Optimizing multiple output parameters for a given input

Question

Problem statement:

I'm trying to solve a problem statement using C# as programming language. In the problem system for an input (double/decimal) say $H_i$, the output generated is a form of dataset containing number of parameters ($F_i$, $P_i$ and $T_i$). I somehow have to filter out only those entries in the data set which would satisfy the following conditions:

• $F_i > F_\min$, where $F_\min$ is some constant;
• $P_i > P_\min$, where $P_\min$ is some constant; and
• $T_i < T_\max$, where $T_\max$ is some constant.

Is there an efficient algorithm I could use in such cases where I could zero in on an optimal set of values for $H_i$ for which the output parameter values are well within the constraints. Also I thought using Genetic Algorithms in this case makes sense but somehow I'm not able to formulate and derive a fitness function for my requirement

Any suggestions on how to approach to solve such problem is truly appreciated.

Kindly do not downvote this question as vague.

Answer 1

Actually what are you trying to do is to solve a nonlinear optimization problem. As far as I understood, you have a dataset and according to the particular input applied, then you get an answer.

One way to approach this problem would be to consider a grid of points for Hi with respect to evaluate the parameters coming from the dataset.

Then you can formulate your fitness function such that in case the resulting parameters do not respect the constraints, then the cost of your objective will go to 10^53 for instance.

After you have evaluated all the grid points, you can choose the best solution and refine the grid to have a better result.

Consider that in this case you don't have any guarantee of the optimality of the obtained solution.

Alternatively you can investigate the usage of the Simulated annealing approach to solve your problem (https://en.wikipedia.org/wiki/Simulated_annealing)