how to model a GEKKO constraint to guarantee the count of variables with same value > k

[ZiadJanpih]

x= [8,8,8,6,6,9,9,9] i want to make sure that x[i] is appeared at least k times in x for example : k =2 x is ok, but k=3 is not x[i] is always an integer

[shayandavoodii]

Hi, x represents the value of each variable?

[ZiadJanpih]

Hi Shayan, x is a vector of variables

[APMonitor]

One way is to create binary variables with conditional statements such as m.if3() statements:

from gekko import GEKKO
m = GEKKO()
# create x / xi arrays
x=[8,8,8,6,6,9,9,9]; n=len(x)
xi = [m.Param(i,lb=6,ub=9,integer=True) for i in x]
# count functions
bins = [6,7,8,9]; nb = len(bins)
bC = m.Array(m.Var,(nb,n))
for j,b in enumerate(bins):
    bL = [m.if3(xi[i]-(b-0.1),0,1) for i in range(n)]
    bU = [m.if3(xi[i]-(b+0.1),1,0) for i in range(n)]
    m.Equations([bC[j,i]==bU[i]*bL[i] for i in range(n)])
k = m.Array(m.Var,nb)
m.Equations([k[j]==m.sum(bC[j,:]) for j in range(nb)])
m.solve()
print('bC=',bC)
print('k=',k)

The result counts the number of elements in the bins [6,7,8,9] as k= [[2.0] [0.0] [3.0] [3.0]] for array [8,8,8,6,6,9,9,9]. You can add additional constraints to the variables k[i] and make xi a variable with xi = [m.Var(i,lb=6,ub=9,integer=True) for i in x]

 --------- APM Model Size ------------
 Each time step contains
   Objects      :            0
   Constants    :            0
   Variables    :          300
   Intermediates:            0
   Connections  :            0
   Equations    :          228
   Residuals    :          228

 Number of state variables:            292
 Number of total equations: -          228
 Number of slack variables: -          128
 ---------------------------------------
 Degrees of freedom       :            -64

 * Warning: DOF <= 0
 ----------------------------------------------
 Steady State Optimization with APOPT Solver
 ----------------------------------------------
Iter:     1 I:  0 Tm:      0.03 NLPi:    3 Dpth:    0 Lvs:    0 Obj:  0.00E+00 Gap:  0.00E+00
 Successful solution

 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :   6.839999998919666E-002 sec
 Objective      :   0.000000000000000E+000
 Successful solution
 ---------------------------------------------------

bC= [[[0.0] [0.0] [0.0] [1.0] [1.0] [0.0] [0.0] [0.0]]
 [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
 [[1.0] [1.0] [1.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
 [[0.0] [0.0] [0.0] [0.0] [0.0] [1.0] [1.0] [1.0]]]
k= [[2.0] [0.0] [3.0] [3.0]]

Could you post this question on StackOverflow with tag Gekko? This GitHub is typically for reporting and tracking bugs and development of feature requests.

[ZiadJanpih]

thank you for helping, I have posted it on StackOverflow-post

[APMonitor]

Thanks!