scholarly journals Converting MST to TSP Path by Branch Elimination

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.

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

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.

scholarly journals Comparison of eleven measures for estimating difficulty of open-loop TSP instances

2021 ◽  
Vol 1 (1) ◽  
pp. 1-30
Author(s):  
Lahari Sengupta ◽  
◽  
Pasi Fränti
Keyword(s):  
Spanning Tree ◽  
Time Complexity ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Open Loop ◽  
Problem Instance ◽  
Computer Performance ◽  
Prediction Capability ◽  
Better Than ◽  
Number Of Branches

<abstract> <p>From the theory of algorithms, we know that the time complexity of finding the optimal solution for a traveling salesman problem (TSP) grows exponentially with the number of targets. However, the size of the problem instance is not the only factor that affects its difficulty. In this paper, we review existing measures to estimate the difficulty of a problem instance. We also introduce MST branches and two other measures called greedy path and greedy gap. The idea of MST branches is to generate minimum spanning tree (MST) and then calculate the number of branches in the tree. A branch is a target, which is connected to at least two other targets. We perform an extensive comparison of 11 measures to see how well they correlate to human and computer performance. We evaluate the measures based on time complexity, prediction capability, suitability, and practicality. The results show that while the MST branches measure is simple, fast to compute, and does not need to have the optimal solution as a reference unlike many other measures. It correlates equally good or even better than the best of the previous measures ‑ the number of targets, and the number of targets on the convex hull.</p> </abstract>

scholarly journals The Volatility Forecasting Power of Financial Network Analysis

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Nicolás S. Magner ◽  
Jaime F. Lavin ◽  
Mauricio A. Valle ◽  
Nicolás Hardy
Keyword(s):  
Spanning Tree ◽  
Predictive Power ◽  
Minimum Spanning Tree ◽  
Financial Networks ◽  
Order Effects ◽  
Structural Factors ◽  
Financial Variables ◽  
Road Map ◽  
Daily Returns

This investigation connects two crucial economic and financial fields, financial networks, and forecasting. From the financial network’s perspective, it is possible to enhance forecasting tools, since econometrics does not incorporate into standard economic models, second-order effects, nonlinearities, and systemic structural factors. Using daily returns from July 2001 to September 2019, we used minimum spanning tree and planar maximally filtered graph techniques to forecast the stock market realized volatility of 26 countries. We test the predictive power of our core models versus forecasting benchmarks models in and out of the sample. Our results show that the length of the minimum spanning tree is relevant to forecast volatility in European and Asian stock markets, improving forecasting models’ performance. As a new contribution, the evidence from this work establishes a road map to deepening the understanding of how financial networks can improve the quality of prediction of financial variables, being the latter, a crucial factor during financial shocks, where uncertainty and volatility skyrocket.

scholarly journals EFFICIENT ALGORITHMS FOR TRAVELLING SALESMAN PROBLEMS ARISING IN WAREHOUSE ORDER PICKING

2015 ◽  
Vol 57 (2) ◽  
pp. 166-174 ◽  
Author(s):  
H. CHARKHGARD ◽  
M. SAVELSBERGH
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Optimal Solution ◽  
Efficient Algorithms ◽  
Order Picking ◽  
Travelling Salesman ◽  
Routing Problems ◽  
Parallel Lines

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.

When Causality Does Not Imply Correlation: More Spadework at the Foundations of Scientific Psychology

2011 ◽  
Vol 108 (3) ◽  
pp. 943-954 ◽  
Author(s):  
Richard S. Marken ◽  
Brittany Horth
Keyword(s):  
Sensory Input ◽  
Closed Loop ◽  
Causal Model ◽  
Open Loop ◽  
Tracking Performance ◽  
Loop Model ◽  
Surprising Result ◽  
Scientific Psychology ◽  
Mouse Movements

Experimental research in psychology is based on an open-loop causal model which assumes that sensory input causes behavioral output. This model was tested in a tracking experiment where participants were asked to control a cursor, keeping it aligned with a target by moving a mouse to compensate for disturbances of differing difficulty. Since cursor movements (inputs) are the only observable cause of mouse movements (outputs), the open-loop model predicts that there will be a correlation between input and output that increases as tracking performance improves. In fact, the correlation between sensory input and motor output is very low regardless of the quality of tracking performance; causality, in terms of the effect of input on output, does not seem to imply correlation in this situation. This surprising result can be explained by a closed-loop model which assumes that input is causing output while output is causing input.

scholarly journals Development of Gis Tool for the Solution of Minimum Spanning Tree Problem using Prim's Algorithm

2014 ◽  
Vol XL-8 ◽  
pp. 1105-1114 ◽  
Author(s):  
S. Dutta ◽  
D. Patra ◽  
H. Shankar ◽  
P. Alok Verma
Keyword(s):  
Spanning Tree ◽  
Road Network ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Transportation Network ◽  
Travelling Salesman Problem ◽  
Optimal Path ◽  
Road Transportation ◽  
Gis Technology ◽  
Weighted Network

minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it’s minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.

scholarly journals A Self-Adaptive Discrete PSO Algorithm with Heterogeneous Parameter Values for Dynamic TSP

2019 ◽  
Author(s):  
Łukasz Strąk ◽  
Rafał Skinderowicz ◽  
Urszula Boryczka ◽  
Arkadiusz Nowakowski
Keyword(s):  
Travelling Salesman Problem ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Discrete Particle Swarm Optimization ◽  
Travelling Salesman ◽  
Discrete Pso ◽  
Parameter Values ◽  
Positive Effect ◽  
Uniform Parameter

This paper presents a discrete particle swarm optimization (DPSO) algorithm with heterogeneous (non-uniform) parameter values for solving the dynamic travelling salesman problem (DTSP). The DTSP can be modelled as a sequence of static sub-problems, each of which is an instance of the TSP. We present a method for automatically setting the values of the DPSO parameters without three parameters, which can be defined based on the size of the problem, the size of the particle swarm, the number of iterations, and the particle neighbourhood size. We show that the diversity of parameter values has a positive effect on the quality of the generated results. We compare the performance of the proposed heterogeneous DPSO with two ant colony optimization (ACO) algorithms. The proposed algorithm outperforms the base DPSO and is competitive with the ACO.

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