I do not know how code this model?
回答済みI want to write a Python code for the mentioned model:
where the p, y, and p_bar are the variables and the others are the parameters and t is:0,1,...,6 and j is 1,2,3.
I wrote the code as:
import numpy as np
import pandas as pd
import scipy.sparse as sp
import gurobipy as gp
from gurobipy import *
T=7
n = 3
m=gp.Model('Initial')
p = {}
for j in range(1,4):
for t in range(T):
p[j,t] = m.addVar(vtype=gp.GRB.BINARY,
name='p'+str(j)+'_'+str(t))
pm = {}
for j in range(1,4):
for t in range(T):
pm[j,t] = m.addVar(vtype=gp.GRB.BINARY,
name='pm'+str(j)+'_'+str(t))
v = {}
for j in range(1,4):
for t in range(T):
v[j,t] = m.addVar(vtype=gp.GRB.BINARY,
name='v'+str(j)+'_'+str(t))
y = {}
for j in range(1,4):
for t in range(T):
y[j,t] = m.addVar(vtype=gp.GRB.BINARY,
name='y'+str(j)+'_'+str(t))
z = {}
for j in range(1,4):
for t in range(T):
z[j,t] = m.addVar(vtype=gp.GRB.BINARY,
name='z'+str(j)+'_'+str(t))
c = np.array([5.0, 15.0, 30.0])
cU = np.array([800.0, 500.0, 250.0])
Pmin = np.array([80.0, 50.0, 30.0])
Pmax = np.array([300.0, 200.0, 100.0])
SU = np.array([100.0, 70.0, 40.0])
SD = np.array([80.0, 50.0, 30.0])
RU = np.array([50.0, 60.0, 70.0])
RD = np.array([30.0, 40.0, 50.0])
TU = np.array([3.0, 2.0, 1.0])
TD = np.array([2.0, 2.0, 2.0])
for t in range(0,7):
R= [0,10,10,10,10,10,10]
D= [0, 240, 250, 200, 170, 230, 190]
DR = list(map(lambda x,y: x+y, DD,R))
m.setObjective((gp.quicksum((5 * p[1,t]+ 15 * p[2,t]+ 30 * p[3,t] + 800 * y[1,t]+ 500 * y[2,t]+ 250 * y[3,t])
for t in range(1,7))), GRB.MINIMIZE)
for t in range(1,7):
m.addConstr(((gp.quicksum(p[j,t]) for j in range(1,4))) == (D[t]))
Questions:
1)
BUT I DO NOT KNOW HOW TO WRITE A CODE FOR THE SECOND CONSTRAINT.
2)
How to write a code for this constraint:
Would you help me?
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Gurobi Staff
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These constraints:
for t in range(1,7):
m.addConstr(((gp.quicksum(p[j,t]) for j in range(1,4))) == (D[t]))do not do what you want. You should move the \( \texttt{for j in range(1, 4)} \) into the quicksum() function:
for t in range(1, 7):
m.addConstr(gp.quicksum(p[j, t] for j in range(1, 4)) == D[t])Additionally, \( T = \{0, \ldots, 6\} \), but you only add these constraints for the set \( \{1, \ldots, 6\} \). The summation in your objective is similar. So the mathematical formulation and the code are inconsistent.
The second constraint family can be written in a similar way as the first, assuming \( \texttt{pm} \) corresponds to \( \bar{p} \) in the model formulation:
for t in range(T):
m.addConstr(gp.quicksum(pm[j, t] for j in range(1, 4)) >= D[t] + R[t])For the last constraint family, you should add the constraint for all \( t \in T \setminus \{0\} \) instead of for all \( t \in T \). The constraint for \( t = 0 \) doesn't make sense, because you use \( t - 1 \) to index \( p \) and \( v_j \). Note that you have to be careful how you index \( R_j^U \) and \( S_j^U \) in the code, since Python uses zero-based indexing (\( \{0, 1, 2\} \)), but \( J = \{1, 2, 3\} \):
for t in range(1, T):
for j in range(1, 4):
m.addConstr(p[j, t] - p[j, t-1] <= RU[j-1] * v[j, t-1] + SU[j-1] * y[j, t])You can verify the model is written correctly by writing an LP file to disk for manual inspection:
m.write('mymodel.lp')A couple of comments that could help make your code more concise:
- The code would be easier to read if you define \( \texttt{T = range(7)} \) and \( \texttt{J = range(1, 4)} \) at the beginning. Then, you can just loop over \( \texttt{T} \) and \( \texttt{J} \) in the code. This also matches the formulation better, where \( T \) is a set rather than a number.
- You can use Model.addVars() to add each set of variables in a single line and obtain a tupledict storing variable objects.
E.g.:
T = range(7)
J = range(1, 4)
p = m.addVars(J, T, vtype=gp.GRB.BINARY, name='p')1 -
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Thank you very much. It works nicely.
Best Wishes to you Eli.
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