def add_lazy_oa_cuts(self,
target_model,
dual_values,
solve_data,
config,
opt,
linearize_active=True,
linearize_violated=True):
"""
Linearizes nonlinear constraints; add the OA cuts through Cplex inherent function self.add()
For nonconvex problems, turn on 'config.add_slack'. Slack variables will
always be used for nonlinear equality constraints.
Parameters
----------
target_model:
this is the MIP/MILP model for the OA algorithm; we want to add the OA cuts to 'target_model'
dual_values:
contains the value of the duals for each constraint
solve_data: MindtPy Data Container
data container that holds solve-instance data
config: ConfigBlock
contains the specific configurations for the algorithm
opt: SolverFactory
the mip solver
linearize_active: bool, optional
this parameter acts as a Boolean flag that signals whether the linearized constraint is active
linearize_violated: bool, optional
this parameter acts as a Boolean flag that signals whether the nonlinear constraint represented by the
linearized constraint has been violated
"""
config.logger.info("Adding OA cuts")
for (constr,
dual_value) in zip(target_model.MindtPy_utils.constraint_list,
dual_values):
if constr.body.polynomial_degree() in (0, 1):
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb(
) and constr.upper == constr.lower:
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = constr.lower if constr.has_lb() and constr.has_ub(
) else rhs
# since the cplex requires the lazy cuts in cplex type, we need to transform the pyomo expression into cplex expression
pyomo_expr = copysign(
1, sign_adjust * dual_value) * (sum(
value(jacs[constr][var]) * (var - value(var))
for var in list(EXPR.identify_variables(constr.body)))
+ value(constr.body) - rhs)
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="L",
rhs=cplex_rhs)
else: # Inequality constraint (possibly two-sided)
if constr.has_ub() \
and (linearize_active and abs(constr.uslack()) < config.bound_tolerance) \
or (linearize_violated and constr.uslack() < 0) \
or (config.linearize_inactive and constr.uslack() > 0):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) + value(constr.body)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="L",
rhs=constr.upper.value + cplex_rhs)
if constr.has_lb() \
and (linearize_active and abs(constr.lslack()) < config.bound_tolerance) \
or (linearize_violated and constr.lslack() < 0) \
or (config.linearize_inactive and constr.lslack() > 0):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - self.get_values(
opt._pyomo_var_to_solver_var_map[var]))
for var in constr_vars) + value(constr.body)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="G",
rhs=constr.lower.value + cplex_rhs)
def add_affine_cuts(solve_data, config):
"""Adds affine cuts using MCPP.
Parameters
----------
solve_data : MindtPySolveData
Data container that holds solve-instance data.
config : ConfigBlock
The specific configurations for MindtPy.
"""
with time_code(solve_data.timing, 'Affine cut generation'):
m = solve_data.mip
config.logger.debug('Adding affine cuts')
counter = 0
for constr in m.MindtPy_utils.nonlinear_constraint_list:
vars_in_constr = list(
identify_variables(constr.body))
if any(var.value is None for var in vars_in_constr):
continue # a variable has no values
# mcpp stuff
try:
mc_eqn = mc(constr.body)
except MCPP_Error as e:
config.logger.debug(
'Skipping constraint %s due to MCPP error %s' % (constr.name, str(e)))
continue # skip to the next constraint
ccSlope = mc_eqn.subcc()
cvSlope = mc_eqn.subcv()
ccStart = mc_eqn.concave()
cvStart = mc_eqn.convex()
# check if the value of ccSlope and cvSlope is not Nan or inf. If so, we skip this.
concave_cut_valid = True
convex_cut_valid = True
for var in vars_in_constr:
if not var.fixed:
if ccSlope[var] == float('nan') or ccSlope[var] == float('inf'):
concave_cut_valid = False
if cvSlope[var] == float('nan') or cvSlope[var] == float('inf'):
