Genetic Optimization with Probabilistic Constraints

Hello, I am modelling the removal of a contaminant in a pond. Given the large variability of environmental inputs, I run a Monte Carlo simulation which, given ranges of input variables and their individual probabilistic distributions, spits out an effluent value associated with the 95th percentile. I am designing my code to reduce the land use of the pond as much as possible while making sure it meets legal limits at a 95th percentile. The way my genetic optimization code is currently set up is the following:

Objective = @ Area f(Pond Dimensions)

A = [];

B = [];

Aeq = [];

Beq = [];

LB= [Pond_Dimension1min Pond_Dimension2min];

UB= [Pond_Dimension1max Pond_Dimension1max];

fun = @(x)this function runs a Monte Carlo simulation and compares the 95th percentile effluent concentration to the set limit concentration given the pond dimensions, making "c" negative if the limit is not met.

[a]=ga(Objective,3,A,B,Aeq,Beq,LB,UB,fun);

As it stands, the code does not seem to find the best solutions given the minimum and maximum pond dimensions. Is my nonlinear constraint set up wrong?

[Arvind Narayanan]

Hi,

Please refer the documentation for ga function: https://in.mathworks.com/help/gads/ga.html#d119e36098

Here, it lists that the non-linear constraints for the ga function are to be specified in such a way that it returns two arrays, c(x) and ceq(x).

c(x) is the array of nonlinear inequality constraints at x. ga attempts to satisfy

c(x) <= 0

for all entries of c.

ceq(x) is the array of nonlinear equality constraints at x. ga attempts to satisfy

ceq(x) = 0

for all entries of ceq. I hope you have taken this into consideration appropriately when specifying the arguments to the ga function.

Additionally, it would be a good idea for you to share the script that you are using to test the behavior of the ga function in this scenario. Please share the original script or a sample so that we can understand this further.

Thanks,

Arvind