scholarly journals An Improved Approximation Algorithm for the Subpath Planning Problem and Its Generalization

2017 ◽  
Author(s):  
Hanna Sumita ◽  
Yuma Yonebayashi ◽  
Naonori Kakimura ◽  
Ken-ichi Kawarabayashi
Keyword(s):  
Artificial Intelligence ◽  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Numerical Experiments ◽  
Traveling Salesman ◽  
Planning Problem ◽  
Solution Quality ◽  
The Traveling Salesman Problem ◽  
Direct Use ◽  
And Robotics

This paper focuses on a generalization of the traveling salesman problem (TSP), called the subpath planning problem (SPP). Given 2n vertices and n independent edges on a metric space, we aim to find a shortest tour that contains all the edges. SPP is one of the fundamental problems in both artificial intelligence and robotics. Our main result is to design a 1.5-approximation algorithm that runs in polynomial time, improving the currently best approximation algorithm. The idea is direct use of techniques developed for TSP. In addition, we propose a generalization of SPP called the subgroup planning problem (SGPP). In this problem, we are given a set of disjoint groups of vertices, and we aim to find a shortest tour such that all the vertices in each group are traversed sequentially. We propose a 3-approximation algorithm for SGPP. We also conduct numerical experiments. Compared with previous algorithms, our algorithms improve the solution quality by more than 10% for large instances with more than 10,000 vertices.

scholarly journals On the Traveling Salesman Problem in Nautical Environments: an Evolutionary Computing Approach to Optimization of Tourist Route Paths in Medulin, Croatia

2019 ◽  
Vol 57 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Sandi Baressi Šegota ◽  
Ivan Lorencin ◽  
Kazuhiro Ohkura ◽  
Zlatan Car
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Path ◽  
Solution Space ◽  
Evolutionary Computing ◽  
Problem Formulation ◽  
Computing Methods ◽  
Traveling Salesman ◽  
Planning Problem ◽  
Extensive Search ◽  
The Traveling Salesman Problem

The Traveling salesman problem (TSP) defines the problem of finding the optimal path between multiple points, connected by paths of a certain cost. This paper applies that problem formulation in the maritime environment, specifically a path planning problem for a tour boat visiting popular tourist locations in Medulin, Croatia. The problem is solved using two evolutionary computing methods – the genetic algorithm (GA) and the simulated annealing (SA) - and comparing the results (are compared) by an extensive search of the solution space. The results show that evolutionary computing algorithms provide comparable results to an extensive search in a shorter amount of time, with SA providing better results of the two.

scholarly journals Heuristic Approaches to Solve Traveling Salesman Problem

2015 ◽  
Vol 15 (2) ◽  
pp. 390
Author(s):  
Malik Muneeb Abid ◽  
Iqbal Muhammad
Keyword(s):  
Exact Solution ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Solution Quality ◽  
Heuristic Approaches ◽  
The Traveling Salesman Problem

This paper provides the survey of the heuristics solution approaches for the traveling salesman problem (TSP). TSP is easy to understand, however, it is very difficult to solve. Due to complexity involved with exact solution approaches it is hard to solve TSP within feasible time. That’s why different heuristics are generally applied to solve TSP. Heuristics to solve TSP are presented here with detailed algorithms. At the end, comparison among selected approaches shows the efficiency of approaches in terms of solution quality and time consumed to solve TSP.

scholarly journals ISLAND MIGRATION MODEL WITH PARALLEL MUTATION STRATEGIES FOR COMPUTING THE TRAVELING SALESMAN PROBLEM ON MULTICOMPUTER PLATFORM

2014 ◽  
pp. 96-102
Author(s):  
Plamenka I. Borovska ◽  
Subhi A. Bahudaila ◽  
Milena K. Lazarova
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Coarse Grained ◽  
Mutation Rates ◽  
Solution Quality ◽  
Suggested Approach ◽  
Mutation Strategy ◽  
The Traveling Salesman Problem ◽  
The Impact

This paper investigates the efficiency of a model of parallel genetic computation of the traveling salesman problem with circular periodic chromosomes migration. The parallel model is verified by MPI-based program implementation on a multicomputer platform. The correlation of the application and architectural spaces has been investigated by exploring the impact of the scalability of the application and the parallel machine size over the efficiency of the parallel system. Performance profiling, evaluation and analysis have been made for different numbers of cities and different sizes of the multicomputer platform. The paper also investigates the impact of the mutation strategy on the solution quality of coarse-grained parallel genetic algorithm with circular periodic migration for the traveling salesman problem. We propose an approach to improve the quality of solution by applying parallel variable mutation rates for the local evolutions in the concurrent processes. A series of experiments has been carried out with parallel fixed and variable mutation rates in order to estimate the efficiency of the suggested approach. The best quality solutions have been obtained for the strategy with parallel fixed mutation rates.

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.

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 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.

New Genetic Operator (Jump Crossover) for the Traveling Salesman Problem

2016 ◽  
pp. 1739-1752 ◽  
Author(s):  
Hicham El Hassani ◽  
Said Benkachcha ◽  
Jamal Benhra
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Methods ◽  
Search Space ◽  
Traveling Salesman ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Hard Problems ◽  
The Traveling Salesman Problem ◽  
Np Hard Problems

Inspired by nature, genetic algorithms (GA) are among the greatest meta-heuristics optimization methods that have proved their effectiveness to conventional NP-hard problems, especially the traveling salesman problem (TSP) which is one of the most studied supply chain management problems. This paper proposes a new crossover operator called Jump Crossover (JMPX) for solving the travelling salesmen problem using a genetic algorithm (GA) for near-optimal solutions, to conclude on its efficiency compared to solutions quality given by other conventional operators to the same problem, namely, Partially matched crossover (PMX), Edge recombination Crossover (ERX) and r-opt heuristic with consideration of computational overload. The authors adopt a low mutation rate to isolate the search space exploration ability of each crossover. The experimental results show that in most cases JMPX can remarkably improve the solution quality of the GA compared to the two existing classic crossover approaches and the r-opt heuristic.

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