convex_cut_valid = False
# check if the value of ccSlope and cvSlope all equals zero. if so, we skip this.
if not any(list(ccSlope.values())):
concave_cut_valid = False
if not any(list(cvSlope.values())):
convex_cut_valid = False
if ccStart == float('nan') or ccStart == float('inf'):
concave_cut_valid = False
if cvStart == float('nan') or cvStart == float('inf'):
convex_cut_valid = False
if not (concave_cut_valid or convex_cut_valid):
continue
ub_int = min(value(constr.upper), mc_eqn.upper()
) if constr.has_ub() else mc_eqn.upper()
lb_int = max(value(constr.lower), mc_eqn.lower()
) if constr.has_lb() else mc_eqn.lower()
aff_cuts = m.MindtPy_utils.cuts.aff_cuts
if concave_cut_valid:
concave_cut = sum(ccSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + ccStart >= lb_int
aff_cuts.add(expr=concave_cut)
counter += 1
if convex_cut_valid:
convex_cut = sum(cvSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + cvStart <= ub_int
aff_cuts.add(expr=convex_cut)
counter += 1
config.logger.debug('Added %s affine cuts' % counter)
def add_lazy_affine_cuts(self, solve_data, config, opt):
"""
Adds affine cuts using MCPP; add affine cuts through Cplex inherent function self.add()
Parameters
----------
solve_data: MindtPy Data Container
data container that holds solve-instance data
config: ConfigBlock
contains the specific configurations for the algorithm
opt: SolverFactory
the mip solver
"""
m = solve_data.mip
config.logger.info("Adding affine cuts")
counter = 0
for constr in m.MindtPy_utils.constraint_list:
if constr.body.polynomial_degree() in (1, 0):
continue
vars_in_constr = list(identify_variables(constr.body))
if any(var.value is None for var in vars_in_constr):
continue # a variable has no values
# mcpp stuff
try:
mc_eqn = mc(constr.body)
except MCPP_Error as e:
config.logger.debug(
"Skipping constraint %s due to MCPP error %s" %
(constr.name, str(e)))
continue # skip to the next constraint
# TODO: check if the value of ccSlope and cvSlope is not Nan or inf. If so, we skip this.
ccSlope = mc_eqn.subcc()
cvSlope = mc_eqn.subcv()
ccStart = mc_eqn.concave()
cvStart = mc_eqn.convex()
concave_cut_valid = True
convex_cut_valid = True
for var in vars_in_constr:
if not var.fixed:
if ccSlope[var] == float('nan') or ccSlope[var] == float(
'inf'):
concave_cut_valid = False
if cvSlope[var] == float('nan') or cvSlope[var] == float(
'inf'):
convex_cut_valid = False
if ccStart == float('nan') or ccStart == float('inf'):
concave_cut_valid = False
if cvStart == float('nan') or cvStart == float('inf'):
convex_cut_valid = False
# check if the value of ccSlope and cvSlope all equals zero. if so, we skip this.
if not any(list(ccSlope.values())):
concave_cut_valid = False
if not any(list(cvSlope.values())):
convex_cut_valid = False
if (concave_cut_valid or convex_cut_valid) is False:
continue
ub_int = min(
constr.upper,
mc_eqn.upper()) if constr.has_ub() else mc_eqn.upper()
lb_int = max(
constr.lower,
mc_eqn.lower()) if constr.has_lb() else mc_eqn.lower()
parent_block = constr.parent_block()
# Create a block on which to put outer approximation cuts.
# TODO: create it at the beginning.
aff_utils = parent_block.component('MindtPy_aff')
if aff_utils is None:
aff_utils = parent_block.MindtPy_aff = Block(
doc="Block holding affine constraints")
aff_utils.MindtPy_aff_cons = ConstraintList()
aff_cuts = aff_utils.MindtPy_aff_cons
if concave_cut_valid:
pyomo_concave_cut = sum(ccSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + ccStart
cplex_concave_rhs = generate_standard_repn(
pyomo_concave_cut).constant
cplex_concave_cut, _ = opt._get_expr_from_pyomo_expr(
pyomo_concave_cut)
self.add(constraint=cplex.SparsePair(
ind=cplex_concave_cut.variables,
val=cplex_concave_cut.coefficients),
sense="G",
rhs=lb_int - cplex_concave_rhs)
counter += 1
if convex_cut_valid:
pyomo_convex_cut = sum(cvSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + cvStart
cplex_convex_rhs = generate_standard_repn(
pyomo_convex_cut).constant
cplex_convex_cut, _ = opt._get_expr_from_pyomo_expr(
pyomo_convex_cut)
self.add(constraint=cplex.SparsePair(
ind=cplex_convex_cut.variables,
val=cplex_convex_cut.coefficients),
sense="L",
rhs=ub_int - cplex_convex_rhs)
# aff_cuts.add(expr=convex_cut)
counter += 1
config.logger.info("Added %s affine cuts" % counter)
def add_ecp_cuts(target_model, solve_data, config,
linearize_active=True,
linearize_violated=True):
"""Linearizes nonlinear constraints. Adds the cuts for the ECP method.
