LETTERS TO S&C
Several articles have appeared in S&C wherein optimization was discussed. I would like to discuss
something I encountered at least six years ago when I first tried optimizing. Some of your readers may
have had the same experience and can further comment on the subject.
The best way to explain this subject may be by example.
The example is extremely simple. It involves optimizing, in one of my programs, only two parameters—a
decimal for an exponential average for buying and a decimal for an exponential average for selling. The
buy decimal was stepped from .1 to .3 in increments of .05 while the sell decimal was stepped from .15 to
.35 in increments of .05. The same database was, of course, used for all combinations of parameter
values. The resulting outputs are shown in the enclosed figure (see Figure 1). The MADecBuy values lie
along the x-axis and the MADecSell values lie along the y-axis. The outputs from the program are
written at the appropriate intersections. (Sorry, just ran out of 3D graph paper.)
Please note the outputs form a multi-peak "mountain range." For example, there is a peak of 37.4 and
another of 31.0. Also, there is a "valley" along the MADecSell = .25 value. Furthermore, several dips
exist such as the one at MADecBuy = .20 when moving along MADecSell = .15. Still further, increasing
values for MADecBuy (i.e. values > 0.3) should produce more peaks—but what we have is sufficient.
From the above, it should be apparent we do not have a monotonic rise to a single peak and a monotonic
decline from that peak for the range of parameter values in this simple example. (I am fully aware the
previous statement is redundant—if it is monotonic it must be single—but I am trying to emphasize!)
What happens when you are optimizing more than two parameter values? I suspect the situation becomes
even more complex.
HUGH L. LOGAN