def _f(m: Block):
m.lmbda = Var(vertices, domain=NonNegativeReals) # 非负
m.y = Var(simplices, domain=Binary) # 二进制
m.a0 = Constraint(dimensions, rule=lambda m, d: sum(m.lmbda[v] * pointsT[d][v] for v in vertices) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(m.lmbda[v] * values[v] for v in vertices))
elif bound == 'lb':
m.a1 = Constraint(expr=output <= sum(m.lmbda[v] * values[v] for v in vertices))
elif bound == 'ub':
m.a1 = Constraint(expr=output >= sum(m.lmbda[v] * values[v] for v in vertices))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b = Constraint(expr=sum(m.lmbda[v] for v in vertices) == 1)
# generate a map from vertex index to simplex index,
# which avoids an n^2 lookup when generating the
# constraint
vertex_to_simplex = [[] for _ in vertices]
for s, simplex in enumerate(tri.simplices):
for v in simplex:
vertex_to_simplex[v].append(s)
m.c0 = Constraint(vertices, rule=lambda m, v: m.lmbda[v] <= sum(m.y[s] for s in vertex_to_simplex[v]))
m.c1 = Constraint(expr=sum(m.y[s] for s in simplices) == 1)
return m
def dlog(m: Block,
tri: qhull.Delaunay,
values: List[float],
input: List[SimpleVar] = None,
output: SimpleVar = None,
bound: str = 'eq',
**kw):
values = np.array(values).tolist()
ndim = len(input)
nsimplices = len(tri.simplices)
npoints = len(tri.points)
pointsT = list(zip(*tri.points))
# create index objects
dimensions = list(range(ndim))
simplices = list(range(nsimplices)) # 跟单纯形 数量一致
vertices = list(range(npoints))
bound = bound.lower()
L = int(math.ceil(math.log2(nsimplices)))
L_Range = list(range(L))
vp = [0, 1, 2]
#
m.lmbda = Var(simplices, vp, domain=NonNegativeReals) # 非负
m.a0 = Constraint(
dimensions,
rule=lambda m, d: sum(m.lmbda[s, v] * pointsT[d][tri.simplices[s][v]]
for s in simplices for v in vp) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(
m.lmbda[s, v] * values[tri.simplices[s][v]] for s in simplices
for v in vp))
elif bound == 'lb':
m.a1 = Constraint(
expr=output <= sum(m.lmbda[s, v] * values[tri.simplices[s][v]]
for s in simplices for v in vp))
elif bound == 'ub':
m.a1 = Constraint(
expr=output >= sum(m.lmbda[s, v] * values[tri.simplices[s][v]]
for s in simplices for v in vp))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b1 = Constraint(expr=sum(m.lmbda[s, v] for s in simplices
for v in vp) == 1)
m.y = Var(L_Range, domain=Binary) # 二进制
m.c0 = Constraint(L_Range,
rule=lambda m, l: sum(m.lmbda[s, v] for s in simplices
if bin(s)[2:].zfill(L)[l] == '1'
for v in vp) <= m.y[l])
m.c1 = Constraint(L_Range,
rule=lambda m, l: sum(m.lmbda[s, v] for s in simplices
if bin(s)[2:].zfill(L)[l] == '0'
for v in vp) <= 1 - m.y[l])
return m
def cc(m: Block,
tri: qhull.Delaunay,
values: List[float],
input: List[SimpleVar] = None,
output: SimpleVar = None,
bound: str = 'eq',
**kw):
values = np.array(values).tolist()
ndim = len(input)
nsimplices = len(tri.simplices)
npoints = len(tri.points)
pointsT = list(zip(*tri.points))
# create index objects
dimensions = list(range(ndim))
simplices = list(range(nsimplices)) # 跟单纯形 数量一致
vertices = list(range(npoints))
bound = bound.lower()
m.lmbda = Var(vertices, domain=NonNegativeReals) # 非负
m.y = Var(simplices, domain=Binary) # 二进制
# m.y = Var(simplices, domain=NonNegativeReals, bounds=(0, 1)) # 二进制
m.a0 = Constraint(dimensions,
