EFFICIENT ALGORITHMS FOR TRAVELLING SALESMAN PROBLEMS ARISING IN WAREHOUSE ORDER PICKING

We investigate two routing problems that arise when order pickers traverse an aisle in a warehouse. The routing problems can be viewed as Euclidean travelling salesman problems with points on two parallel lines. We show that if the order picker traverses only a section of the aisle and then returns, then an optimal solution can be found in linear time, and if the order picker traverses the entire aisle, then an optimal solution can be found in quadratic time. Moreover, we show how to approximate the routing cost in linear time by computing a minimum spanning tree for the points on the parallel lines.

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Converting MST to TSP Path by Branch Elimination

Applied Sciences ◽

10.3390/app11010177 ◽

2020 ◽

Vol 11 (1) ◽

pp. 177

Author(s):

Pasi Fränti ◽

Teemu Nenonen ◽

Mingchuan Yuan

Keyword(s):

Spanning Tree ◽

Closed Loop ◽

Minimum Spanning Tree ◽

Travelling Salesman Problem ◽

Open Loop ◽

Travelling Salesman ◽

Elimination Algorithm ◽

Number Of Iterations ◽

Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

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On the Euclidean Minimum Spanning Tree Problem

Computing Letters ◽

10.1163/1574040053326325 ◽

2005 ◽

Vol 1 (1) ◽

pp. 11-14 ◽

Cited By ~ 7

Author(s):

Sanguthevar Rajasekaran

Keyword(s):

Spanning Tree ◽

Euclidean Distance ◽

Minimum Spanning Tree ◽

Linear Time ◽

Randomized Algorithm ◽

Weighted Graph ◽

Deterministic Algorithm ◽

Probabilistic Algorithms ◽

Tree Algorithms ◽

Minimum Spanning Tree Problem

Given a weighted graph G(V;E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP). The minimum spanning tree algorithms alluded to before will run in time O(n2) (or nearly O(n2)) on this graph. In this note we point out that it is possible to devise simple algorithms for EMSTP in k- dimensions (for any constant k) whose expected run time is O(n), under the assumption that the points are uniformly distributed in the space of interest.CR Categories: F2.2 Nonnumerical Algorithms and Problems; G.3 Probabilistic Algorithms

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Efficient algorithms for finding the most vital edge of a minimum spanning tree

Information Processing Letters ◽

10.1016/0020-0190(93)90082-k ◽

1993 ◽

Vol 48 (5) ◽

pp. 211-213 ◽

Cited By ~ 16

Author(s):

Kazuo Iwano ◽

Naoki Katoh

Keyword(s):

Spanning Tree ◽

Minimum Spanning Tree ◽

Efficient Algorithms

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.886.593 ◽

2014 ◽

Vol 886 ◽

pp. 593-597 ◽

Cited By ~ 2

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.

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A New Algorithm for Vehicle Routing Problems with Capacity Limited Based on Minimum Spanning Tree

2010 International Conference on Optoelectronics and Image Processing ◽

10.1109/icoip.2010.323 ◽

2010 ◽

Author(s):

Yang Yuewu

Keyword(s):

Vehicle Routing ◽

Spanning Tree ◽

Minimum Spanning Tree ◽

Vehicle Routing Problems ◽

Routing Problems

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Does Determination of Initial Cluster Centroids Improve the Performance of K-Means Clustering Algorithm? Comparison of Three Hybrid Methods by Genetic Algorithm, Minimum Spanning Tree, and Hierarchical Clustering in an Applied Study

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/7636857 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Saeedeh Pourahmad ◽

Atefeh Basirat ◽

Amir Rahimi ◽

Marziyeh Doostfatemeh

Keyword(s):

Genetic Algorithm ◽

Hierarchical Clustering ◽

Spanning Tree ◽

Clustering Algorithm ◽

Spanning Trees ◽

Minimum Spanning Tree ◽

Hybrid Methods ◽

Optimal Solution ◽

Initial Cluster ◽

Algorithm Comparison

Random selection of initial centroids (centers) for clusters is a fundamental defect in K-means clustering algorithm as the algorithm’s performance depends on initial centroids and may end up in local optimizations. Various hybrid methods have been introduced to resolve this defect in K-means clustering algorithm. As regards, there are no comparative studies comparing these methods in various aspects, the present paper compared three hybrid methods with K-means clustering algorithm using concepts of genetic algorithm, minimum spanning tree, and hierarchical clustering method. Although these three hybrid methods have received more attention in previous researches, fewer studies have compared their results. Hence, seven quantitative datasets with different characteristics in terms of sample size, number of features, and number of different classes are utilized in present study. Eleven indices of external and internal evaluating index were also considered for comparing the methods. Data indicated that the hybrid methods resulted in higher convergence rate in obtaining the final solution than the ordinary K-means method. Furthermore, the hybrid method with hierarchical clustering algorithm converges to the optimal solution with less iteration than the other two hybrid methods. However, hybrid methods with minimal spanning trees and genetic algorithms may not always or often be more effective than the ordinary K-means method. Therefore, despite the computational complexity, these three hybrid methods have not led to much improvement in the K-means method. However, a simulation study is required to compare the methods and complete the conclusion.

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Linear-time algorithms for parametric minimum spanning tree problems on planar graphs

LATIN '95: Theoretical Informatics - Lecture Notes in Computer Science ◽

10.1007/3-540-59175-3_94 ◽

1995 ◽

pp. 257-271 ◽

Cited By ~ 2

Author(s):

David Fernández-Baca ◽

Giora Slutzki

Keyword(s):

Planar Graphs ◽

Spanning Tree ◽

Minimum Spanning Tree ◽

Linear Time ◽

Linear Time Algorithms

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Comparative Study of Prim and Genetic Algorithms in Minimum Spanning Tree and Travelling Salesman Problem

10.31227/osf.io/8awms ◽

2018 ◽

Author(s):

Andysah Putera Utama Siahaan ◽

Andre Hasudungan Lubis

Keyword(s):

Genetic Algorithm ◽

Spanning Tree ◽

Minimum Spanning Tree ◽

Travelling Salesman Problem ◽

Operational Cost ◽

Travelling Salesman ◽

Maximum Value ◽

Large Numbers ◽

Crossover And Mutation ◽

Better Than

Optimization is the essential thing in an algorithm. It can save the operational cost of an activity. At the Minimum Spanning Tree, the goal to be achieved is how all nodes are connected with the smallest weights. Several algorithms can calculate the use of weights in this graph. Genetic and Primary algorithms are two very popular algorithms for optimization. Prim calculates the weights based on the short-est distance from a graph. This algorithm eliminates the connected loop to minimize circuit. The nature of this algorithm is to trace all nodes to the smallest weights on a given graph. The genetic algorithm works by determining the random value as first initialization. This algorithm will perform selection, crossover, and mutation by the number of rounds specified. It is possible that this algorithm can not achieve the maximum value. The nature of the genetic algorithm is to work with probability. The results obtained are the most optimal results according to this algorithm. The results of this study indicate that the Prim is better than Genetics in determining the weights at the minimum spanning tree while Genetic algorithm is better for travelling salesman problem. Genetics will have maximum results when using large numbers of rotations and populations.

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