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.
