# How to define constraint in Optimization such that difference in value between two consecutive unknowns is not greater than 50%

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Ankur Shah on 6 Oct 2021
Edited: Matt J on 6 Oct 2021
Hello everyone,
I have prepared code in matlab for genetic algorithm from toolbox
The function code is a bit long. In summary, There are 30 unknowns with upper and lower bounds as 1.
How to apply a constraint while running such that difference in value between two consecutive unknowns obtained is not greater than 50% ?.
##### 2 CommentsShowHide 1 older comment
Ankur Shah on 6 Oct 2021
Yes, 50% greater than the previous.

Matt J on 6 Oct 2021
Here is a way to set up the constraint matrices using prob2matrices from,
x=optimvar('x',30,'Lower',0,'Upper',1);
Constraints.diffUB=diff(x)<=+0.5*x(1:end-1);
Constraints.diffLB=diff(x)>=-0.5*x(1:end-1);
p=prob2matrices({x},'Constraints',Constraints)
p = struct with fields:
intcon: [] lb: [30×1 double] ub: [30×1 double] Aineq: [58×30 double] bineq: [58×1 double] Aeq: [] beq: []
Matt J on 6 Oct 2021
The code in my original answer generates the matrices for you. You can use them directly in the call to ga:
x=optimvar('x',30,'Lower',0,'Upper',1);
Constraints.diffUB=diff(x)<=+0.5*x(1:end-1);
Constraints.diffLB=diff(x)>=-0.5*x(1:end-1);
p=prob2matrices({x},'Constraints',Constraints);
x=ga(fun,30,p.Aineq,p.bineq,p.Aeq,p.beq,p.lb,p.ub);

Bjorn Gustavsson on 6 Oct 2021
Perhaps a constraint-function like this would get the job done (might be used with fmincon for example):
function [c,ceq] = your_con(x,a,b)
if nargin < 3
b = 0.1;
end
if nargin < 2
a = 1/2;
end
dx = diff(x);
c = 2*abs(dx)./(max(abs(x(1:end-1))+abs(x((2:end))),...
max(b,...
max(abs(x(1:end-1)),abs(x(2:end)))...
)...
))-a;
ceq = [];
To read up on the details of using this read the help and documentation of fmincon.
HTH

R2020a

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