def optimize_picef(cfg, check_edge_success=False):
"""create and solve a picef model, and return the solution"""
if cfg.m is None:
create_picef_model(cfg, check_edge_success=check_edge_success)
optimize(cfg.m)
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob)
else:
matching_chains = []
cycles_used = [c for c, v in zip(cfg.cycles, cfg.cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cfg.cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(
ip_model=cfg.m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
return cycle_obj, matching_chains, sol
def solve_kep(cfg, formulation, use_relabelled=True):
formulations = {
"uef": ("Uncapped edge formulation", kidney_ip.optimise_uuef),
"eef": ("EEF", kidney_ip.optimise_eef),
"eef_full_red": ("EEF with full reduction by cycle generation",
kidney_ip.optimise_eef_full_red),
"hpief_prime": ("HPIEF'", kidney_ip.optimise_hpief_prime),
"hpief_prime_full_red":
("HPIEF' with full reduction by cycle generation",
kidney_ip.optimise_hpief_prime_full_red),
"hpief_2prime": ("HPIEF''", kidney_ip.optimise_hpief_2prime),
"hpief_2prime_full_red":
("HPIEF'' with full reduction by cycle generation",
kidney_ip.optimise_hpief_2prime_full_red),
"picef": ("PICEF", kidney_ip.optimise_picef),
"cf": ("Cycle formulation", kidney_ip.optimise_ccf)
}
if formulation in formulations:
formulation_name, formulation_fun = formulations[formulation]
if use_relabelled:
opt_result = kidney_ip.optimise_relabelled(formulation_fun, cfg)
else:
opt_result = formulation_fun(cfg)
if cfg.multi > 1: # added by Duncan
for sol in opt_result.solutions:
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds,
cfg.max_cycle, cfg.max_chain)
else:
kidney_utils.check_validity(opt_result, cfg.digraph, cfg.ndds,
cfg.max_cycle, cfg.max_chain)
opt_result.formulation_name = formulation_name
return opt_result
else:
raise ValueError("Unrecognised IP formulation name")
def solve_kep(cfg, formulation, use_relabelled=True):
formulations = {
"uef": ("Uncapped edge formulation", kidney_ip.optimise_uuef),
"eef": ("EEF", kidney_ip.optimise_eef),
"eef_full_red": ("EEF with full reduction by cycle generation", kidney_ip.optimise_eef_full_red),
"hpief_prime": ("HPIEF'", kidney_ip.optimise_hpief_prime),
"hpief_prime_full_red": ("HPIEF' with full reduction by cycle generation", kidney_ip.optimise_hpief_prime_full_red),
"hpief_2prime": ("HPIEF''", kidney_ip.optimise_hpief_2prime),
"hpief_2prime_full_red": ("HPIEF'' with full reduction by cycle generation", kidney_ip.optimise_hpief_2prime_full_red),
"picef": ("PICEF", kidney_ip.optimise_picef),
"cf": ("Cycle formulation",
kidney_ip.optimise_ccf)
}
if formulation in formulations:
formulation_name, formulation_fun = formulations[formulation]
if use_relabelled:
opt_result = kidney_ip.optimise_relabelled(formulation_fun, cfg)
else:
opt_result = formulation_fun(cfg)
kidney_utils.check_validity(opt_result, cfg.digraph, cfg.ndds, cfg.max_cycle, cfg.max_chain)
opt_result.formulation_name = formulation_name
return opt_result
else:
raise ValueError("Unrecognised IP formulation name")
def solve_picef_model(cfg, remove_edges=[]):
"""
solve a picef model using a config object, and return the solution
if remove_edges is provided, disallow these edges from being used.
