How to store time value to multidict form a constraint in Gurobi
回答済みHello
I need to create multidict variable that stores the arrival time of the truck in each node.
I expect values to store in a variable format something like this. TA = {(node,truck): time}
To find TA (arrival time) I have an equation (constraint): departure time truck at previous node + time between the previous node and this node
Part 1 = \( \sum_{ij}\ x_{ij}^h\ast d_{ij}^h/speed\ \ h\forall H \)
Waiting time = part2
Part 2 = \(\sum_{i}max\left(TA_i^h\right)–jTDjh+dij/speedxijhifoh!=ih∀H\)
\( x_{ij}^h \) decision variable if 1 truck travel at edge i,j otherwise 0
And start node and end node time of departure and arrival time = 0 for all truck
TA = model.addVars(node_list, truck, vtype=gp.GRB.CONTINUOUS, name="TA")
TD = model.addVars(node_list, truck, vtype=gp.GRB.CONTINUOUS, name="TD")
model.addConstrs(TA[origin[h],h] == 0 for h in truck)
model.addConstrs(TD[origin[h],h] == 0 for h in truck)
objective_second_part_1 = gp.LinExpr()
for edge in road_network.edges():
for h in truck:
objective_second_part_1 += x[edge][h] * road_network.get_edge_data(*edge)["weight"]/speed
objective_second_part_2 = gp.LinExpr()
for i in node_list:
for h in truck:
objective_second_part_2 += max(TA[i,h])- quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-98-03a0f644063a> in <module>
3 for i in node_list:
4 for h in truck:
----> 5 objective_second_part_2 += max(TA[i,h])- quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])
TypeError: 'Var' object is not iterable
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正式なコメント
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Gurobi Staff
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Hi John,
I guess that the term
max(TA[i,h])
shall be used to model the maximum of all \(\texttt{TA[i,h]}\) for a fixed \(\texttt{i}\).
Note that Gurobi's max_ function has an additional underscore and it requires a list of variables and not just a single one. Moreover, it has to be modeled via an auxiliary variable and an equality constraint. So very likely, your \(\texttt{for}\)-loop should read something like
for i in node_list:
max_list = []
for h in truck:
objective_second_part_2 -= quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])
max_list.append(TA[i,h])
aux = model.addVar(lb=-gp.GRB.INFINITY, name="auxVar_%d"%(i))
model.addConstr(aux == gp.max_(max_list), name="auxConstr_%d"%(i))
objective_second_part_2 += auxBest regards,
Jaromił0 -
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Hello Jaromił,
TA[i,h] = arrival time of truck at node i. That is calculatemodel.addConstrs(TA[origin[h],h] == 0 for h in truck)
model.addConstrs(TD[origin[h],h] == 0 for h in truck)
for j in nodelist:
for h in truck:
TA[i,h] = quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])And to find departure time of truck h at node i = max arrival time of all truck at node i
for i in nodelist:
for h in tuck:
model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))
TD[i,h] = auxobjective_second_part_2 += (TD[i,h]-TA[i,h] for i in nodelist for j in nodelist)
this is what I need.
please help me0 -
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Hi John,
As explained in my previous comment, the constraint
model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))
will not work because \(\texttt{TA[i,h]}\) is a single variable. However, to my understanding, you want to compute the maximum value of all truck at node \(\texttt{i}\). Thus the \(\texttt{for}\)-loop should be
aux = {}
for i in node_list:
max_list = []
for h in truck:
max_list.append(TA[i,h])
aux[i] = model.addVar(lb=-gp.GRB.INFINITY, name="auxVar_%d"%(i))
# add constraint aux_i = max(TA[i,0], TA[i,1],...)
model.addConstr(aux[i] == gp.max_(max_list), name="auxConstr_%d"%(i))The \(\texttt{for}\)-loop you are currently using
for i in nodelist:
for h in tuck:
model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))
TD[i,h] = auxjust sets \(TD_{i,h} = TA_{i,h}\) because \(\texttt{TA[i,h]}\) is one element and thus \(\max(TA_{i,h}) = TA_{i,h}\).
Best regards,
Jaromił0 -
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