Parameters
----------
target_model : Pyomo model
The relaxed linear model.
solve_data : MindtPySolveData
Data container that holds solve-instance data.
config : ConfigBlock
The specific configurations for MindtPy.
linearize_active : bool, optional
Whether to linearize the active nonlinear constraints, by default True.
linearize_violated : bool, optional
Whether to linearize the violated nonlinear constraints, by default True.
"""
with time_code(solve_data.timing, 'ECP cut generation'):
for constr in target_model.MindtPy_utils.nonlinear_constraint_list:
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
if constr.has_lb() and constr.has_ub():
config.logger.warning(
'constraint {} has both a lower '
'and upper bound.'
'\n'.format(
constr))
continue
if constr.has_ub():
try:
upper_slack = constr.uslack()
except (ValueError, OverflowError):
config.logger.warning(
'constraint {} has caused either a '
'ValueError or OverflowError.'
'\n'.format(
constr))
continue
if (linearize_active and abs(upper_slack) < config.ecp_tolerance) \
or (linearize_violated and upper_slack < 0) \
or (config.linearize_inactive and upper_slack > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.cuts.slack_vars.add()
target_model.MindtPy_utils.cuts.ecp_cuts.add(
expr=(sum(value(jacs[constr][var])*(var - var.value)
for var in constr_vars)
- (slack_var if config.add_slack else 0)
<= upper_slack)
)
if constr.has_lb():
try:
lower_slack = constr.lslack()
except (ValueError, OverflowError):
config.logger.warning(
'constraint {} has caused either a '
'ValueError or OverflowError.'
'\n'.format(
constr))
continue
if (linearize_active and abs(lower_slack) < config.ecp_tolerance) \
or (linearize_violated and lower_slack < 0) \
or (config.linearize_inactive and lower_slack > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.cuts.slack_vars.add()
target_model.MindtPy_utils.cuts.ecp_cuts.add(
expr=(sum(value(jacs[constr][var])*(var - var.value)
for var in constr_vars)
+ (slack_var if config.add_slack else 0)
>= -lower_slack)
)
def add_oa_cuts(target_model, dual_values, solve_data, config,
cb_opt=None,
linearize_active=True,
linearize_violated=True):
"""Adds OA cuts.
Generates and adds OA cuts (linearizes nonlinear constraints).
For nonconvex problems, turn on 'config.add_slack'.
Slack variables will always be used for nonlinear equality constraints.
Parameters
----------
target_model : Pyomo model
The relaxed linear model.
dual_values : list
The value of the duals for each constraint.
solve_data : MindtPySolveData
Data container that holds solve-instance data.
config : ConfigBlock
The specific configurations for MindtPy.
cb_opt : SolverFactory, optional
Gurobi_persistent solver, by default None.
linearize_active : bool, optional
Whether to linearize the active nonlinear constraints, by default True.
linearize_violated : bool, optional
Whether to linearize the violated nonlinear constraints, by default True.
