@Carl Love 103 websites

@Carl Love thank you so much you have been so helpful. thanks again

@Carl Love thanks, i ran the code on maple 2019 but  it gave several errors please see the errors :

Error, Slice is not a command in the ListTools package
Error, bad index into Array
Error, (in Optimization:-LPSolve) constraints must be specified as a set or list of equalities and inequalities
Error, invalid input: eval received sol[2], which is not valid for its 2nd argument, eqns

Group groups:
Error, improper op or subscript selector
Objective Value (Minimized Maximum Website Overlap): 
Error, (in fprintf) integer expected for integer format

Download MinimaxILP1.mw

@mmcdara i am a newbie, thanks for your help. 

@Carl Love please have you been able to fix the bug

@Carl Love ok. I will wait for the update and thanks again for your help.

@Carl Love the group creation using partition has to be done automatically with members sequentially generated, this is because a large number is been considered for profiles. expected profile is 256 and 16 groups, furthermore i need to be able to vary the entries numbers of profiles, group number to get the number of members in the group, as well as the websites by . also i checked for the article but i cannot find it, is it a journal publication. 

@Carl Love thank you very much, i will make recourse to the document and also for the codes, i will run them and revert. thanks so much again

@Carl Love i am not able to do the formulation algebraically of some constraints to capture the role of groups. can you assist with it.

for clarity: the profiles are sequentially assigned to groups and the number of profiles in the group is derived by dividing the total number of profiles by the total number of groups.

my actual constraint is: every group must be assigned to every website (that is every website must have a representation from every group) but only one profile will represent the group on each website. the current formulation still allows all members of a group to be assigned to a single website and some groups have no representation at all, which negates my constraints.

what this means in an example: assuming i have 4 profiles, 3 websites and these 4profiles are divided into 2 groups, so that group A:= {1,2}, group B:={3,4}. on all three websites, group A and B must be present but will be represented by either 1 or 2 for A and 3 or 4 for B on each website but not the two elements from  each group. my goal is to minimize the maximum overlap between any two profiles the rest of the formulation seem correct to me.

please kindly assist me i have been battling with this for sometime now and not arriving at my expected result.

@Carl Love num_group is relevant as the constraints hang on the representation of each group on a website by a member of a group. furthermore it is supposed to be only one group member that is to represent each group, but the output is not enforcing this, hence there are some groups not represented on each website in the assignment.

@Carl Love i have ran the codes, while it worked it is not enforcing my constraint: of each group must be represented on every website and  only one of the members of that group is to represent the group. please if you could help with looking at my constraints if the current structure satisfies my desired constraint. I am quite new to both optimization and maple. thanks

@mmcdara thanks i didnot see the comments except that you asked me to upload the .mw file. I thank you for taking time to go through the file. Thanks so much.

@Carl Love saying thank you again for the help. I have been on it for sometime and made no head way. thanks again.

@Carl Love thank you so much for this I will work and this and revert on the output

@mmcdara thanks for the response, i will do the upload now.