Dear ALL,
Part 1: Problem Statement
(1) I have an objective function, which is calculated from the simulation results of an external executable. That is to say, I don't have the exact formula for my objective function. Therefore, I don't know whether it is smooth or not.
(2) I totally have 8 parameters to optimize:
4 discrete parameters: (a) Opt_PerfNo (4 variables), (b) Opt_PerfDia (4 variables), (c) Opt_ProppSize (1 variable), (d) Opt_ProppDen (1 variable)
4 continous parameters/variables: (e) Opt_ClusterSpacing (1 variable), (f) Opt_MaxInjRate (1 variable), (g) Opt_MaxPropConc (1 variable), (h) Opt_RampUpSpeed (1 variable)
Note 0: For parameter (a) and (b), each parameter will have 4 variables. Therefore, totally, I have 14 (=4+4+1+1+1+1+1+1) variables.
Note 1: Please note that sometimes I might optimize all the variables, but sometimes I might ONLY optimize one variable, eg., 1 discrete variable.
Note 2: (f) (g) (h) (the last three variables) must be optimized together. That is to say, I have ONLY two options: (1) optimize (f) (g) (h) together; (2) (f) (g) (h) all these three are not optimized.
(3) Linear inequality constraint
I will have this constraint ONLY when I choose to optimize: (a) or (f,g,h) or both (a) and (f,g,h).
(4) Non-linear inequality constraint
I will have this constraint ONLY when I choose to optimize (f,g,h).
I want to run this optimization in a systematic way (more efficient way).
Part 2: Motivation
Previously, I always choose to run Genetic Algorithm (GA) to do the optimization. Then, I realized one problem.
For example, I am optimizing ONLY 1 discrete variable (parameter (d)) and I am giving GA two options.
Then, I thought GA only needs to run 2 cases since I only give it 2 options, and then compare the objective function values of these two cases and get the optimal solution.
However, GA actually runs a lot of cases, which is a waste of time.
Essentially, if I ONLY optimize parameter (d), then, according to the Problem Statement in Part 1, I don't have any constraints at all.
My point here is, sometimes, if I choose to optimize a lot of parameters, then my problem would be very complex, then at some point the only option I have is to use GA. However, in some cases, if I choose to optimize only several of them, then my problem would be degraded to be simple ones, then GA is not necessary at all.
Therefore, I want to do my optimization in a more efficient way.
Part 3: My Current Idea and Questions
My current strategy is as follows (Any comments and suggestions would be greatly appreciated!!!):
(1) If I only optimize (e), which is a continuous variable
Then I don't have any constraints.
Q1: Which optimization method I should use? Is GA a good option?
(2) If I only optimize (f,g,h), which are three continuous variables
Then I will have both the linear and non-linear constraints.
Q2: Which optimization method I should use? Is GA a good option?
(3) If I only optimize (b) and/or (c) and/or (d), which means I only have discrete variables
Then I I don't have any constraints.
Actually, in these cases, I can calculate the total number of valid combinations of variables based on the options of each parameter.
For example, if (b) has 8 options, (c) has 5 options, (d) has 4 options, then the total number of valid combinations = 8^4 * 5 * 4 = 81,920.
Usually, one run of my external executable will take around 50 seconds.
Then, the first idea in my mind is, wow, that's a lot of cases! Then, it is impossible to run all the forward models... Then let's use GA!!
Q3: Is GA a good option?
However (second thought...), if I only optimize (c) and/or (d), in this case, total number of valid combinations = 5 * 4 = 20.
Then, I would say, please run all the 20 cases of forward model and find the global optima. But how?
Q4: Am I correct?
Then, I would do like this (please remember that here I don't have any constraints):
Step 1: based on the options the user gives, I will first calculate the total number of valid combinations = A.
Step 2: Is A > 200 (Q5: how to choose this threshold)?
If "yes", please run GA. Q6: Is GA a good option? How about pattern search? Or Mixed-Integer Linear Programming?
If "no", please run all the forward models. Q7: But how? I mean for example I have 150 valid combinations, how could I run all these cases one by one?
Q8: What do you think of this strategy?
(4) If I choose to optimize (a)
Then I will have the linear constraint.
For example, if (a) has 7 options, then the total number of valid combinations = 7^4 = 2401.
Q9: Is GA a good option? How about pattern search? Or Mixed-Integer Linear Programming?
Any comments and suggestions would be greatly appreciated!
Thanks in advance!