"""
with time_code(solve_data.timing, 'OA cut generation'):
for index, constr in enumerate(target_model.MindtPy_utils.constraint_list):
# TODO: here the index is correlated to the duals, try if this can be fixed when temp duals are removed.
if constr.body.polynomial_degree() in {0, 1}:
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb() and value(constr.lower) == value(constr.upper) and config.equality_relaxation:
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = constr.lower
if config.add_slack:
slack_var = target_model.MindtPy_utils.cuts.slack_vars.add()
target_model.MindtPy_utils.cuts.oa_cuts.add(
expr=copysign(1, sign_adjust * dual_values[index])
* (sum(value(jacs[constr][var]) * (var - value(var))
for var in EXPR.identify_variables(constr.body))
+ value(constr.body) - rhs)
- (slack_var if config.add_slack else 0) <= 0)
if config.single_tree and config.mip_solver == 'gurobi_persistent' and solve_data.mip_iter > 0 and cb_opt is not None:
cb_opt.cbLazy(
target_model.MindtPy_utils.cuts.oa_cuts[len(target_model.MindtPy_utils.cuts.oa_cuts)])
else: # Inequality constraint (possibly two-sided)
if (constr.has_ub()
and (linearize_active and abs(constr.uslack()) < config.zero_tolerance)
or (linearize_violated and constr.uslack() < 0)
or (config.linearize_inactive and constr.uslack() > 0)) or ('MindtPy_utils.objective_constr' in constr.name and constr.has_ub()):
# always add the linearization for the epigraph of the objective
if config.add_slack:
slack_var = target_model.MindtPy_utils.cuts.slack_vars.add()
target_model.MindtPy_utils.cuts.oa_cuts.add(
expr=(sum(value(jacs[constr][var])*(var - var.value)
for var in constr_vars) + value(constr.body)
- (slack_var if config.add_slack else 0)
<= value(constr.upper))
)
if config.single_tree and config.mip_solver == 'gurobi_persistent' and solve_data.mip_iter > 0 and cb_opt is not None:
cb_opt.cbLazy(
target_model.MindtPy_utils.cuts.oa_cuts[len(target_model.MindtPy_utils.cuts.oa_cuts)])
if (constr.has_lb()
and (linearize_active and abs(constr.lslack()) < config.zero_tolerance)
or (linearize_violated and constr.lslack() < 0)
or (config.linearize_inactive and constr.lslack() > 0)) or ('MindtPy_utils.objective_constr' in constr.name and constr.has_lb()):
if config.add_slack:
slack_var = target_model.MindtPy_utils.cuts.slack_vars.add()
target_model.MindtPy_utils.cuts.oa_cuts.add(
expr=(sum(value(jacs[constr][var])*(var - var.value)
for var in constr_vars) + value(constr.body)
+ (slack_var if config.add_slack else 0)
>= value(constr.lower))
)
if config.single_tree and config.mip_solver == 'gurobi_persistent' and solve_data.mip_iter > 0 and cb_opt is not None:
cb_opt.cbLazy(
target_model.MindtPy_utils.cuts.oa_cuts[len(target_model.MindtPy_utils.cuts.oa_cuts)])
def add_lazy_affine_cuts(self, solve_data, config, opt):
"""Adds affine cuts using MCPP.
Add affine cuts through Cplex inherent function self.add().
Parameters
----------
solve_data : MindtPySolveData
Data container that holds solve-instance data.
config : ConfigBlock
The specific configurations for MindtPy.
opt : SolverFactory
The cplex_persistent solver.
"""
with time_code(solve_data.timing, 'Affine cut generation'):
m = solve_data.mip
config.logger.debug('Adding affine cuts')
counter = 0
for constr in m.MindtPy_utils.nonlinear_constraint_list:
vars_in_constr = list(identify_variables(constr.body))
if any(var.value is None for var in vars_in_constr):
continue # a variable has no values
# mcpp stuff
try:
mc_eqn = mc(constr.body)
except MCPP_Error as e:
config.logger.debug(
'Skipping constraint %s due to MCPP error %s' %
(constr.name, str(e)))