"""
for e in remove_edges:
e.used_var.setAttr(GRB.Attr.UB, 0.0)
optimize(cfg.m)
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob)
else:
matching_chains = []
cycles_used = [c for c, v in zip(cfg.cycles, cfg.cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cfg.cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(
ip_model=cfg.m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
# allow removed edges to be used again
for e in remove_edges:
e.used_var.setAttr(GRB.Attr.UB, 1.0)
return sol
def solve_kep(cfg, formulation, use_relabelled=True):
formulations = {
"picef": ("PICEF", kidney_ip.optimise_picef),
"pctsp": ("PC-TSP", kidney_ip.optimise_pctsp),
"pitsp": ("PI-TSP", kidney_ip.optimize_pitsp),
"rob_picef": ("ROBUST PICEF", kidney_ip.optimise_robust_picef),
"edge_weight_uncertainty": ("var. budget edge weight uncertainty", kidney_ip.solve_edge_weight_uncertainty),
"rob_pctsp": ("ROBUST PC-TSP", kidney_ip.optimize_robust_pctsp)
}
if formulation in formulations:
formulation_name, formulation_fun = formulations[formulation]
if use_relabelled:
opt_result = kidney_ip.optimise_relabelled(formulation_fun, cfg)
else:
opt_result = formulation_fun(cfg)
kidney_utils.check_validity(opt_result, cfg.digraph, cfg.ndds, cfg.max_cycle, cfg.max_chain)
opt_result.formulation_name = formulation_name
return opt_result
else:
raise ValueError("Unrecognised IP formulation name")
def optimize_SAA_picef(cfg, num_weight_measurements, gamma, alpha):
m, cycles, cycle_vars, _ = create_picef_model(cfg)
# add cycle objects
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = failure_aware_cycle_weight(c_obj.vs, cfg.digraph,
cfg.edge_success_prob)
c_obj.grb_var = var
cycle_list.append(c_obj)
# add variables for each edge weight measurement
weight_vars = m.addVars(num_weight_measurements,
vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for i in range(num_weight_measurements):
m.addConstr(weight_vars[i] == -(quicksum(e.used_var * e.weight_list[i]
for e in cfg.digraph.es) +
quicksum(e.weight_list[i] * e.edge_var
for ndd in cfg.ndds
for e in ndd.edges)))
# auxiliary variable
d_var = m.addVar(vtype=GRB.CONTINUOUS, lb=-GRB.INFINITY, ub=GRB.INFINITY)
# add pi variables & constraints for SAA
pi_vars = m.addVars(num_weight_measurements,
vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for i in range(num_weight_measurements):
m.addConstr(pi_vars[i] >= weight_vars[i])
m.addConstr(pi_vars[i] >= (1 + gamma / alpha) * weight_vars[i] -
(d_var * gamma) / alpha)
# objective
obj = (1.0 /
float(num_weight_measurements)) * quicksum(pi_vars) + gamma * d_var
m.setObjective(obj, sense=GRB.MINIMIZE)
if not cfg.use_chains:
raise Exception("not implemented")
elif cfg.edge_success_prob == 1:
pass
else:
raise Exception("not implemented")
optimize(m)
pair_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob)
ndd_chain_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_chain_edges = []
matching_chains = []
matching_edges = pair_edges + ndd_chain_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges)))
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
return sol, matching_edges
def optimise_robust_picef(cfg):
m, cycles, cycle_vars, num_edges_var = create_picef_model(cfg)
# for use later
floor_gamma = np.floor(cfg.gamma)
ceil_gamma = np.ceil(cfg.gamma)
gamma_frac = cfg.gamma - floor_gamma
# add cycle vars
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = cycle_weight(c_obj.vs, cfg.digraph)
c_obj.grb_var = var
cycle_list.append(c_obj)
m.update()
# gamma is integer
if gamma_frac == 0:
if cfg.use_chains:
for ndd in cfg.ndds:
for e in ndd.edges:
g_var = m.addVar(vtype=GRB.BINARY)
d_var = m.addVar(vtype=GRB.BINARY)
e.g_var = g_var
e.d_var = d_var
m.addGenConstrAnd(e.d_var, [e.g_var, e.edge_var])
m.update()
# add g and d variables for pair-pair edges
for e in cfg.digraph.es:
g_var = m.addVar(vtype=GRB.BINARY)
