Having problems creating inequality constraints for genetic algorithm

Hi! I am having some problems with my GA, I use a fitness function that gives me the min cost of operation and creates values of power generated in each generator, in my case 6, to which i called Pg. My Pg will be a vector of 1x6 and for every value of Pg, i.e. Pg1,...,Pg6, I will have some prohibited operation zones: Pg1-> [210 240] [350 380]; Pg2-> [90 110] [140 160]; Pg3-> [150 170] [210 240]; Pg4-> [80 90] [110 120]; Pg5-> [90 110] [140 150]; Pg6-> [75 85] [100 105]; My problem is that every time I see people doing something with intervals it is usualy as boundaries, but I cant do it because I already have them as Pgmax for UB and Pgmin for LB. How can I create the constraints function in order to make these as prohibited zones for my Pg values? Thanks and Im sorry if I didnt explain something properly, I am still new to GA. EDIT: Im going to put some code in case I didnt explain myself properly.

    %%My main
    ...
    Pmin=[100  50   80   50   50   50 ];
    Pmax=[500   200   300   150   200   120];
    LB=Pmin;
    UB=Pmax;
    nvars=6;
    [Pg,Fval] = ga(ObjFcn,nvars,[],[],[],[],LB,UB,ConsFcn,Options);
 --------------
   %%My fitness function
   ...
   z=0;
   for i=1:1:6
      z=a(i)*(Pg(i)^2)+b(i)*Pg(i)+c(i)+abs(e(i)*sin(f(i)*(Pmin(i)-Pg(i))))+pen*
      (Pdemand-Ploss-sum(Pg))^2+z;
   end

Answer 1

[Alan Weiss]

You need to represent these nonconvex constraints either as nonlinear constraints OR reformulate your problem to have 2^6 different possibilities, and investigate all 2^6 = 64 possibilities.

1. For the nonlinear constraint approach, I will give you just one example, you generalize to the other constraints. For a 2-element real vector t with t(1) < t(2) define

function f = nomiddle(x,t)
f = (x-t(1))*(t(2)-x);

This f is positive when t(1) < x < t(2) and is negative otherwise. So it represents the constraint that x <= t(1) OR x >= t(2). So one of your constraints, that x is not in the region [240,350], could be

 function [c,ceq] = cons1(x)
 ceq = [];
 c = nomiddle(x,[240,350]);

2. Set your bounds to allow only the regions that are OK, such as x(1) is in [210 240], x(2) is in [140 160], etc. Do that for each of the 2^6 possibilities.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Luis Manito]

Thanks! I noticed you made a mistake in interpreting my problem. Those intervals (i.e. Pg3-> [150 170] [210 240]) are actually the ones that my vector cannot be in, so I just changed "c = nomiddle(x,[240,350])" with the right intervals "c = nomiddle(x,[210 240])" for example.

Now my problem is that there are still ocasions in that these constraints are violated, I did it like this:

    %values inside these intervals must not be used for Pg
    c = nomiddle(Pg(1),[210,240]); 
    c = nomiddle(Pg(1),[350,380]);

    c = nomiddle(Pg(2),[90,110]);
    c = nomiddle(Pg(2),[140,160]);

[Alan Weiss]

I don't understand what you mean with your code. If you have nonlinear constraints, you need to define a separate coordinate for each constraint, you can't just overwrite each c value with a new c as you seem to be doing. See Nonlinear Constraints.

By the way, it is easy to write a similar function that takes a 4-element ordered vector and makes a nonlinear constraint, such as

function f = nomiddle2(x,t)
f = (x-t(1))*(t(2)-x)*(t(3)-x)*(t(4)-x);

If x is smaller than t(1), and t(1) < t(2) < t(3) < t(4), then f < 0, meaning that is a feasible point. The function changes sign every time x crosses a t value, so it does what we want: has the intervals from t(1) to t(2) be disallowed, and from t(3) to t(4) be disallowed as well.

Alan Weiss

MATLAB mathematical toolbox documentation

[Luis Manito]

Ups sry I actually didnt implement it that way in my program, I did "c(1)=...; to c(6)=...;". Now in this new one you showed me I implemented it like this:

 c(1) = nomiddle(Pg(1),[210,240,350,380]);
 c(2) = nomiddle(Pg(2),[90,110,140,160]);
 c(3) = nomiddle(Pg(3),[150,170,210,240]);
 c(4) = nomiddle(Pg(4),[80,90,110,120]);
 c(5) = nomiddle(Pg(5),[90,110,140,150]);
 c(6) = nomiddle(Pg(6),[75,85,100,105]);

This way I should have no Pg values inside [t(1),t(2)] and inside [t(3),t(4)], however sometimes that doesnt happen and some intervals are violated. Perhaps it has something to do with my fitness function... Thanks for helping!

EDIT:

    %One of my results for Pg values 
(unfortunatly the values dont stay consistent for each run I do...)
    Pg = [408.450  185.710  241.536  112.851  199.396  102.224]

you can see Pg(4) and Pg(6) violate the intervals [110,120] and [100,105] respectively.

[Luis Manito]

nvm already figured the problem! Thank you!!

Answer 2

[ASIF]

I am also facing the same problem to implement these Prohibited operation zone values as; Pg1-> [210 240] [350 380]; Pg2-> [90 110] [140 160]; Pg3-> [150 170] [210 240]; Pg4-> [80 90] [110 120]; Pg5-> [90 110] [140 150]; Pg6-> [75 85] [100 105]; for 6 generators using LSA. My problem is that i want to try this vector values with ramp limit coefficnets. kindly help me in this to implement POZ values in LSA Code;