def callback(cb: CallbackModel, where: Where):
if where == Where.PathMIPCuts:
epsilon = 1e-4
relax = cb.x
# Enumerate cuts for |S| = 2
for i in range(n)[1:-1]:
for j in range(n)[1:-1]:
# not depot nodes in S
if i == 0 or j == n - 1 or i == j:
continue
rhs = math.ceil((d[i] + d[j]) / Q)
lhs = 0
lhsIdxs = []
for e, edge in enumerate(E):
# inside S
if (i, j) == edge or (j, i) == edge:
continue
# if either end of edge is in S
if i == edge[0] or i == edge[1] or j == edge[0] or j == edge[1]:
lhs += relax[e]
lhsIdxs += [e]
if lhs < rhs - epsilon:
cb.addCut(xsum(g.vars[e] for e in lhsIdxs) >= rhs)
path = []
index = E.index((0, i))
path.append(index)
cost += c[index]
index = E.index((i, n - 1))
path.append(index)
cost += c[index]
cb.addPath(cost, path)
m.setCallback(callback)
# set partition constriants
for i in range(n)[1:-1]:
m += xsum(x * 1 for x in g.vars if i == x.source) == 1
# packing set
for i in range(n)[1:-1]:
m.addPackingSet([x for x in g.vars if i == x.source])
status = m.optimize()
# print(f"ObjectiveValue {round(m.objectiveValue, 1)}")
# get the variable values
# for var in m.vars:
# if var.x > 0:
# print(f"{var.name} = {round(var.x, 1)}")
# sum_(j) x_ji - sum_(j) x_ij = 0 , forall i
for i in range(n)[1:-1]:
expr = LinExpr()
[expr.addTerm(1, x) for x, e in zip(xsk, E) if e[1] == i]
[expr.addTerm(-1, x) for x, e in zip(xsk, E) if e[0] == i]
m.addConstr(expr == 0)
# sum_(j,n-1) x_j,n-1 = 1
expr = LinExpr()
[expr.addTerm(1, x) for x, e in zip(xsk, E) if e[1] == n - 1]
m.addConstr(expr + xFeasiblity == 1)
# capacity constraint
# sum_(ij) d_i * x_ij <= Q
m.addConstr(xsum(x * d[e[0]] for x, e in zip(xsk, E)) <= Q)
# time stamp per vertex
qt = [
m.addVar(lb=0, ub=max(b), obj=0, type="C", name=f"q_t_{i}_{k}")
for i in range(n)
]
# time winwos
# q_ik + t_ij - q_jk <= (1 - x_ijk)M , forall (i,j)
for j, e in enumerate(E):
bigM = b[e[0]] + t[j]
m.addConstr(qt[e[0]] * 1 - qt[e[1]] * 1 + xsk[j] * bigM <= bigM - t[j])
# a_i sum_(j) x_ijk <= q_ik
for i in range(n)[1:-1]:
expr = LinExpr()
# keep track of voyageEdges for constraints later
tmp = list([eid["index"] for eid in voyageEdgeIds])
for j, e in enumerate(es):
for h, eid in enumerate(tmp):
if g.edges[e]["index"] == eid:
voyageEdgeVarsIds[eid][i] = j
tmp.remove(eid)
break
# graph vars
vars = [gs[i].vars for i in range(k)]
# sum_( i,j \in delta+(o^k)) x_ijk = 1 , forall k
for i in range(k):
source = gs[i].source
m.addConstr(xsum((1, x) for x in vars[i] if source == x.source) == 1)
for j, ks in enumerate(voyageEdgeVarsIds):
expr = LinExpr()
for i, h in ks.items():
x = vars[i][h]
expr.addTerm(builder.demand["FFEPerWeek"][i], x)
m.addConstr(expr <= builder.capacity[j])
status = m.optimize()
# print(f"ObjectiveValue {round(m.objectiveValue, 5)}")
# get the variable values
# for var in m.vars:
# if var.x > 0:
# print(f"{var.name} = {round(var.x, 5)}")
# 0-1 Knapsack problem
from flowty import Model, xsum
from or_datasets import pisinger
bunch = pisinger.fetch_knapsack("small", instance="knapPI_1_50_1000_1")
name, n, c, p, w, z, x = bunch["instance"]
m = Model()
m.setParam("Algorithm", "MIP")
for i in range(n):
m.addVar(lb=0, ub=1, obj=-p[i], type="B")
m.addConstr(xsum(w[i] * v for i, v in enumerate(m.vars)) <= c)
status = m.optimize()
# print(f"ObjectiveValue {round(m.objectiveValue)} == {-z}")
# get the variable values
# for var in m.vars:
# if var.x > 0:
# print(f"{var.name} = {round(var.x, 1)}")
index = E.index((i, n - 1))
xEdges[index] = 1
cost += c[index]
cb.addSolution(cost, xEdges)
# Verify solution
if where == Where.PathMIPSolution:
x = cb.x # candidate solution
# check is solution is infeasible and skip it if so
isInfeasible = False
if isInfeasible:
cb.skip()
m.setCallback(callback)
# set partitioning constraints
for i in range(n)[1:-1]:
m.addConstr(xsum(1 * x for x in g.vars if i == x.source) == 1)
m.addPackingSet([x for x in g.vars if i == x.source])
status = m.optimize()
# print(f"ObjectiveValue {round(m.objectiveValue, 1)}")
# get the variable values
# for var in m.vars:
# if var.x > 0:
# print(f"{var.name} = {round(var.x, 1)}")