continue # skip to the next constraint
# TODO: check if the value of ccSlope and cvSlope is not Nan or inf. If so, we skip this.
ccSlope = mc_eqn.subcc()
cvSlope = mc_eqn.subcv()
ccStart = mc_eqn.concave()
cvStart = mc_eqn.convex()
concave_cut_valid = True
convex_cut_valid = True
for var in vars_in_constr:
if not var.fixed:
if ccSlope[var] == float(
'nan') or ccSlope[var] == float('inf'):
concave_cut_valid = False
if cvSlope[var] == float(
'nan') or cvSlope[var] == float('inf'):
convex_cut_valid = False
if ccStart == float('nan') or ccStart == float('inf'):
concave_cut_valid = False
if cvStart == float('nan') or cvStart == float('inf'):
convex_cut_valid = False
# check if the value of ccSlope and cvSlope all equals zero. if so, we skip this.
if not any(ccSlope.values()):
concave_cut_valid = False
if not any(cvSlope.values()):
convex_cut_valid = False
if not (concave_cut_valid or convex_cut_valid):
continue
ub_int = min(
value(constr.upper),
mc_eqn.upper()) if constr.has_ub() else mc_eqn.upper()
lb_int = max(
value(constr.lower),
mc_eqn.lower()) if constr.has_lb() else mc_eqn.lower()
if concave_cut_valid:
pyomo_concave_cut = sum(ccSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + ccStart
cplex_concave_rhs = generate_standard_repn(
pyomo_concave_cut).constant
cplex_concave_cut, _ = opt._get_expr_from_pyomo_expr(
pyomo_concave_cut)
self.add(constraint=cplex.SparsePair(
ind=cplex_concave_cut.variables,
val=cplex_concave_cut.coefficients),
sense='G',
rhs=lb_int - cplex_concave_rhs)
counter += 1
if convex_cut_valid:
pyomo_convex_cut = sum(cvSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + cvStart
cplex_convex_rhs = generate_standard_repn(
pyomo_convex_cut).constant
cplex_convex_cut, _ = opt._get_expr_from_pyomo_expr(
pyomo_convex_cut)
self.add(constraint=cplex.SparsePair(
ind=cplex_convex_cut.variables,
val=cplex_convex_cut.coefficients),
sense='L',
rhs=ub_int - cplex_convex_rhs)
counter += 1
config.logger.info('Added %s affine cuts' % counter)
def add_lazy_oa_cuts(self,
target_model,
dual_values,
solve_data,
config,
opt,
linearize_active=True,
linearize_violated=True):
"""Linearizes nonlinear constraints; add the OA cuts through Cplex inherent function self.add()
For nonconvex problems, turn on 'config.add_slack'. Slack variables will always be used for
nonlinear equality constraints.
Parameters
----------
target_model : Pyomo model
The MIP main problem.
dual_values : list
The value of the duals for each constraint.
solve_data : MindtPySolveData
Data container that holds solve-instance data.
config : ConfigBlock
The specific configurations for MindtPy.
opt : SolverFactory
The cplex_persistent solver.
linearize_active : bool, optional
Whether to linearize the active nonlinear constraints, by default True.
linearize_violated : bool, optional
Whether to linearize the violated nonlinear constraints, by default True.
"""
config.logger.debug('Adding OA cuts')
with time_code(solve_data.timing, 'OA cut generation'):
for index, constr in enumerate(
target_model.MindtPy_utils.constraint_list):
if constr.body.polynomial_degree(
) in solve_data.mip_constraint_polynomial_degree:
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb() and value(
constr.lower) == value(constr.upper):
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = constr.lower
# since the cplex requires the lazy cuts in cplex type, we need to transform the pyomo expression into cplex expression
pyomo_expr = copysign(
1, sign_adjust *
dual_values[index]) * (sum(
value(jacs[constr][var]) * (var - value(var))
for var in EXPR.identify_variables(constr.body)) +
value(constr.body) - rhs)
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense='L',
