Neural Networks in Optimization
People are facing more and more NP-complete
or NP-hard problems of a combinatorial nature and of a continuous nature in economic, military and management practice. There
are two ways in which one can enhance the efficiency of searching for the solutions of these problems. The first is to improve
the speed and memory capacity of hardware. We all have witnessed the computer industry's amazing achievements with hardware
and software developments over the last twenty years. On one hand many computers, bought only a few years ago, are being sent
to elementary schools for children to learn the ABC's of computing. On the other hand, with economic, scientific and military
developments, it seems that the increase of intricacy and the size of newly arising problems have no end. We all realize then
that the second way, to design good algorithms, will definitely compensate for the hardware limitations in the case of complicated
problems. It is the collective and parallel computation property of artificial neural net works that has activated the enthusiasm
of researchers in the field of computer science and applied mathematics. It is hard to say that artificial neural networks
are solvers of the above-mentioned dilemma, but at least they throw some new light on the difficulties we face. We not only
anticipate that there will be neural computers with intelligence but we also believe that the research results of artificial
neural networks might lead to new algorithms on von Neumann's computers.
List of Figures. Preface. Part I: Concepts
and Models of Optimization. 1. Preliminaries. 2. Introduction to Mathematical Programming. 3. Unconstrained Nonlinear Programming.
4. Constrained Nonlinear Programming. Part II: Basic Artificial Neural Network Models. 5. Introduction to Artificial Neural
Network. 6. Feedforward Neural Networks. 7. Feedback Neural Networks. 8. Self-Organized Neural Networks. Part III: Neural
Algorithms for Optimization. 9. NN Models for Combinatorial Problems. 10. NN For Quadratic Programming Problems. 11. NN
For General Nonlinear Programming. 12. NN For Linear Programming. 13. A Review on NN for Continuious Optimization. References.
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