II. SIMPLE EXPLANATIONS OF KEY IDEAS IN ORDINAL OPTIMIZATION
II.4 THE IMPORTANCE OF REPRESENTATION IN SEARCHES
- Suppose you have a design space of 10 billion which is small by most
combinatorial standards. You uniformly and randomly sample 10,000
designs in this space which by definition is the limit of your
computing budget. What is the probability that NONE OF YOUR SAMPLES
will fall in the top-50, top-500, top-5,000, top-50,000 of the
Answer: 0.99995, 0.9995, 0.99501, 0.951 respectively, i.e.,
virtually no chance pure random search will get you anything good.
- Now suppose you have a representation which can focus your sampling
within the top-1 million designs exclusively, what will your answers be
Answer: 0.606, 0.00673, 1.7x10-22, and >
1x10-222 or zero essentially, i.e., you can't fail.
- One can interpolate in between to see the truth of the statement: WITH
THE RIGHT REPRESENTATION ANYTHING WOULD WORK; WITHOUT THE RIGHT
REPRESENTATION, FORGET IT.
Philosophically this is comforting since it says that there is room for
human beings who have to dream up the right representation. We have not
learned to automate that step as yet. I personally do not subscribe
to the idea that anytime soon some general purpose optimization scheme
such as simulated annealing or genetic algorithms can be let loose on
a computer without human supervision and expected to perform well
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