rhs=cplex_rhs)
else: # Inequality constraint (possibly two-sided)
if (constr.has_ub() and
(linearize_active
and abs(constr.uslack()) < config.zero_tolerance) or
(linearize_violated and constr.uslack() < 0) or
(config.linearize_inactive and constr.uslack() > 0)
) or ('MindtPy_utils.objective_constr' in constr.name
and constr.has_ub()):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) + value(constr.body)
cplex_rhs = - \
generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(
pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables,
val=cplex_expr.coefficients),
sense='L',
rhs=value(constr.upper) + cplex_rhs)
if (constr.has_lb() and
(linearize_active
and abs(constr.lslack()) < config.zero_tolerance) or
(linearize_violated and constr.lslack() < 0) or
(config.linearize_inactive and constr.lslack() > 0)
) or ('MindtPy_utils.objective_constr' in constr.name
and constr.has_lb()):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - self.get_values(
opt._pyomo_var_to_solver_var_map[var]))
for var in constr_vars) + value(constr.body)
cplex_rhs = - \
generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(
pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables,
val=cplex_expr.coefficients),
sense='G',
rhs=value(constr.lower) + cplex_rhs)
def add_lazy_oa_cuts(self,
target_model,
dual_values,
solve_data,
config,
opt,
linearize_active=True,
linearize_violated=True,
linearize_inactive=False):
"""Add oa_cuts through Cplex inherent function self.add()"""
for (constr,
dual_value) in zip(target_model.MindtPy_utils.constraint_list,
dual_values):
if constr.body.polynomial_degree() in (0, 1):
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb(
) and constr.upper == constr.lower:
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = ((0 if constr.upper is None else constr.upper) +
(0 if constr.lower is None else constr.lower))
rhs = constr.lower if constr.has_lb() and constr.has_ub(
) else rhs
# since the cplex requires the lazy cuts in cplex type, we need to transform the pyomo expression into cplex expression
pyomo_expr = copysign(
1, sign_adjust * dual_value) * (sum(
value(jacs[constr][var]) * (var - value(var))
for var in list(EXPR.identify_variables(constr.body)))
+ value(constr.body) - rhs)
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="L",
rhs=cplex_rhs)
else: # Inequality constraint (possibly two-sided)
if constr.has_ub() \
and (linearize_active and abs(constr.uslack()) < config.zero_tolerance) \
or (linearize_violated and constr.uslack() < 0) \
or (linearize_inactive and constr.uslack() > 0):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) + value(constr.body)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="L",
rhs=constr.upper.value + cplex_rhs)
if constr.has_lb() \
and (linearize_active and abs(constr.lslack()) < config.zero_tolerance) \
or (linearize_violated and constr.lslack() < 0) \
or (linearize_inactive and constr.lslack() > 0):
pyomo_expr = sum(
value(jacs[constr][var]) * (var - self.get_values(
opt._pyomo_var_to_solver_var_map[var]))
for var in constr_vars) + value(constr.body)
cplex_rhs = -generate_standard_repn(pyomo_expr).constant
cplex_expr, _ = opt._get_expr_from_pyomo_expr(pyomo_expr)
self.add(constraint=cplex.SparsePair(
ind=cplex_expr.variables, val=cplex_expr.coefficients),
sense="G",
rhs=constr.lower.value + cplex_rhs)
def add_oa_cuts(target_model,
dual_values,
solve_data,
config,
linearize_active=True,
linearize_violated=True,
linearize_inactive=False,
use_slack_var=False):
"""Linearizes nonlinear constraints.
For nonconvex problems, turn on 'use_slack_var'. Slack variables will
always be used for nonlinear equality constraints.
