如何在PuLP问题中仅访问特定变量？

Question

In an LP model that I solve with PuLP in python I have two sets of decision variables, for example

#Variables x 
x = LpVariable.dicts("Decision_x",(range(3),range(3)),0,1,LpInteger)
#Variables y 
y = LpVariable.dicts("Decision_y",(range(3),range(3)),0,1,LpInteger)

After solving the model I am only interested in those variables where x[i][j] takes value 1. I know that with

for v in prob.variables():
    if v.varValue == 1:
        print(v)

I can print all variables with their value equal to one. Hence, all x and all y variables with their value equal to 1 are printed. How can I manage to access only the x variables so that the y variables do not get printed? I tried prob.variables(x) , or prob.variables()[x] but nothing has worked so far.

Then in a next step I would like to extract the indices of the x variables for which x is equal to 1. For example, if x[1][3] == 1 then I want to find those indices 1 and 3. Is their any clever way in PuLP to achieve this?

Answer 1

x is a dict. Given two indices i,j at x[i][j] you have a pulp.LpVariable .
You know in advance the indices of you x variable, so one way is for example the following

for i,j in itertools.product(range(3),range(3)):
    if x[i][j].varValue > 0:
        print((i,j), x[i][j].name, x[i][j].varValue)

or if you prefer to keep the indices:

x_vars_indices = [(i,j) for i,j in itertools.product(range(3),range(3)) if x[i][j].varValue > 0]

Another way is to iterate the nested dictionary x and get the variables, which are the values in the last layers of the dict.

x = {0: {0: Decision_x_0_0, 1: Decision_x_0_1, 2: Decision_x_0_2},...
                ^                  ^                   ^
                |                  |                   |
                              LpVariable