def add_moma_optcom(community, min_growth, linear=False):
"""Add a dualized MOMA version of OptCom.
Solves a MOMA (minimization of metabolic adjustment) formulation of OptCom
given by::
minimize cooperativity_cost
s.t. maximize community_objective
s.t. Sv = 0
lb >= v >= ub
where community_cost = sum (growth_rate - max_growth)**2
if linear=False or
community_cost = sum |growth_rate - max_growth|
if linear=True
Arguments
---------
community : micom.Community
The community to modify.
min_growth : positive float or array-like object.
The minimum growth rate for each individual in the community. Either
a single value applied to all individuals or one value for each.
linear : boolean
Whether to use a non-linear (sum of squares) or linear version of the
cooperativity cost. If set to False requires a QP-capable solver.
"""
logger.info("adding dual %s moma to %s" %
("linear" if linear else "quadratic", community.id))
check_modification(community)
min_growth = _format_min_growth(min_growth, community.taxa)
prob = community.solver.interface
old_obj = community.objective
coefs = old_obj.get_linear_coefficients(old_obj.variables)
# Get maximum individual growth rates
max_gcs = community.optimize_all(progress=False)
_apply_min_growth(community, min_growth)
dual_coefs = fast_dual(community)
coefs.update({v: -coef for v, coef in dual_coefs.items()})
obj_constraint = prob.Constraint(Zero,
lb=0,
ub=0,
name="optcom_suboptimality")
community.add_cons_vars([obj_constraint])
community.solver.update()
obj_constraint.set_linear_coefficients(coefs)
obj_expr = Zero
logger.info("adding expressions for %d taxa" % len(community.taxa))
for sp in community.taxa:
v = prob.Variable("gc_constant_" + sp, lb=max_gcs[sp], ub=max_gcs[sp])
community.add_cons_vars([v])
taxa_obj = community.constraints["objective_" + sp]
ex = v - taxa_obj.expression
if not linear:
ex = ex**2
obj_expr += ex.expand()
community.objective = prob.Objective(obj_expr, direction="min")
community.modification = "moma optcom"
logger.info("finished dual moma to %s" % community.id)
def add_dualized_optcom(community, min_growth):
"""Add dual Optcom variables and constraints to a community.
Uses the original formulation of OptCom and solves the following
multi-objective problem::
maximize community_growth
s.t. maximize growth_rate_i for all i
s.t. Sv_i = 0
lb_i >= v_i >= ub_i
Notes
-----
This method will only find one arbitrary solution from the Pareto front.
There may exist several other optimal solutions.
Arguments
---------
community : micom.Community
The community to modify.
min_growth : positive float or array-like object.
The minimum growth rate for each individual in the community. Either
a single value applied to all individuals or one value for each.
"""
logger.info("adding dual optcom to %s" % community.id)
check_modification(community)
min_growth = _format_min_growth(min_growth, community.taxa)
prob = community.solver.interface
# Temporarily subtitute objective with sum of individual objectives
# for correct dual variables
old_obj = community.objective
community.objective = Zero
for sp in community.taxa:
taxa_obj = community.constraints["objective_" + sp]
community.objective += taxa_obj.expression
_apply_min_growth(community, min_growth)
dual_coefs = fast_dual(community)
logger.info("adding expressions for %d taxa" % len(community.taxa))
for sp in community.taxa:
primal_const = community.constraints["objective_" + sp]
coefs = primal_const.get_linear_coefficients(primal_const.variables)
coefs.update({
dual_var: -coef
for dual_var, coef in dual_coefs.items() if sp in dual_var.name
})
obj_constraint = prob.Constraint(Zero,
lb=0,
ub=0,
name="optcom_suboptimality_" + sp)
community.add_cons_vars([obj_constraint])
community.solver.update()
obj_constraint.set_linear_coefficients(coefs)
community.objective = old_obj
community.modification = "dual optcom"
logger.info("finished adding dual optcom to %s" % community.id)