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GROUPING.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GROUPING
* Problem :
* *********
*
* A nonlinear formulation of a 0-1 combinatorial problem
* which can be described as grouping and clustering.
* This version of the problem consists in grouping 20 cans
* into 5 groups and the objective is to obtain groups that
* are as homogeneous as possible with respect to the characteristics
* of the cans.
* Note that the initial point is feasible.
* This problem is the contribution of a LANCELOT user in order to fulfill
* the package licence agreement.
* Source :
* D. Tuyttens, M. Pirlot, J. Teghem, E. Trauwaert and B. Liegeois,
* "Homogeneous grouping of nuclear fuel cans through simulated
* annealing and tabu search",
* Annals of Operations Research 50 (1994) 575-607.
* SIF input: D. Tuyttens (FPMs, Mons, Belgium) Dec 1994.
* classification SQR2-MN-100-125
* Problem parameters : Number of cans, groups and characteristics
IE 1 1
IE LOTS 5
IE POTS 20
IE CAR 2
* The cans and their characteristics
* First characteristic
RE T1,1 4.37
RE T2,1 4.56
RE T3,1 4.26
RE T4,1 4.56
RE T5,1 4.30
RE T6,1 4.46
RE T7,1 3.84
RE T8,1 4.57
RE T9,1 4.26
RE T10,1 4.37
RE T11,1 3.49
RE T12,1 4.43
RE T13,1 4.48
RE T14,1 4.01
RE T15,1 4.29
RE T16,1 4.42
RE T17,1 4.23
RE T18,1 4.42
RE T19,1 4.23
RE T20,1 3.49
* Second characteristic
RE T1,2 5.23
RE T2,2 5.74
RE T3,2 4.93
RE T4,2 5.74
RE T5,2 5.19
RE T6,2 5.46
RE T7,2 4.65
RE T8,2 5.27
RE T9,2 5.57
RE T10,2 5.12
RE T11,2 5.73
RE T12,2 5.45
RE T13,2 5.42
RE T14,2 4.05
RE T15,2 4.26
RE T16,2 4.58
RE T17,2 3.94
RE T18,2 4.18
RE T19,2 4.18
RE T20,2 5.89
* Average characteristics
RE XM1 17.1
RE XM2 20.1
* Variables of the problem
* X(j,k) = 1 can j belongs to group k
* = 0 otherwise
VARIABLES
DO J 1 POTS
DO K 1 LOTS
X X(J,K)
ND
* Objective function and Constraints
GROUPS
DO K 1 LOTS
DO I 1 CAR
DO J 1 POTS
ZN OBJ(K,I) X(J,K) T(J,I)
ND
* Linear constraints
DO K 1 LOTS
DO J 1 POTS
XE CL1(K) X(J,K) 1.0
ND
DO J 1 POTS
DO K 1 LOTS
XE CL2(J) X(J,K) 1.0
ND
* Non-Linear constraints
DO J 1 POTS
DO K 1 LOTS
XE CNL(J,K)
ND
* The constants of the problem.
CONSTANTS
RE POTLOT 4.0
DO K 1 LOTS
DO I 1 CAR
Z GROUPING OBJ(K,I) XM(I)
ND
DO K 1 LOTS
Z GROUPING CL1(K) POTLOT
ND
DO J 1 POTS
X GROUPING CL2(J) 1.0
ND
* The bounds on the variables
BOUNDS
DO J 1 POTS
DO K 1 LOTS
XL GROUPING X(J,K) 0.0
XU GROUPING X(J,K) 1.0
ND
* The starting point
START POINT
DO J 1 POTS
DO K 1 LOTS
XV GROUPING X(J,K) 0.0
ND
* A feasible solution
* This solution consists into setting the first 4 cans in
* group 1 and the next 4 ones in the next group and so on.
XV GROUPING X1,1 1.0
XV GROUPING X2,1 1.0
XV GROUPING X3,1 1.0
XV GROUPING X4,1 1.0
XV GROUPING X5,2 1.0
XV GROUPING X6,2 1.0
XV GROUPING X7,2 1.0
XV GROUPING X8,2 1.0
XV GROUPING X9,3 1.0
XV GROUPING X10,3 1.0
XV GROUPING X11,3 1.0
XV GROUPING X12,3 1.0
XV GROUPING X13,4 1.0
XV GROUPING X14,4 1.0
XV GROUPING X15,4 1.0
XV GROUPING X16,4 1.0
XV GROUPING X17,5 1.0
XV GROUPING X18,5 1.0
XV GROUPING X19,5 1.0
XV GROUPING X20,5 1.0
* The nonlinear elements functions
ELEMENT TYPE
EV BIN XX
ELEMENT USES
DO J 1 POTS
DO K 1 LOTS
XT BEL(J,K) BIN
ZV BEL(J,K) XX X(J,K)
ND
* The group functions
GROUP TYPE
GV SQUARE ALPHA
GROUP USES
DO K 1 LOTS
DO I 1 CAR
XT OBJ(K,I) SQUARE
ND
DO J 1 POTS
DO K 1 LOTS
XE CNL(J,K) BEL(J,K) 1.0
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GROUPING
INDIVIDUALS
T BIN
F XX * ( XX - 1.0 )
G XX 2.0 * XX - 1.0
H XX XX 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS GROUPING
INDIVIDUALS
T SQUARE
F ALPHA * ALPHA
G 2.0 * ALPHA
H 2.0
ENDATA