Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

SIMULATED ANNEALING METHOD IN THE CLASSIC BOLTZMANN MACHINES

The classical Boltzmann machine is understood as a neural network proposed by Hinton and his colleagues in 1985. They added noise interferences to the Hopfield model and called this network a Boltzmann machine drawing an analogy between its behaviour and physical systems with the presence of interferences. This study explains the definition of “simulated annealing” and “thermal equilibrium” using the example of a partial network. A technique for calculating the probabilities of transition states at different temperatures using Markov chains is described, an example of the application of the SA - travelling salesman problem is given. Boltzmann machine is used for pattern recognition and in classification problems. As a disadvantage, a slow learning algorithm is mentioned, but it makes it possible to get out of local minima. The main purpose of this article is to show the capabilities of the simulated annealing algorithm in solving practical tasks.

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Review of Neural Network Algorithms

The artificial neural network is the core tool of machine learning to realize intelligence. It has shown its advantages in the fields of sound, image, sound, picture, and so on. Since entering the 21st century, the progress of science and technology and people\u27s pursuit of artificial intelligence have introduced the research of artificial neural networks into an upsurge. Firstly, this paper introduces the application background and development process of the artificial neural network in order to clarify the research context of neural networks. Five branches and related applications of single-layer perceptron, linear neural network, BP neural network, Hopfield neural network, and depth neural network are analyzed in detail. The analysis shows that the development trend of the artificial neural network is developing towards a more general, flexible, and intelligent direction. Finally, the future development of the artificial neural network in training mode, learning mode, function expansion, and technology combination has prospected