d_var = m.addVar(vtype=GRB.BINARY)
e.g_var = g_var
e.d_var = d_var
m.addGenConstrAnd(e.d_var, [e.g_var, e.used_var])
m.update()
# gamma is not integer
else:
if cfg.use_chains:
# use both gf (full discount if gf=1, gp=0) and gp (partial discount, if gf=gp=1)
for ndd in cfg.ndds:
for e in ndd.edges:
gf_var = m.addVar(vtype=GRB.BINARY)
df_var = m.addVar(vtype=GRB.BINARY)
e.gf_var = gf_var
e.df_var = df_var
m.addGenConstrAnd(e.df_var, [e.gf_var, e.edge_var])
gp_var = m.addVar(vtype=GRB.BINARY)
dp_var = m.addVar(vtype=GRB.BINARY)
e.gp_var = gp_var
e.dp_var = dp_var
m.addGenConstrAnd(e.dp_var, [e.gp_var, e.edge_var])
m.update()
for e in cfg.digraph.es:
gf_var = m.addVar(vtype=GRB.BINARY)
df_var = m.addVar(vtype=GRB.BINARY)
e.gf_var = gf_var
e.df_var = df_var
m.addGenConstrAnd(e.df_var, [e.gf_var, e.used_var])
gp_var = m.addVar(vtype=GRB.BINARY)
dp_var = m.addVar(vtype=GRB.BINARY)
e.gp_var = gp_var
e.dp_var = dp_var
m.addGenConstrAnd(e.dp_var, [e.gp_var, e.used_var])
m.update()
# discount indicators g follow same ordering as the edge discount values (sort in increasing order)
if cfg.use_chains:
ndd_e = [e for ndd in cfg.ndds for e in ndd.edges]
else:
ndd_e = []
all_edges = cfg.digraph.es + ndd_e
e_sorted = sorted(all_edges, key=lambda x: x.discount, reverse=False)
# ordering constraints over g
# gamma is integer
if gamma_frac == 0:
for i in range(len(e_sorted) - 1):
m.addConstr(e_sorted[i].g_var <= e_sorted[i + 1].g_var)
# gamma is not integer
else:
for i in range(len(e_sorted) - 1):
m.addConstr(e_sorted[i].gf_var <= e_sorted[i + 1].gf_var)
m.addConstr(e_sorted[i].gp_var <= e_sorted[i + 1].gp_var)
# number of edges used in matching (include all position-indexed vars)
# uncertainty budget (number of discounted edges)
gamma_var = m.addVar(vtype=GRB.CONTINUOUS)
m.addGenConstrMin(gamma_var, [num_edges_var, cfg.gamma])
# add a cardinality restriction if necessary
if cfg.cardinality_restriction is not None:
m.addConstr(num_edges_var <= cfg.cardinality_restriction)
m.update()
# limit number of discounted variables
# gamma is integer
if gamma_frac == 0:
m.addConstr(quicksum(e.d_var for e in all_edges) == gamma_var)
# gamma is not integer
else:
h_var = m.addVar(vtype=GRB.BINARY)
m.addConstr(cfg.gamma - num_edges_var <= W_small * h_var)
m.addConstr(num_edges_var - cfg.gamma <= W_small * (1 - h_var))
m.addConstr(
quicksum(e.dp_var for e in all_edges) == h_var * num_edges_var +
(1 - h_var) * ceil_gamma)
m.addConstr(
quicksum(e.df_var for e in all_edges) == h_var * num_edges_var +
(1 - h_var) * floor_gamma)
# total discount (by edge)
# gamma is integer
if gamma_frac == 0:
total_discount = quicksum(e.discount * e.d_var for e in all_edges)
# gamma is not integer
else:
total_discount = quicksum((1 - gamma_frac) * e.discount * e.df_var for e in all_edges) + \
quicksum(gamma_frac * e.discount * e.dp_var for e in all_edges)
# set a variable for the total (optimistic matching weight)
total_weight = m.addVar(vtype=GRB.CONTINUOUS)
m.update()
if not cfg.use_chains:
m.addConstr(total_weight == quicksum(
failure_aware_cycle_weight(c, cfg.digraph, cfg.edge_success_prob) *
var for c, var in zip(cycles, cycle_vars)))
obj_expr = total_weight - total_discount
elif cfg.edge_success_prob == 1:
m.addConstr(total_weight == (quicksum(
cycle_weight(c, cfg.digraph) * var
for c, var in zip(cycles, cycle_vars)) +
quicksum(e.weight * e.edge_var
for ndd in cfg.ndds
for e in ndd.edges) +
quicksum(e.weight * var
for e in cfg.digraph.es
for var in e.grb_vars)))
obj_expr = total_weight - total_discount
else:
raise Warning("not implemented")
m.setObjective(obj_expr, GRB.MAXIMIZE)
optimize(m)
if gamma_frac == 0: # gamma is integer
discounted_pair_edges = [e for e in cfg.digraph.es if e.d_var.x > 0]
for e in discounted_pair_edges:
e.discount_frac = e.d_var.x
if cfg.use_chains:
discounted_ndd_edges = [(i_ndd, e)
for i_ndd, ndd in enumerate(cfg.ndds)
