony Optimization Based on an Adaptive Heuristic Factor for the Traveling Salesman Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Pengzhen Du ◽  
Ning Liu ◽  
Haofeng Zhang ◽  
Jianfeng Lu
Keyword(s):  
Traveling Salesman Problem ◽  
Large Scale ◽  
Traveling Salesman ◽  
Local Optimum ◽  
Solution Quality ◽  
Movement Strategies ◽  
Comparison Algorithms ◽  
Adaptive Heuristic ◽  
The Traveling Salesman Problem ◽  
Local Optimizer

The traveling salesman problem (TSP) is a typical combinatorial optimization problem, which is often applied to sensor placement, path planning, etc. In this paper, an improved ACO algorithm based on an adaptive heuristic factor (AHACO) is proposed to deal with the TSP. In the AHACO, three main improvements are proposed to improve the performance of the algorithm. First, the k-means algorithm is introduced to classify cities. The AHACO provides different movement strategies for different city classes, which improves the diversity of the population and improves the search ability of the algorithm. A modified 2-opt local optimizer is proposed to further tune the solution. Finally, a mechanism to jump out of the local optimum is introduced to avoid the stagnation of the algorithm. The proposed algorithm is tested in numerical experiments using 39 TSP instances, and results shows that the solution quality of the AHACO is 83.33% higher than that of the comparison algorithms on average. For large-scale TSP instances, the algorithm is also far better than the comparison algorithms.

scholarly journals Dynamic Reduction-Expansion Operator to Improve Performance of Genetic Algorithms for the Traveling Salesman Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Santiago-Omar Caballero-Morales ◽  
Jose-Luis Martinez-Flores ◽  
Diana Sanchez-Partida
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Traveling Salesman ◽  
Initial Population ◽  
Transportation Industry ◽  
Routing Problem ◽  
Population Strategy ◽  
Minimum Distances ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is an important routing problem within the transportation industry. However, finding optimal solutions for this problem is not easy due to its computational complexity. In this work, a novel operator based on dynamic reduction-expansion of minimum distance is presented as an initial population strategy to improve the search mechanisms of Genetic Algorithms (GA) for the TSP. This operator, termed as RedExp, consists of four stages: (a) clustering to identify candidate supply/demand locations to be reduced, (b) coding of clustered and nonclustered locations to obtain the set of reduced locations, (c) sequencing of minimum distances for the set of reduced locations (nearest neighbor strategy), and (d) decoding (expansion) of the reduced set of locations. Experiments performed on TSP instances with more than 150 nodes provided evidence that RedExp can improve convergence of the GA and provide more suitable solutions than other approaches focused on the GA’s initial population.

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 Approximation result toward nearest neighbor heuristic

2002 ◽  
Vol 12 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Jér"me Monnot
Keyword(s):  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Traveling Salesman ◽  
Performance Ratio ◽  
Approximation Result ◽  
The Traveling Salesman Problem

In this paper, we revisit the famous heuristic called nearest neighbor (N N) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Sa;taC for a>0 and t>1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t+1)/2t-approximation for maxTSPSa;taC and a 2/(t+1)-approximation for minTSPSa;taC under the standard performance ratio. Moreover, we show that these ratios are tight for some instances.

scholarly journals Basic Evolutionary Approach to the Traveling Salesman Problem

2018 ◽  
Vol 1 (2) ◽  
pp. 30-38
Author(s):  
Débora Regina De São José ◽  
Mauricio Garcia Hernandez
Keyword(s):  
Traveling Salesman Problem ◽  
Evolutionary Programming ◽  
Traveling Salesman ◽  
Evolutionary Approach ◽  
Average Error ◽  
Test Case ◽  
Simple Simulation ◽  
Alternative Approach ◽  
Benchmark Instances ◽  
The Traveling Salesman Problem

Evolutionary programming (EP) is a metaheuristic method developed as an alternative approach to artificial intelligence. The aim of this paper is to bring an introduction to EP algorithms through the implementation of the basic D. B. Fogel’s Evolutionary Programing approach of 1988 and the emulation of his results in order to analyze the performance of the evolutionary programming method on solving a benchmark test case. The EP approach is implemented thru a simple simulation of natural evolution and the allowance of probabilistic survival of individuals. The novelty of this paper relies on testing the algorithm performance in some problems of well-known benchmark instances of the Traveling Salesman Problem, where that 1988 evolutionary approach was not tested. The reproduction of 1988 D. B. Fogel’s approach was possible, the found average error of this method for 200000 offspring applied to the benchmark instances was found to be in the order of the 10%.

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