Originally posted by: michael_in_Boston

Hello,

I am trying to do create groups from which I pick features (one or more), but the feature(s) can only originate from one single group.

Example:

Group A = {feature1_A, feature2_A, feature3_A}

Group B = {feature1_B, feature2_B}

Group A + Group B <=1

So I would like to pick 1 or more features that belong either to A or B but not both.

How could I formulate such constraints in CPLEX? 

Much appreciate any hints or examples.

Best,

Michael

Originally posted by: Anjikum

Hello,

Following constraint formulation can help:

x1a=selecting feature 1 from group A

x1b=selecting feature 1 from group B and similarly other variables

ya = variable indicating selection of atleast one feature from group A

yb = variable indicating selection of  atleast one feature from group B

x1a+x2a+x3a <= 3*ya 

x1b+x2b <= 2*yb 

ya+yb<=1

x1a,x2a,x3z,x1b,x2b,ya,yb belongs to {0,1}

Above formulation might lead to none getting seleceted. If you want to ensure that, change ya+yb<=1 to ya+yb =1.

Best Wishes.