V. 7:1 (35-35): Letters To S&C

LETTERS TO S&C

Optimization

Editor,

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

Hendersonville, TN