"""
for (constr, dual_value) in zip(target_model.MindtPy_utils.constraint_list,
dual_values):
if constr.body.polynomial_degree() in (0, 1):
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb(
) and constr.upper == constr.lower:
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = ((0 if constr.upper is None else constr.upper) +
(0 if constr.lower is None else constr.lower))
rhs = constr.lower if constr.has_lb() and constr.has_ub() else rhs
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=copysign(1, sign_adjust * dual_value) *
(sum(
value(jacs[constr][var]) * (var - value(var))
for var in list(EXPR.identify_variables(constr.body))) +
value(constr.body) - rhs) - slack_var <= 0)
else: # Inequality constraint (possibly two-sided)
if constr.has_ub() \
and (linearize_active and abs(constr.uslack()) < config.zero_tolerance) \
or (linearize_violated and constr.uslack() < 0) \
or (linearize_inactive and constr.uslack() > 0):
if use_slack_var:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=(sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) -
(slack_var if use_slack_var else 0) <= constr.upper))
if constr.has_lb() \
and (linearize_active and abs(constr.lslack()) < config.zero_tolerance) \
or (linearize_violated and constr.lslack() < 0) \
or (linearize_inactive and constr.lslack() > 0):
if use_slack_var:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=(sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) +
(slack_var if use_slack_var else 0) >= constr.lower))
def add_affine_cuts(solve_data, config):
"""
Adds affine cuts using MCPP; modifies the model to include affine cuts
Parameters
----------
solve_data: MindtPy Data Container
data container that holds solve-instance data
config: ConfigBlock
contains the specific configurations for the algorithm
"""
m = solve_data.mip
config.logger.info("Adding affine cuts")
counter = 0
for constr in m.MindtPy_utils.constraint_list:
if constr.body.polynomial_degree() in (1, 0):
continue
vars_in_constr = list(identify_variables(constr.body))
if any(var.value is None for var in vars_in_constr):
continue # a variable has no values
# mcpp stuff
try:
mc_eqn = mc(constr.body)
except MCPP_Error as e:
config.logger.debug("Skipping constraint %s due to MCPP error %s" %
(constr.name, str(e)))
continue # skip to the next constraint
ccSlope = mc_eqn.subcc()
cvSlope = mc_eqn.subcv()
ccStart = mc_eqn.concave()
cvStart = mc_eqn.convex()
# check if the value of ccSlope and cvSlope is not Nan or inf. If so, we skip this.
concave_cut_valid = True
convex_cut_valid = True
for var in vars_in_constr:
if not var.fixed:
if ccSlope[var] == float('nan') or ccSlope[var] == float(
'inf'):
concave_cut_valid = False
if cvSlope[var] == float('nan') or cvSlope[var] == float(
'inf'):
convex_cut_valid = False
# check if the value of ccSlope and cvSlope all equals zero. if so, we skip this.
if not any(list(ccSlope.values())):
concave_cut_valid = False
if not any(list(cvSlope.values())):
convex_cut_valid = False
if ccStart == float('nan') or ccStart == float('inf'):
concave_cut_valid = False
if cvStart == float('nan') or cvStart == float('inf'):
convex_cut_valid = False
if (concave_cut_valid or convex_cut_valid) is False:
continue
ub_int = min(constr.upper,
mc_eqn.upper()) if constr.has_ub() else mc_eqn.upper()
lb_int = max(constr.lower,
mc_eqn.lower()) if constr.has_lb() else mc_eqn.lower()
parent_block = constr.parent_block()
# Create a block on which to put outer approximation cuts.
# TODO: create it at the beginning.
aff_utils = parent_block.component('MindtPy_aff')
if aff_utils is None:
aff_utils = parent_block.MindtPy_aff = Block(
doc="Block holding affine constraints")
aff_utils.MindtPy_aff_cons = ConstraintList()
aff_cuts = aff_utils.MindtPy_aff_cons
if concave_cut_valid:
concave_cut = sum(ccSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + ccStart >= lb_int
aff_cuts.add(expr=concave_cut)
counter += 1
if convex_cut_valid:
convex_cut = sum(cvSlope[var] * (var - var.value)
for var in vars_in_constr
if not var.fixed) + cvStart <= ub_int
aff_cuts.add(expr=convex_cut)
counter += 1
config.logger.info("Added %s affine cuts" % counter)
def add_ecp_cuts(target_model,
solve_data,
config,
linearize_active=True,
linearize_violated=True):
"""
Linearizes nonlinear constraints. Adds the cuts for the ECP method.
For nonconvex problems, turn on 'config.add_slack'. Slack variables will
always be used for nonlinear equality constraints.
Parameters
----------
target_model:
this is the MIP/MILP model for the OA algorithm; we want to add the OA cuts to 'target_model'
solve_data: MindtPy Data Container
data container that holds solve-instance data
config: ConfigBlock
contains the specific configurations for the algorithm
linearize_active: bool, optional
this parameter acts as a Boolean flag that signals whether the linearized constraint is active
linearize_violated: bool, optional
this parameter acts as a Boolean flag that signals whether the nonlinear constraint represented by the
linearized constraint has been violated
"""
for constr in target_model.MindtPy_utils.constraint_list:
if constr.body.polynomial_degree() in (0, 1):
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
if constr.has_lb() and constr.has_ub():
config.logger.warning('constraint {} has both a lower '
'and upper bound.'
