I am working on an optimization problem involving Boolean expressions and wanted some help as I have very little knowledge about the topic. The problem statement is as follows:
There are a set of functions, say, f1 to fn outputting either 0 or 1 only and three Boolean operations, AND, OR and NOT, a logical expression involving the functions is expected to be generated as follows:
F1 or F2 and F3 or ………. [ The logical expression need not necessarily include all n variables, n is expected to be ~10].
The logical expression generated is expected to generate a true or false signal, which drives the functioning of a black box. The “success” of the logical expression is measurable by a metric, however, apart from the metric, no other data is readily available from the black box.
Furthermore, the following is expected regarding the nature of the solutions [though not entirely confident]:
- Vast majority of the solutions is expected to have a negative metric, optimal solution is to have a positive metric.
- Majority of solutions are expected to have a metric close to zero, the metric of the best solution is also anticipated to be close to zero, but marginally positive.
- Multiple optimal solutions are anticipated, however variation between the metric for the optimal solutions is not anticipated to be very large.
Is there a way to find an optimal logical rule that gives the “best” measured performance of the black box?