How to formulate conditional constaints

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Gurobi Staff

2025年11月16日 23:37

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Jaromił Najman

Gurobi Staff

2022年05月17日 06:10 編集済み

In the following I assume that all \(B2R_{b,i}\) variables are binary variables. For simplicity, I will omit the \(b\) index.

First, we define an auxiliary integer variable \(x \in \{0,\dots,r\}\) and the equality constraint

\[x = \sum_{i=0}^{r-1} B2R_{i}\]

We model the statement if \(x=1\) then \(y=1\) and \(y=0\) else.

\[\begin{align*}
y + 1.5y^+ \leq x &\leq 0.5 y^- + y + r y^+\\
y^- + y^+ + y &= 1\\
y^-,y^+, y &\in \{0,1\}
\end{align*}\]

You can now use Gurobi's indicator constraint to model

\[y = 1 \rightarrow \text{Constraint-1}\]

From the above, we know that \(y^+=1\) if \(x \geq 2\). You can introduce an additional binary variable \(z\) and use Gurobi's And Constraint to model

\[z= B2R_{r} \land y^+\]

and then use Gurobi's indicator constraint to model

\[z = 1 \rightarrow \text{Constraint-2}\]

Best regards,
Jaromił

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Deepak Nagar

2022年05月17日 04:34

Thank you jaromil for the solution. I am facing some challenge while implementation, in the following part

x = model.addVars(lb=0, ub=10, vtype=GRB.INTEGER, name="x")

for b in range(self.no_of_bags):
   for r in range(self.no_of_rooms):
      self.model.addConstr(self.x == gp.quicksum([self.b2r[(self.bag_id[b], self.room_id[i])]
      for i in range(r)]))

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Jaromił Najman

Gurobi Staff

2022年05月17日 06:20

Hi Deepak,

You have to introduce a new \(x,y,y^+,y^-\) variable for every loop iterate, i.e., for every index \(b\) and \(r\).

So your code should look something like

import gurobipy as gp
from gurobipy import GRB

B = 3
R = 4
m = gp.Model()

btwor = m.addVars(B, R, vtype=GRB.BINARY, name="b2r")
x     = m.addVars(B, R, ub=R, vtype=GRB.INTEGER, name="x")
y     = m.addVars(B, R, vtype=GRB.BINARY, name="y")
ym    = m.addVars(B, R, vtype=GRB.BINARY, name="ym")
yp    = m.addVars(B, R, vtype=GRB.BINARY, name="yp")
z     = m.addVars(B, R, vtype=GRB.BINARY, name="z")

for b in range(B):
  for r in range(2,R):
    m.addConstr(x[b,r] == gp.quicksum(btwor[b,i] for i in range(r-1)), name="x_eq_sum_%d_%d"%(b,r))
    m.addConstr(y[b,r] + 1.5 *yp[b,r] <= x[b,r], name="aux_leq_constr_%dd_%d"%(b,r))
    m.addConstr(x[b,r] <= 0.5*ym[b,r] + y[b,r] + r*yp[b,r], name="aux_geq_constr_%dd_%d"%(b,r))
    # here you have to introduce your constraint1
    m.addConstr((y[b,r] == 1) >> (constraint1), name="constraint1_indicator_%d_%d"%(b,r))

    m.addGenConstrAnd(z[b,r], [btwor[b,r],yp[b,r]], name="andconstr_%d_%d"%(b,r))
    # here you have to introduce your constraint2
    m.addConstr((z[b,r] == 1) >> (constraint2), name="constraint2_indicator_%d_%d"%(b,r))

m.write("myLP.lp")

Note that you still have to adjust a few things, because I just used some fixed values for your \(b\) and \(r\) indices.

Best regards,
Jaromił

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Deepak Nagar

2022年05月22日 03:16

Thanks for the reply. It worked.

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Deepak Nagar

2022年05月25日 04:10

Hi jaromil,

I am not able to define the following constraint

Here B2R is binary and others are constant, can you please help me to define this

self.model.addConstr((self.z2[(b, r)] == 1) >>
                     (b2r[(b, r)] * d[r]) <= gp.min_((c[b] + 100), (c[b] + 100 + Q * (s[r] - gp.max_(b2r[(b, i)] * e[i] for i in range(r))))

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Jaromił Najman

Gurobi Staff

2022年05月25日 12:38

Hi Deepak,

When you are using one of the general constraints such as max or min, you have to introduce auxiliary variables for all of your linear expressions passed as arguments to the general function. In you case, you have to introduce an auxiliary variable for every \(z_i = B2R_{b,r} \cdot E_i \) for every \(i\) and an additional variable holding the result of the \(\max\) function. Your code might look something like

z = self.model.addVars(lb=-GRB.INFINITY, name="auxvar")
self.model.addConstrs(z[i] == b2r[(b, i)] * e[i] for i in range(r), name="aux_constr")
auxmax = self.model.addVars(lb=-GRB.INFINITY, name="auxmax)
self.model.addConstr(auxmax = gp.max_(z), name="max_constr")

The min function works analogously.