for e in ndd.edges if e.d_var.x > 0.0]
for _, e in discounted_ndd_edges:
e.discount_frac = e.d_var.x
else: # gamma is not integer
discounted_pair_edges = [e for e in cfg.digraph.es \
if ((e.df_var.x > 0.0) or (e.dp_var.x > 0.0))]
for e in discounted_pair_edges:
e.discount_frac = (
1 - gamma_frac) * e.df_var.x + gamma_frac * e.dp_var.x
if cfg.use_chains:
discounted_ndd_edges = [(i_ndd, e) for i_ndd, ndd in enumerate(cfg.ndds) for e in ndd.edges \
if ((e.df_var.x > 0.0) or (e.dp_var.x > 0.0))]
for _, e in discounted_ndd_edges:
e.discount_frac = (
1 - gamma_frac) * e.df_var.x + gamma_frac * e.dp_var.x
if cfg.use_chains:
ndd_matching_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_matching_edges = []
used_matching_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
matching_edges = ndd_matching_edges + used_matching_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges)))
chains_used = kidney_utils.get_optimal_chains(cfg.digraph, cfg.ndds, cfg.edge_success_prob) if cfg.use_chains \
else []
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=chains_used,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
gamma=cfg.gamma,
robust_weight=m.objVal,
optimistic_weight=total_weight.x,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
return sol, matching_edges
def optimize_picef(cfg):
m, cycles, cycle_vars, _ = create_picef_model(cfg)
# add cycle objects
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = failure_aware_cycle_weight(c_obj.vs, cfg.digraph,
cfg.edge_success_prob)
c_obj.grb_var = var
cycle_list.append(c_obj)
if not cfg.use_chains:
obj_expr = quicksum(
failure_aware_cycle_weight(c, cfg.digraph, cfg.edge_success_prob) *
var for c, var in zip(cycles, cycle_vars))
elif cfg.edge_success_prob == 1:
obj_expr = (quicksum(
cycle_weight(c, cfg.digraph) * var
for c, var in zip(cycles, cycle_vars)) +
quicksum(e.weight * e.edge_var for ndd in cfg.ndds
for e in ndd.edges) +
quicksum(e.weight * var for e in cfg.digraph.es
for var in e.grb_vars))
else:
obj_expr = (quicksum(
failure_aware_cycle_weight(c, cfg.digraph, cfg.edge_success_prob) *
var for c, var in zip(cycles, cycle_vars)) +
quicksum(e.weight * cfg.edge_success_prob * e.edge_var
for ndd in cfg.ndds for e in ndd.edges) +
quicksum(
e.weight * cfg.edge_success_prob**(pos + 1) * var
for e in cfg.digraph.es
for var, pos in zip(e.grb_vars, e.grb_var_positions)))
m.setObjective(obj_expr, GRB.MAXIMIZE)
optimize(m)
pair_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob)
ndd_chain_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_chain_edges = []
matching_chains = []
matching_edges = pair_edges + ndd_chain_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges)))
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
return sol, matching_edges
def optimize_DRO_SAA_picef(cfg, num_weight_measurements, gamma, alpha, theta,
w_min, w_max):
"""Solve the DRO-SAA formulation of (Ren, 2020)
Arguments:
cfg: (OptConfig object)
num_weight_measurements: (int). number of weight measurements associated with each edge
gamma: (float). parameter balancing between a pure CVar objective (gamma->infinity) and a pure max-expectation
objective (gamma=0)
alpha: (float). CVar protection level, should be on [0, 1]
theta: prediction of distance between assumed distribution and true distribution
w_min: (float). assumed minimum edge weight of unknown distribution
w_max: (float). assumed maximum edge weight of unknown distribution
"""
m, cycles, cycle_vars, _ = create_picef_model(cfg)
# add cycle objects
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = failure_aware_cycle_weight(c_obj.vs, cfg.digraph,
cfg.edge_success_prob)
c_obj.grb_var = var
cycle_list.append(c_obj)
# add variables for each edge weight measurement
weight_vars = m.addVars(num_weight_measurements,
vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for i in range(num_weight_measurements):
