"out of memory" error for defining variable and constraint

回答済み

2023年11月21日 00:28

There is a constraint that I should implement in my project which is x[i, j, s, t] + x[j, k, s, t] ) <= 1 for (i, j) in E0 for (j, k) in E0 for (s, t) in D_s_t, for this constraint, I define a variable like the following:

for i, j in E0:

for j, k in E0:

for (s, t) in D_s_t:

x[i, j, s, t] = model.addVar(vtype=gp.GRB.BINARY, name=f'x({i},{j},{s},{t})')

x[j, k, s, t] = model.addVar(vtype=gp.GRB.BINARY, name=f'x({j},{k},{s},{t})')

but since the E0 is very huge (its len is 2592), If I run this code, you will notice that all RAM in your pc will be occupied. Although my laptop has 20 GB RAM, all of it consumes. is there a better way to implement the variable that can run with lower RAM?

関連

5件のコメント

正式なコメント
Simranjit Kaur

Gurobi Staff

2026年11月13日 01:34
This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
Eli Towle

Gurobi Staff

2023年11月21日 17:19
Based how you described the problem, I assume there should be one variable for every combination of an element/pair from \(\texttt{E0}\) and an element/pair from \(\texttt{D_s_t}\). Is that correct? This would result in \(|\texttt{E0}| \cdot |\texttt{D_s_t}|\) variables. However, your code adds \(2 \cdot |\texttt{E0}|^2 \cdot |\texttt{D_s_t}|\) variables to the model. Many of these variables are duplicates of each other (meaning they use the same indices and have the same name), because you iterate over \(\texttt{E0}\) in its entirety twice.

Instead, I would define your variables using Model.addVars():
```
x = model.addVars(E0, D_s_t, vtype=gp.GRB.BINARY, name="x")
```
This creates a variable for every combination of an element in \(\texttt{E0}\) and an element in \(\texttt{D_s_t}\). The variables will be indexed and named accordingly.

Regarding your constraints:
```
x[i, j, s, t] + x[j, k, s, t]  <= 1 for (i, j) in E0 for (j, k) in E0 for (s, t) in D_s_t
```
Are you trying to model the following?

\begin{align*}x_{i,j,s,t} + x_{j,k,s,t} \leq 1 \qquad \forall (s, t) \in \texttt{D_s_t},\ (i, j, k) : (i, j) \in \texttt{E0},\ (j, k) \in \texttt{E0}\end{align*}

If so, then depending on how exactly you define \(\texttt{E0}\) and \(\texttt{D_s_t}\), this can be accomplished with code similar to the following:
```
E0 = gp.tuplelist(E0)
for s, t in D_s_t:
    for i, j in E0:
        for _, k in E0.select(j, "*"):
            m.addConstr(
                x[i, j, s, t] + x[j, k, s, t] <= 1,
                name=f"limit[{i},{j},{k},{s},{t}]",
            )
```
0
Arsalan Modirkhazeni

2023年11月23日 14:27
Thank you for your comment, it works well. However, I have another question that is related to the previous question. I have several constraints related to x an example:

I have two constraints on x with two different variables:

1. x[i, j , s, t] + x[j, k, s, t] <= 1 for each (s, t) in D_s_t for each (i, j) in E0 for each (j, i) in E0

2. x[i, j, s, t] * v[s, t] <= 10 for each (s, t) in D_s_t for each (i, j) in (E + E1 + E2)

how should I define x?

should I implement the x = model.addVars(E0 + E + E1+ E2, D_s_t, type = gp.GRB.BINARY, name = ''x"), and sometimes I've got an error duplicate Var because two sets (E0) and (E + E1 + E2) may have duplicate value.
0
Eli Towle

Gurobi Staff

2023年11月28日 00:41
If you intend to use the same \( x \) variable for each \((i, j)\) in \(\texttt{E0}\) that also exists in \(\texttt{E + E1 + E2}\), you could define the \( x \) variables using only the unique elements of the union of these lists. For example:
```
U = list(set(E0 + E + E1 + E2))
x = m.addVars(U, D_s_t, vtype=gp.GRB.BINARY, name="x")
```
0
Arsalan Modirkhazeni

2023年12月04日 22:58
Thank you for your comment. It perfectly works.
0

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"out of memory" error for defining variable and constraint

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