The self-organized map, an architecture suggested for artificial neural networks, is explained by presenting simulation experiments and practical applications. The self-organizing map has the property of effectively creating spatially organized internal representations of various features of input signals and their abstractions. One result of this is that the self-organization process can discover semantic relationships in sentences. Brain maps, semantic maps, and early work on competitive learning are reviewed. The self-organizing map algorithm (an algorithm which order responses spatially) is reviewed, focusing on best matching cell selection and adaptation of the weight vectors. Suggestions for applying the self-organizing map algorithm, demonstrations of the ordering process, and an example of hierarchical clustering of data are presented. Fine tuning the map by learning vector quantization is addressed. The use of self-organized maps in practical speech recognition and a simulation experiment on semantic mapping are discussed. >

The self-organizing map

From the Publisher:
"Covering the latest issues and achievements, this well documented, precisely presented text is timely and suitable for graduate and upper undergraduate students in knowledge engineering, intelligent systems, AI, neural networks, fuzzy systems, and related areas. The author's goal is to explain the principles of neural networks and fuzzy systems and to demonstrate how they can be applied to building knowledge-based systems for problem solving. Especially useful are the comparisons between different techniques (AI rule-based methods, fuzzy methods, connectionist methods, hybrid systems) used to solve the same or similar problems."
-- Anca Ralescu, Associate Professor of Computer Science, University of Cincinnati Neural networks and fuzzy systems are different approaches to introducing human-like reasoning into expert systems. This text is the first to combine the study of these two subjects, their basics and their use, along with symbolic AI methods to build comprehensive artificial intelligence systems. 
In a clear and accessible style, Kasabov describes rule- based and connectionist techniques and then their combinations, with fuzzy logic included, showing the application of the different techniques to a set of simple prototype problems, which makes comparisons possible. A particularly strong feature of the text is that it is filled with applications in engineering, business, and finance. AI problems that cover most of the application-oriented research in the field (pattern recognition, speech and image processing, classification, planning, optimization, prediction, control, decision making, and game simulations) are discussed and illustrated with concrete examples.
Intended both as a text for advanced undergraduate and postgraduate students as well as a reference for researchers in the field of knowledge engineering, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering has chapters structured for various levels of teaching and includes original work by the author along with the classic material. 
Data sets for the examples in the book as well as an integrated software environment that can be used to solve the problems and do the exercises at the end of each chapter are available free through anonymous ftp.

Foundations of neural networks, fuzzy systems, and knowledge engineering

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items.

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Neural Combinatorial Optimization with Reinforcement Learning

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E H L Aarts and J K Lenstra (eds), John Wiley and Sons, London, 1997, pp 215-310 The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including classical local optimization techniques as well as many of the more recent variants on local optimization, such as simulated annealing, tabu search, neural networks, and genetic algorithms This chapter discusses how these various approaches have been adapted to the TSP and evaluates their relative success in this perhaps atypical domain from both a theoretical and an experimental point of view

The Traveling Salesman Problem: A Case Study in Local Optimization

Metaheuristics are the most exciting development in approximate optimization techniques of the last two decades. They have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas. This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics. Metaheuristics include but are not limited to constraint logic programming; greedy random adaptive search procedures; natural evolutionary computation; neural networks; non-monotonic search strategies; space-search methods; simulated annealing; tabu search; threshold algorithms and their hybrids. References are presented in alphabetical order under a number of subheadings.

Bernard Angéniol

Papers

Self-organizing feature maps and the travelling salesman problem