scholarly journals A COMPARATIVE STUDY OF VARIOUS METHODS OF ANN FOR SOLVING TSP PROBLEM

2013 ◽  
Vol 4 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Sharadindu Roy ◽  
Prof Samer Sen Sarma ◽  
Soumyadip Chakravorty ◽  
Suvodip Maity
Keyword(s):  
Comparative Study ◽  
Optimization Problem ◽  
Travelling Salesman Problem ◽  
Recurrent Network ◽  
Hopfield Network ◽  
The Other ◽  
Self Organization ◽  
Travelling Salesman ◽  
Combinational Optimization ◽  
Fully Connected

Abstract This paper represents TSP (Travelling Salesman Problem) by using Artificial Neural Networks.A comparative study of various methods of ANN is shown here for solving TSP problem.The Travelling Salesman Problem is a classical combinational optimization problem, which is a simple to state but very difficult to solve. This problem is to find the shortest possible tour through a set of N vertices so that each vertex is visited exactly once. TSP can be solved by Hopfield Network, Self-organization Map, and Simultaneous Recurrent Network. Hopfield net is a fully connected network, where every vertex is connected with each other forwardly and backwardly. So starting the walk from a vertex we can travel all the other vertex exactly once and return to starting vertex again.

scholarly journals Ants Colony Optimisation of a Measuring Path of Prismatic Parts on a CMM

2016 ◽  
Vol 23 (1) ◽  
pp. 119-132 ◽  
Author(s):  
Slavenko M. Stojadinovic ◽  
Vidosav D. Majstorovic ◽  
Numan M. Durakbasa ◽  
Tatjana V. Sibalija
Keyword(s):  
Travelling Salesman Problem ◽  
Ant Colony ◽  
The Other ◽  
Ant Colony Optimisation ◽  
Travelling Salesman ◽  
Prismatic Parts ◽  
On Line ◽  
Optimisation Model ◽  
Set Of Points ◽  
The Mathematical Model

AbstractThis paper presents optimisation of a measuring probe path in inspecting the prismatic parts on a CMM. The optimisation model is based on: (i) the mathematical model that establishes an initial collision-free path presented by a set of points, and (ii) the solution of Travelling Salesman Problem (TSP) obtained with Ant Colony Optimisation (ACO). In order to solve TSP, an ACO algorithm that aims to find the shortest path of ant colony movement (i.e. the optimised path) is applied. Then, the optimised path is compared with the measuring path obtained with online programming on CMM ZEISS UMM500 and with the measuring path obtained in the CMM inspection module of Pro/ENGINEER®software. The results of comparing the optimised path with the other two generated paths show that the optimised path is at least 20% shorter than the path obtained by on-line programming on CMM ZEISS UMM500, and at least 10% shorter than the path obtained by using the CMM module in Pro/ENGINEER®.

2. Four types of problem

2016 ◽  
pp. 7-27
Author(s):  
Robin Wilson
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
Counting Problems ◽  
Problem Construction ◽  
Colour Problem ◽  
Efficiency Of Algorithms ◽  
Enumeration Problems ◽  
Knight’S Tour

‘Four types of problem’ explains that combinatorics is concerned with four types of problem: existence problems (does x exist?); construction problems (if x exists, how can we construct it?); enumeration problems (how many x are there?); and optimization problems (which x is best?). Existence problems discussed include tilings, placing dominoes on a chess board, the knight’s tour problem, the Königsberg bridges problem, the Gas–Water–Electricity problem, and the map-colour problem. Construction problems include solving mazes, and the two types of enumeration problems considered are counting problems and listing problems. Examples of an optimization problem include the minimum connector problem and the travelling salesman problem. The efficiency of algorithms is also explained.

scholarly journals Travelling Salesman Problem Generalized Interval Arithmetic

2021 ◽  
Vol 9 (12) ◽  
pp. 2281-2284
Author(s):  
Priya Dharshini. A
Keyword(s):  
Combinatorial Optimization ◽  
Fuzzy Sets ◽  
Interval Arithmetic ◽  
Optimization Problem ◽  
Travelling Salesman Problem ◽  
Arithmetic Operation ◽  
Combinatorial Optimization Problem ◽  
Common Method ◽  
Travel Times ◽  
Travelling Salesman

Abstract: The travelling salesman problem is one of the famous combinatorial optimization problem and has been intensively studied in the last decades. We present a new extension of the basics problem, where travel times are specified as a range of possible values. Keywords: Fuzzy sets, Arithmetic operation on interval, least common method, travelling salesman problem.

Evolutionary algorithm based on discrete ITO process for travelling salesman problems

2015 ◽  
Vol 06 (03) ◽  
pp. 1550032
Author(s):  
Wenyong Dong ◽  
Kang Sheng ◽  
Chuanhua Yang ◽  
Yunfei Yi
Keyword(s):  
Optimization Problem ◽  
Continuous Optimization ◽  
Population Diversity ◽  
Travelling Salesman ◽  
Local Search Methods ◽  
Combinational Optimization ◽  
Metaheuristic Methods ◽  
Ant Colony Algorithms ◽  
Ito Process ◽  
Move Operator

Since dozens years ago, various metaheuristic methods, such as genetic algorithm, ant colony algorithms, have been successfully applied to combinational optimization problem. However, as one of the members, ITO algorithm has only been employed in continuous optimization, it needs further design for combinational optimization problem. In this paper, a discrete ITO algorithm inspired by ITO stochastic process is proposed for travelling salesman problems (TSPs). Some key operators, such as move operator, wave operator, are redesigned to adapt to combinational optimization. Moreover, the performance of ITO algorithm in different parameter selections and the maintenance of population diversity information are also studied. By combining local search methods (such as 2-opt and LK-opt) with ITO algorithm, our computational results of the TSP problems show that ITO algorithm is currently one of the best-performing algorithms for these problems.

A Survey of Quantum Genetic Algorithm for Combinatorial Optimization Problems

2014 ◽  
Vol 568-570 ◽  
pp. 822-826 ◽  
Author(s):  
Feng Mei Wei ◽  
Jian Pei Zhang ◽  
Bing Li ◽  
Jing Yang
Keyword(s):  
Genetic Algorithm ◽  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Job Shop ◽  
Optimization Problems ◽  
The Other ◽  
Quantum Genetic Algorithm ◽  
Combinatorial Optimization Problems ◽  
Combinational Optimization ◽  
Rotation Strategy

Combined with quantum computing and genetic algorithm, quantum genetic algorithm (QGA) shows considerable ability of parallelism. Experiments have shown that QGA performs quite well on TSP, job shop problem and some other typical combinatorial optimization problems. The other problems like nutritional diet which can be transformed into specific combinational optimization problem also can be solved through QGA smoothly. This paper sums up the main points of QGA for general combinatorial optimization problems. These points such as modeling of the problem, qubit decoding and rotation strategy are useful to enhance the convergence speed of QGA and avoid premature at the same time.

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