Optimization using random searches

[Namir]

Optimization using random search is an algorithm that is easy to code. This approach searches for the best values of the independent variables, each within a trusted range. The trick is to use a large number of iterations. The best solution tends to deviate from the true solutions as the number of variables increase and as the optimized function is more complex to evaluate.

There are a few approaches that I recently used to possibly enhance random searching:

1) If the independent variables can be grouped by categories (such as temperature, pressure, concentration, length, and so on), then you can add more sets of searches in the main iterations loop. Each set obtains random values for variable in a specific category, while setting the other variables to their best values obtained so far.

2) If you notice, while running tests on your problem, that the values of the independent variables oscillate above and below their correct optimum values, then you can add another set of calculations to the main loop. This additional set looks at the averages of the best values obtained so far for each independent variable. It then generates random number that are in ranges of, say, 20% or 30% around the averages. You have the option of including the values of independent variables that produce better minima in the running totals of the best independent variable values. This step will tend to favor the average best values of the independent variables. However, remember that each loop has the free hand to pick at random values for the independent variables, each within its prescribed range.

I should be soon posting HP-71B programs showing the general random search and also a version that uses the averages of the best values.

Namir