1. SCIP Optimization Suite1

2. SCIP Optimization Suite
Three main software
zimpl: Compiler of ZIMPL modeling language
soplex: LP solver (implementation of Simplex)
scip: An advanced implementation of B&B to solve ILP
All these are available in single packages
SCIP optimization suite
Source code
zimpl, soplex, scip are standalone applications
Binary (Linux & Windows)
Single executable scip application that is linked by zimpl & soplex 2

3. How Does It Work? As a programming library As a standalone solver
It has API, you can call the functions in C, C++
As a standalone solver
Develop a model in zimpl language
Compile/Translate your model: zimpl model.zpl
Solve it
LP problems: soplex model.lp
ILP, MIP problems: scip -f model.lp
scip by itself calls zimpl if the input file is not .lp
scip -f model.zpl 3

4. 4

5. What we need Parameters Variables Sets Objective function Constraints5

6. Sets
Set of numbers
Set of strings
Set of tuples 6

7. Set operations 7

8. {<1, “hi”>, <2, “hi”>, <3, “hi”>, <1, “ha”>, …}
{1, 6, 7, 8, 9} 8

9. Indexed Sets The arrays of ZIMPL Each element has its own index
A set indexes another set
Refer to i-th element by S[i]
Example
set I := {1, 2, 4};
set A[I] := <1> {10}, <2> {20}, <4> {30,40,50};
set B[ <i> in I] := {10 * i}; 9

10. Parameters set A := {1,2,3}; param B := 10;
param C[A] := <1> 10, <2> 20, <3> 30;
param D[A] := <1> 100 default 0;
param E := min A;
param F := max <i> in A : C[i]; 10

11. These operations are used in zimpl models to generate the numerical model.
Most operations are applicable only on parameters, cannot be used for variables, because they are not linear 11

12. Variables “real”, “binary”, or “integer” var x1; var x2 integer;
Default is “real”
var x1;
var x2 integer;
var x3 binary;
set A := {1,2,3};
var x4[A] real;
var x5[A * A] integer >=0 <= 10; 12

13. Objective “maximize” or “minimize” var x1; var x2; var x3;
maximize obj1: x1 + x2 + x3;
minimize obj2: 2*x1 + 3*x2; 13

14. Objective
set A := {1,2,3};
param B[A] := <1> 10, <2> 20, <3> 30;
var X[A];
maximize obj1: sum <i> in A: X[i];
minimize obj2: sum <i> in A: B[i] * X[i]; 14

15. Constraint subto name: constraint subto c1: x1 <= 10;
“<=“ , “=>”, “==“
There is not “>” and “<“
subto c1: x1 <= 10;
subto c2: x1 + x2 <= 20;
subto c3: x1 + x2 + x3 == 100; 15

16. Constraint
set A := {1,2,3};
param B[A] := <1> 10, <2> 20, <3> 30;
var X[A];
subto c1: forall <i> in A: X[i] <= B[i]; 16

17. Expressions forall expression sum expression if expression
forall <i> in S: x[i] <= b[i];
sum expression
sum <i> in S: x[i];
if expression
forall <i> in S: x[i] <= if (i mod 3 == 0) then A[i] else B[i] end; 17

18. Example 18

19. param c[I] := <1> 1, <2> 20, <3> 300;
set I := {1,2,3};
set J := {1,2};
param c[I] := <1> 1, <2> 20, <3> 300;
param A[J * I] := <1,1> 1, <1,2> 2, <1,3> 3, <2,1> 30, <2,2> 20, <2,3> 10;
param b[J] := <1> 20, <2> 200;
var X[I];
maximize obj: sum <i> in I: c[i] * X[i];
subto const: forall <j> in J:
sum <i> in I: A[j,i] * X[i] <= b[j]; 19

20. Realistic Problems A model for the problem Multiple instances
Each instance has its own data
Separation between model and data
Create a general model
Read data from file 20

21. Reading Set and Parameters from file
“read filename as template”
set A := {read "a.txt" as "<1n>"};
a.txt 1 2 3 4 5 21

22. set A := {read "a.txt" as "<1n>"};
param B[A] := read "b.txt" as "<1n> 2s";
a.txt b.txt aa bb cc 22

23. 23

24. set I := {read "I.txt" as "<1n>"};
set J := {read "J.txt" as "<1n>"};
param c[I] := read "c.txt" as "<1n> 2n";
param A[J * I] := read "A.txt" as "<1n,2n> 3n";
param b[J] := read "b.txt" as "<1n> 2n";
var X[I];
maximize obj: sum <i> in I: c[i] * X[i];
subto const: forall <j> in J:
sum <i> in I: A[j,i] * X[i] <= b[j]; 24

25. 25

26. Integrality  Complexity: An Example
Consider the LP problem
I = 1000
J = 100
If variables are “real”
Solution time = 0.21 sec.
Objective =
If variables are “integer”
Solution time = sec.
Objective = 1724 26