m.addConstr(weight_vars[i] == -(quicksum(e.used_var * e.weight_list[i]
for e in cfg.digraph.es) +
quicksum(e.weight_list[i] * e.edge_var
for ndd in cfg.ndds
for e in ndd.edges)))
# auxiliary variables
d_var = m.addVar(vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY,
name='d')
lam_var = m.addVar(vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY,
name='lambda')
s_vars = m.addVars(num_weight_measurements,
vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY,
name='s')
# add eta and mu vars for each edge
for e in cfg.digraph.es:
e.eta_vars = m.addVars(num_weight_measurements,
2,
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name='eta')
e.mu_vars = m.addVars(num_weight_measurements,
2,
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name='mu')
for n in cfg.ndds:
for e in n.edges:
# also add the used_var here, for convenience
e.used_var = e.edge_var
e.eta_vars = m.addVars(num_weight_measurements,
2,
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name='eta')
e.mu_vars = m.addVars(num_weight_measurements,
2,
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name='mu')
# add variables for each edge weight measurement
weight_vars = m.addVars(num_weight_measurements,
vtype=GRB.CONTINUOUS,
lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for i in range(num_weight_measurements):
m.addConstr(weight_vars[i] == -(quicksum(e.used_var * e.weight_list[i]
for e in cfg.digraph.es) +
quicksum(e.weight_list[i] * e.edge_var
for ndd in cfg.ndds
for e in ndd.edges)))
b1 = 0
b2 = -d_var * gamma / alpha
# construct a list of all edges, for convenience
e_list = cfg.digraph.es + [e for n in cfg.ndds for e in n.edges]
# add main constraints
for i_measurement in range(num_weight_measurements):
# k = 1
edge_sum_1a = quicksum([
e.eta_vars[i_measurement, 0] *
(w_max - e.weight_list[i_measurement]) for e in e_list
])
edge_sum_1b = quicksum([
e.mu_vars[i_measurement, 0] *
(e.weight_list[i_measurement] - w_min) for e in e_list
])
m.addConstr(b1 + weight_vars[i_measurement] + edge_sum_1a + edge_sum_1b
<= s_vars[i_measurement],
name=("s_constr_k1_i%d" % i_measurement))
# k = 2
edge_sum_2a = quicksum([
e.eta_vars[i_measurement, 1] *
(w_max - e.weight_list[i_measurement]) for e in e_list
])
edge_sum_2b = quicksum([
e.mu_vars[i_measurement, 1] *
(e.weight_list[i_measurement] - w_min) for e in e_list
])
m.addConstr(b2 + (1 + gamma / alpha) * weight_vars[i_measurement] +
edge_sum_2a + edge_sum_2b <= s_vars[i_measurement],
name=("s_constr__k2_i%d" % i_measurement))
# now for the norm sum (using the 1-norm)
# for each edge, get |\eta_ik - \mu_ik - a_k|. then sum all of these to obtain the 1-norm
e_norm_plus_vars_k1 = m.addVars(len(e_list),
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name=("e_norm_plus_k1_i%d" %
i_measurement))
e_norm_minus_vars_k1 = m.addVars(len(e_list),
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name=("e_norm_minus_k1_i%d" %
i_measurement))
e_norm_plus_vars_k2 = m.addVars(len(e_list),
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name=("e_norm_plus_k2_i%d" %
i_measurement))
e_norm_minus_vars_k2 = m.addVars(len(e_list),
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=GRB.INFINITY,
name=("e_norm_minus_k2_i%d" %
i_measurement))
for i_e, e in enumerate(e_list):
# k = 1
m.addConstr(
e_norm_plus_vars_k1[i_e] -
e_norm_minus_vars_k1[i_e] == e.eta_vars[i_measurement, 0] -
e.mu_vars[i_measurement, 0] + e.used_var)
# k = 2
m.addConstr(
e_norm_plus_vars_k2[i_e] -
e_norm_minus_vars_k2[i_e] == e.eta_vars[i_measurement, 1] -
e.mu_vars[i_measurement, 1] + (1 + gamma / alpha) * e.used_var)
# the 1-norm must be bounded by lambda, for each measurement and for each k
m.addConstr(
quicksum(e_norm_plus_vars_k2) +
quicksum(e_norm_minus_vars_k2) <= lam_var)
m.addConstr(
quicksum(e_norm_plus_vars_k1) +
quicksum(e_norm_minus_vars_k1) <= lam_var)
# objective
obj = lam_var * theta + (1.0 / float(num_weight_measurements)