'\n'.format(constr))
continue
if constr.has_ub():
try:
upper_slack = constr.uslack()
except (ValueError, OverflowError):
config.logger.warning('constraint {} has caused either a '
'ValueError or OverflowError.'
'\n'.format(constr))
continue
if (linearize_active and abs(upper_slack) < config.ecp_tolerance) \
or (linearize_violated and upper_slack < 0) \
or (config.linearize_inactive and upper_slack > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.ecp_cuts.add(
expr=(
sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) -
(slack_var if config.add_slack else 0) <= upper_slack))
if constr.has_lb():
try:
lower_slack = constr.lslack()
except (ValueError, OverflowError):
config.logger.warning('constraint {} has caused either a '
'ValueError or OverflowError.'
'\n'.format(constr))
continue
if (linearize_active and abs(lower_slack) < config.ecp_tolerance) \
or (linearize_violated and lower_slack < 0) \
or (config.linearize_inactive and lower_slack > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.ecp_cuts.add(
expr=(
sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) +
(slack_var if config.add_slack else 0) >= -lower_slack
))
def add_oa_cuts(target_model,
dual_values,
solve_data,
config,
linearize_active=True,
linearize_violated=True):
"""
Linearizes nonlinear constraints; modifies the model to include the OA cuts
For nonconvex problems, turn on 'config.add_slack'. Slack variables will
always be used for nonlinear equality constraints.
Parameters
----------
target_model:
this is the MIP/MILP model for the OA algorithm; we want to add the OA cuts to 'target_model'
dual_values:
contains the value of the duals for each constraint
solve_data: MindtPy Data Container
data container that holds solve-instance data
config: ConfigBlock
contains the specific configurations for the algorithm
linearize_active: bool, optional
this parameter acts as a Boolean flag that signals whether the linearized constraint is active
linearize_violated: bool, optional
this parameter acts as a Boolean flag that signals whether the nonlinear constraint represented by the
linearized constraint has been violated
"""
for index, constr in enumerate(target_model.MindtPy_utils.constraint_list):
if constr.body.polynomial_degree() in (0, 1):
continue
constr_vars = list(identify_variables(constr.body))
jacs = solve_data.jacobians
# Equality constraint (makes the problem nonconvex)
if constr.has_ub() and constr.has_lb(
) and constr.upper == constr.lower and config.use_dual:
sign_adjust = -1 if solve_data.objective_sense == minimize else 1
rhs = constr.lower if constr.has_lb() and constr.has_ub() else rhs
if config.add_slack:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=copysign(1, sign_adjust * dual_values[index]) *
(sum(
value(jacs[constr][var]) * (var - value(var))
for var in list(EXPR.identify_variables(constr.body))) +
value(constr.body) - rhs) -
(slack_var if config.add_slack else 0) <= 0)
else: # Inequality constraint (possibly two-sided)
if constr.has_ub() \
and (linearize_active and abs(constr.uslack()) < config.zero_tolerance) \
or (linearize_violated and constr.uslack() < 0) \
or (config.linearize_inactive and constr.uslack() > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=(
sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) + value(constr.body) -
(slack_var if config.add_slack else 0) <= constr.upper
))
if constr.has_lb() \
and (linearize_active and abs(constr.lslack()) < config.zero_tolerance) \
or (linearize_violated and constr.lslack() < 0) \
or (config.linearize_inactive and constr.lslack() > 0):
if config.add_slack:
slack_var = target_model.MindtPy_utils.MindtPy_linear_cuts.slack_vars.add(
)
target_model.MindtPy_utils.MindtPy_linear_cuts.oa_cuts.add(
expr=(
sum(
value(jacs[constr][var]) * (var - var.value)
for var in constr_vars) + value(constr.body) +
(slack_var if config.add_slack else 0) >= constr.lower
))
