def pyomo_create_model(options=None, model_options=None):
if model_options is None:
model_options = Bunch()
if model_options.type is None:
model_options.type = 'fixed_set_size'
#
# m - number of elements
#
m = 100 if model_options.m is None else model_options.m
#
# n - number of sets
#
n = 200 if model_options.n is None else model_options.n
seed = 9090 if model_options.seed is None else model_options.seed
random.seed(9090)
#
if model_options.type == 'fixed_set_size':
#
# p - fixed number elements per set
# rho - fixed fraction of elements per set
#
p = model_options.p
if p is None:
if model_options.rho is None:
p = int(math.ceil(m * 0.7))
else:
p = int(math.ceil(m * model_options.rho))
#
def S_rule(model):
ans = set()
for j in range(1, n + 1):
tmp = list(range(1, m + 1))
random.shuffle(tmp)
for i in range(0, p):
ans.add((tmp[i], j))
return ans
elif model_options.type == 'fixed_element_coverage':
#
# p - fixed number of sets that cover each element
# rho - fixed fraction of sets that cover each element
#
p = model_options.p
if p is None:
if model_options.rho is None:
p = int(math.ceil(n * 0.4))
else:
p = int(math.ceil(n * model_options.rho))
#
def S_rule(model):
ans = set()
for i in range(1, m + 1):
tmp = list(range(1, n + 1))
random.shuffle(tmp)
for j in range(0, p):
ans.add((i, tmp[j]))
return ans
elif model_options.type == 'fixed_probability':
#
# rho - probability of selecting element for a set
#
rho = 0.3 if model_options.rho is None else model_options.rho
#
def S_rule(model):
ans = set()
for j in range(1, n + 1):
for i in range(1, m + 1):
if random.uniform(0, 1) < rho:
ans.add((i, j))
return ans
elif model_options.type == 'fixed_fill':
#
# rho - |S|/(I*J)
#
rho = 0.3 if model_options.rho is None else model_options.rho
#
def S_rule(model):
ans = set()
for j in range(1, n + 1):
for i in range(1, m + 1):
if random.uniform(0, 1) < rho:
ans.add((i, j))
return ans
#
# CREATE MODEL
#
model = ConcreteModel()
#
# (i,j) in S if element i in set j
#
model.S = Set(dimen=2, initialize=S_rule)
#
# Dynamically create the I and J index sets, since
# some rows or columns of S may not be populated.
#
def I_rule(model):
return set((i for (i, j) in model.S))
model.I = Set(initialize=I_rule)
def J_rule(model):
return set((j for (i, j) in model.S))
model.J = Set(initialize=J_rule)
#
# Weights
#
model.w = Param(model.J, within=NonNegativeReals, initialize=1.0)
#
# Set selection binary variables
#
model.x = Var(model.J, within=Binary)
#
# Objective
#
def cost_rule(model):
return sum_product(model.w, model.x)
model.cost = Objective(rule=cost_rule)
#
# Constraint
#
def cover_rule(model, i):
expr = 0
for j in model.x:
if (i, j) in model.S:
expr += model.x[j]
#
# WEH - this check is not needed, since I is constructed dynamically
#
#if expr is 0:
#return Constraint.Skip
return expr >= 1
model.cover = Constraint(model.I, rule=cover_rule)
#
print_model_stats(model_options, model)
return model
#
print_model_stats(model_options, model)
return model
def test_model(options=None):
model = pyomo_create_model(model_options=options)
#print_model_stats(options, model)
if __name__ == '__main__':
test_model()
#
options = Bunch()
options.type = 'fixed_set_size'
options.m = 11
options.n = 21
options.rho = 0.3
test_model(options)
#
options = Bunch()
options.type = 'fixed_element_coverage'
test_model(options)
#
options = Bunch()
options.m = 100
options.n = 200
options.type = 'fixed_probability'
test_model(options)
#