rule=lambda m, d: sum(m.lmbda[v] * pointsT[d][v]
for v in vertices) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(m.lmbda[v] * values[v]
for v in vertices))
elif bound == 'lb':
m.a1 = Constraint(expr=output <= sum(m.lmbda[v] * values[v]
for v in vertices))
elif bound == 'ub':
m.a1 = Constraint(expr=output >= sum(m.lmbda[v] * values[v]
for v in vertices))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b = Constraint(expr=sum(m.lmbda[v] for v in vertices) == 1)
# generate a map from vertex index to simplex index,
# which avoids an n^2 lookup when generating the
# constraint
vertex_to_simplex = [[] for _ in vertices]
for s, simplex in enumerate(tri.simplices):
for v in simplex:
vertex_to_simplex[v].append(s)
m.c0 = Constraint(
vertices,
rule=lambda m, v: m.lmbda[v] <= sum(m.y[s]
for s in vertex_to_simplex[v]))
m.c1 = Constraint(expr=sum(m.y[s] for s in simplices) == 1)
return m
def create_submodel_kkt_block(instance, submodel, deterministic,
fixed_upper_vars):
"""
Add optimality conditions for the submodel
This assumes that the original model has the form:
min c1*x + d1*y
A3*x <= b3
A1*x + B1*y <= b1
min c2*x + d2*y + x'*Q*y
A2*x + B2*y + x'*E2*y <= b2
y >= 0
NOTE THE VARIABLE BOUNDS!
"""
fixed_vars = {id(v) for v in fixed_upper_vars}
#
# Populate the block with the linear constraints.
# Note that we don't simply clone the current block.
# We need to collect a single set of equations that
# can be easily expressed.
#
d2 = {}
B2 = {}
vtmp = {}
utmp = {}
sids_set = set()
sids_list = []
#
block = Block(concrete=True)
block.u = VarList(
) # Note: Dual variables associated to bounds in primal problem
block.v = VarList(
) # Note: Dual variables associated to constraints in primal problem
block.c1 = ConstraintList()
block.c2 = ComplementarityList()
block.c3 = ComplementarityList()
#
# Collect submodel objective terms
#
# TODO: detect fixed variables
#
for odata in submodel.component_data_objects(Objective, active=True):
if odata.sense == maximize:
d_sense = -1
else:
d_sense = 1
#
# Iterate through the variables in the representation
#
o_terms = generate_standard_repn(odata.expr, compute_values=False)
#
# Linear terms
#
for i, var in enumerate(o_terms.linear_vars):
if id(var) in fixed_vars:
#
# Skip fixed upper variables
#
continue
#
# Store the coefficient for the variable. The coefficient is
# negated if the objective is maximized.
#
id_ = id(var)
d2[id_] = d_sense * o_terms.linear_coefs[i]
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
#
# Quadratic terms
#
for i, var in enumerate(o_terms.quadratic_vars):
if id(var[0]) in fixed_vars:
if id(var[1]) in fixed_vars:
#
# Skip fixed upper variables
#
continue
#
# Add the linear term
#
id_ = id(var[1])
d2[id_] = d2.get(
id_, 0) + d_sense * o_terms.quadratic_coefs[i] * var[0]
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
elif id(var[1]) in fixed_vars:
#
# Add the linear term
#
id_ = id(var[0])
d2[id_] = d2.get(
id_, 0) + d_sense * o_terms.quadratic_coefs[i] * var[1]
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
else:
raise RuntimeError(
"Cannot apply this transformation to a problem with \
quadratic terms where both variables are in the lower level.")