Best regards,
Jaromił

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Deepak Nagar

2022年07月08日 10:13

Hello Jaromił,

I am try to formulate the following constraint but getting failed optimization error, can you please help me in this regards.

thanks

formulation:

code:

b2r = model.addVars(b, r, vtype=GRB.BINARY, name="B2R")
x = model.addVars(b, r, ub=10, vtype=GRB.INTEGER, name="x")
y = model.addVars(b, r, vtype=GRB.BINARY, name="y")
ym = model.addVars(b, r, vtype=GRB.BINARY, name="ym")
yp = model.addVars(b, r, vtype=GRB.BINARY, name="yp")
z1 = model.addVars(b, r, vtype=GRB.BINARY, name="z1")
z2 = model.addVars(b, r, vtype=GRB.BINARY, name="z2")
t1 = model.addVars(b, vtype=GRB.CONTINUOUS, name="t1")
t2 = model.addVars(b, r, vtype=GRB.CONTINUOUS, name="t2")
t3 = model.addVars(b, r, vtype=GRB.CONTINUOUS, name="t3")
new = model.addVars(b, r, vtype=GRB.CONTINUOUS, name="new")
E = model.addVars(b, ii, vtype=GRB.INTEGER, name="E")
et = model.addVars(b, ii, vtype=GRB.CONTINUOUS, name="et")

for b in range(bags):

model.addConstr(t1[b] == cap[b] * (100 - margin) / 100)
ii = 0

for r in range(balls):

model.addConstr(x[b, r]
== gp.quicksum([b2r[b, i] for i in range(r + 1)]))

model.addConstr(y[b, r] + 1.5 * yp[b, r] <= x[b, r])

model.addConstr(x[b, r] <= 0.5 * ym[b, r] + y[b, r] + r * yp[b, r])

model.addGenConstrAnd(z1[b, r], [b2r[b, r)], y[b, r]])

# Here introduce constraint-1
model.addConstr((z1[b, r] == 1) >>
(E[b, ii] == cap[b] * (C[b] - margin) / 100 - D[r] * F[b, r)]))

model.addConstr((z1[b, r] == 1) >> (et[b, ii] == end[r]))

model.addConstr((z1[b, r] == 1) >> (b2r[b, r] * D[r] * F[b, r] <=
E[b, ii] + D[r] * F[b, r]))

model.addGenConstrAnd(z2[b, r], [b2r[b, r], yp[b, r]])

# Here introduce constraint-2
model.addConstr((z2[b, r] == 1) >> (ii == ii + 1))

model.addConstr((z2[b, r] == 0) >> (t2[b, r] == 0))

model.addConstr((z2[b, r] == 1) >> (t2[b, r] == E[b, ii - 1] + Q * (start[r] - et[b, ii - 1])))

max_list = [t2[b, r], t1[b, r]]

model.addGenConstrMin(t3[b, r], max_list)

model.addConstr((z2[b, r] == 1) >> (new[b, ii] == t3[b, r]))

model.addConstr((z2[b, r] == 1) >> (E[b, ii] == new[b, ii] - D[r] * F[b, r]))

model.addConstr((z2[b, r] == 1) >> (et[b, ii] == end[r]))

model.addConstr((z2[b, r] == 1) >> (b2r[b, r] * D[r] * F[b, r] <= E[b, ii] + D[r] * F[b, r]))

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Jaromił Najman

Gurobi Staff

2022年08月09日 08:09

Hi Deepak,

What exactly do you mean by a "failed optimization error"? Do you mean that your model is declared to be infeasible? If yes, then the article How do I determine why my model is infeasible? should be helpful.

Best regards,
Jaromił

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Deepak Nagar

2022年08月25日 07:06

Hi Jaromił,

I am getting the following error

(E[b,ii] ==
KeyError: ('120', 0)

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Jaromił Najman

Gurobi Staff

2022年08月25日 07:11

Hi Deepak,

The error means that you are trying to access the value \(\texttt{E[120,0]}\) which is not defined. From your post, it is not evident what your \(b\) and \(ii\) are. You should try removing parts of the code containing \(\texttt{E[,]}\) to locate the source of error.

Best regards,
Jaromił

0

How to formulate conditional constaints

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