Hello, I'm currently using SAS 9.4 on Windows. I'm pretty new to OPTMODEL, I've tried to solve this myself, but I just can't seem to figure out how to do it. Essentially, I'm building 5 test forms from a pool of 136 items. I'm using a matrix x[136,5] of binary values that are 1 if the item is selected and 0 if not. Each item has a content domain it belongs to (A B C), and a 'height' value of a curve when used in a psychometric model. The sum of the items' curves create the form's curve.
This is an extension of a previous post from months ago that has some visuals of what the optimization is for and a reference to the optimization method when generating a single form: https://communities.sas.com/t5/Mathematical-Optimization/Proc-OPTMODEL-using-objective-in-4-constrai...
I'm trying to generate 5 forms with the objective:
Minimize:
Subject to:
- An item can appear a maximum of 3 times across the 5 forms
- 9 items from content domain A are selected, 9 from B, and 12 from C
- Maximum of 30 items per form (redundant with current setup)
- 2 constraints
con p16_TCC_pos and con p16_TCC_neg that help minimize deviation between a target test curve height (13.374) and the 5 optimally generated forms' curve values.
With just these constraints the code provided works, however, the last constraint I need is that any pair of forms can not have more than 7 items in common. I'm having problems getting this to work because I don't know how to apply the logic of the conditional compare while also using syntax appropriate for OPTMODEL into an impvar or constraint.
The logic I was thinking I could use to do this is along the lines of:
num count init 0;
for {c in compares} do;
for{j in 1..4, b in j+1..5} do; *for forms 12,13,14,15,23,24,25,34,35,45;
count=count+1;
if count>10 then leave;
for{i in ITEMS} do;
if x[i,j]*x[i,b]=1 then overlap[i,count]=1;
*if x[i,j]=1 and x[i,b]=1 then overlap[i,count]=1;
else overlap[i,count]=0;
put j b i;
end;
end;
end;Running the full code will put j b and i in the log, and it is what I expect. It cycles through form pairs, and their 136 items. I'm just not sure how I would implement this, or something that accomplishes the same thing, in an impvar/constraint. If someone would be able to help me figure this out I would very much appreciate it.
I'm including 3 datasets from my 'help' library that are used in my program below.
proc optmodel;
set <str> BINARIES; *essentially creates variable name list;
read data help.binarytest into BINARIES=[name]; *read dataset into a data matrix, with BINARIES variable names;
set <str> NUMERICS;
read data help.numerictest into NUMERICS=[name];
set <num> ITEMS;
num rnum {ITEMS}; *list of rnum values, {items} in length;
num binary {BINARIES, ITEMS} ; *Creates matrix size [binaries x items] ---tried labeling as var and binary, but when printing at end, does not populate with 1&0 only 0's;
num numeric {NUMERICS, ITEMS};
*probably a better way to do this, but this seems to work;
*read data from pool dataset and put into ITEMS numbered 1->N, put rnum, and binary and numeric data into data matrix;
read data help.test_ref_pool_cln into ITEMS=[_N_] rnum /*was uin instead of rnum*/
{i in BINARIES} <binary[i,_N_]=col(i)>
{i in NUMERICS} <numeric[i,_N_]=col(i)>;
set forms = 1..5;
set compares = 1..10;
*****************************************************************************************************************;
*model specification;
var x{ITEMS,forms} BINARY, y >=0, overlap{ITEMS,compares} BINARY; *x is selection 1/0, y is deviation;
min object=y;
*only impvar total_p16 is in actual use now;
*first theta point, P P^2 P^3;
impvar total_p16 {j in forms} = sum{i in ITEMS}numeric["p1_6",i]*x[i,j];
*Trying to get [items x comparisons] to then sum across items to get a row of 10 columns that contain how many items are in common
in each pair of forms.;
num count init 0;
for {c in compares} do;
for{j in 1..4, b in j+1..5} do;*for 12,13,14,15,23,24,25,34,35,45 items 1 to 136 do;
count=count+1;
if count>10 then leave;
for{i in ITEMS} do;
if x[i,j]*x[i,b]=1 then overlap[i,count]=1;
*if x[i,j]=1 and x[i,b]=1 then overlap[i,count]=1;
else overlap[i,count]=0;
put j b i;
end;
end;
end;
;
*Same item can't appear on more than 3 forms;
con max_three {i in items}: sum{j in forms} x[i,j] <=3;
*constraints for first theta point P();
con p16_TCC_pos {j in forms}: total_p16[j] <= 13.374+y; /*@-.5: P pos deviation*/
con p16_TCC_neg {j in forms}: total_p16[j] >= 13.374-y; /*@-.5: P neg deviation*/
*content constraints;
con Acon {j in forms}: sum{i in ITEMS}binary["con_A",i]*x[i,j] =9; *9 from content A;
con Bcon {j in forms}: sum{i in ITEMS}binary["con_B",i]*x[i,j] =9; *9 from content B;
con Ccon {j in forms}: sum{i in ITEMS}binary["con_C",i]*x[i,j] =12; *12 from content C;
*total number of items per form;
con max_items {j in forms}: sum{i in ITEMS}x[i,j]=30; /*select 30 items from the pool*/
*I want this to be the constraint that makes sure each column of the sums of overlap among pairs is less than 7;
*con overlap {c in compares}: overlap <=7;
solve obj object with milp;
create data testset3 from [id]={i in items}{j in forms} <col("form"||j)=x[i,j]>;
quit;
In the dataset test_ref_pool_cln's variables p2_6, p1_9, and p2_9 are other target curve values. These correspond to additional constraints I have omitted here because I'm having memory usage problems again, probably because I'm doing everything inefficiently, so they aren't used as part of the objective for now.