#
# Stop after the first objective
#
break
#
# Iterate through all lower level variables, adding dual variables
# and complementarity slackness conditions for y bound constraints
#
for vcomponent in instance.component_objects(Var, active=True):
for ndx in vcomponent:
if id(vcomponent[ndx]) in fixed_vars:
#
# Skip fixed upper variables
#
continue
#
# For each index, get the bounds for the variable
#
lb, ub = vcomponent[ndx].bounds
if not lb is None:
#
# Add the complementarity slackness condition for a lower bound
#
v = block.v.add()
block.c3.add(complements(vcomponent[ndx] >= lb, v >= 0))
else:
v = None
if not ub is None:
#
# Add the complementarity slackness condition for an upper bound
#
w = block.v.add()
vtmp[id(vcomponent[ndx])] = w
block.c3.add(complements(vcomponent[ndx] <= ub, w >= 0))
else:
w = None
if not (v is None and w is None):
#
# Record the variables for which complementarity slackness conditions
# were created.
#
id_ = id(vcomponent[ndx])
vtmp[id_] = (v, w)
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
#
# Iterate through all constraints, adding dual variables and
# complementary slackness conditions (for inequality constraints)
#
for cdata in submodel.component_data_objects(Constraint, active=True):
if cdata.equality:
# Don't add a complementary slackness condition for an equality constraint
u = block.u.add()
utmp[id(cdata)] = (None, u)
else:
if not cdata.lower is None:
#
# Add the complementarity slackness condition for a greater-than inequality
#
u = block.u.add()
block.c2.add(complements(-cdata.body <= -cdata.lower, u >= 0))
else:
u = None
if not cdata.upper is None:
#
# Add the complementarity slackness condition for a less-than inequality
#
w = block.u.add()
block.c2.add(complements(cdata.body <= cdata.upper, w >= 0))
else:
w = None
if not (u is None and w is None):
utmp[id(cdata)] = (u, w)
#
# Store the coefficients for the constraint variables that are not fixed
#
c_terms = generate_standard_repn(cdata.body, compute_values=False)
#
# Linear terms
#
for i, var in enumerate(c_terms.linear_vars):
if id(var) in fixed_vars:
continue
id_ = id(var)
B2.setdefault(id_, {}).setdefault(id(cdata),
c_terms.linear_coefs[i])
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
#
# Quadratic terms
#
for i, var in enumerate(c_terms.quadratic_vars):
if id(var[0]) in fixed_vars:
if id(var[1]) in fixed_vars:
continue
id_ = id(var[1])
if id_ in B2:
B2[id_][id(cdata)] = c_terms.quadratic_coefs[i] * var[0]
else:
B2.setdefault(id_, {}).setdefault(
id(cdata), c_terms.quadratic_coefs[i] * var[0])
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
elif id(var[1]) in fixed_vars:
id_ = id(var[0])
if id_ in B2:
B2[id_][id(cdata)] = c_terms.quadratic_coefs[i] * var[1]
else:
B2.setdefault(id_, {}).setdefault(
id(cdata), c_terms.quadratic_coefs[i] * var[1])
if not id_ in sids_set:
sids_set.add(id_)
sids_list.append(id_)
else:
raise RuntimeError(
"Cannot apply this transformation to a problem with \
quadratic terms where both variables are in the lower level.")
#
# Generate stationarity equations
#
tmp__ = (None, None)
for vid in sids_list:
exp = d2.get(vid, 0)
#
lb_dual, ub_dual = vtmp.get(vid, tmp__)
if vid in vtmp:
if not lb_dual is None:
exp -= lb_dual # dual for variable lower bound
if not ub_dual is None:
exp += ub_dual # dual for variable upper bound
#
B2_ = B2.get(vid, {})
utmp_keys = list(utmp.keys())
if deterministic:
utmp_keys.sort(key=lambda x: utmp[x][0].local_name\
if utmp[x][1] is None else utmp[x][1].local_name)
for uid in utmp_keys:
if uid in B2_:
lb_dual, ub_dual = utmp[uid]
if not lb_dual is None:
exp -= B2_[uid] * lb_dual
if not ub_dual is None:
exp += B2_[uid] * ub_dual
if type(exp) in six.integer_types or type(exp) is float:
# TODO: Annotate the model as unbounded
raise IOError("Unbounded variable without side constraints")
block.c1.add(exp == 0)
return block