) * quicksum(s_vars) + gamma * d_var
m.setObjective(obj, sense=GRB.MINIMIZE)
if not cfg.use_chains:
raise Exception("not implemented")
elif cfg.edge_success_prob == 1:
pass
else:
raise Exception("not implemented")
optimize(m)
pair_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob)
# matching_chains = []
ndd_chain_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_chain_edges = []
matching_chains = []
matching_edges = pair_edges + ndd_chain_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges)))
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(sol, cfg.digraph, cfg.ndds, cfg.max_cycle,
cfg.max_chain)
return sol, matching_edges
def optimize_dro_saa_edge_existence(cfg, num_measurements, gamma, alpha):
"""
solve the PICEF model with DRO-SAA objective for edge existence uncertainty
this requires that each edge has the property e.realizations: a binary vector of length num_measurements
"""
m, cycles, cycle_vars, _ = create_picef_model(
cfg, add_o_vars=True, num_o_vars=num_measurements
)
# add cycle objects
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = expected_cycle_weight(c_obj)
c_obj.grb_var = var
# for DRO-SAA - keep track of cycle realizations
c_obj.realizations = [
min(e.realizations[n] for e in c_obj.edges) for n in range(num_measurements)
]
cycle_list.append(c_obj)
# add weight variables for each realization
w_vars = m.addVars(num_measurements, lb=-GRB.INFINITY, ub=GRB.INFINITY)
for n in range(num_measurements):
# objective for the n^th realization
m.addConstr(
w_vars[n]
== (
-quicksum(
e.weight * big_o_var
for i in range(cfg.max_chain - 1)
for v in cfg.digraph.vs
for e, big_o_var in zip(v.edges_in[i], v.big_o_vars_in[i][n])
)
- quicksum(c.weight * c.realizations[n] * c.grb_var for c in cycle_list)
)
)
d_var = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
# define pi variables
pi_vars = m.addVars(num_measurements, lb=0, ub=GRB.INFINITY)
for n in range(num_measurements):
m.addConstr(pi_vars[n] >= w_vars[n] - d_var)
# define objective
obj_expr = (1.0 / float(num_measurements)) * quicksum(w_vars) + gamma * (
d_var + (1.0 / (alpha * float(num_measurements))) * quicksum(pi_vars)
)
m.setObjective(obj_expr, GRB.MINIMIZE)
optimize(m)
pair_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob
)
ndd_chain_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_chain_edges = []
matching_chains = []
matching_edges = pair_edges + ndd_chain_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges))
)
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(
ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction,
)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(
sol, cfg.digraph, cfg.ndds, cfg.max_cycle, cfg.max_chain
)
return cycle_obj, matching_chains
def optimize_picef_heterogeneous_edge_prob(cfg):
"""
solve the PICEF model with heterogeneous edge success probabilities of Ren, McElfresh, Bidkhori, Dickerson (2020)
this requires that each edge has the property edge.success_prob
"""
m, cycles, cycle_vars, _ = create_picef_model(cfg, add_o_vars=True)
# add cycle objects
cycle_list = []
for c, var in zip(cycles, cycle_vars):
c_obj = Cycle(c)
c_obj.add_edges(cfg.digraph.es)
c_obj.weight = expected_cycle_weight(c_obj)
c_obj.grb_var = var
cycle_list.append(c_obj)
# add objective
chain_weight = quicksum(
e.weight * big_o_var
for i in range(cfg.max_chain - 1)
for v in cfg.digraph.vs
for e, big_o_var in zip(v.edges_in[i], v.big_o_vars_in[i])
)
obj_expr = chain_weight + quicksum(c.weight * c.grb_var for c in cycle_list)
m.setObjective(obj_expr, GRB.MAXIMIZE)
optimize(m)
pair_edges = [e for e in cfg.digraph.es if e.used_var.x > 0.5]
if cfg.use_chains:
matching_chains = kidney_utils.get_optimal_chains(
cfg.digraph, cfg.ndds, cfg.edge_success_prob
)
ndd_chain_edges = [
e for ndd in cfg.ndds for e in ndd.edges if e.edge_var.x > 0.5
]
else:
ndd_chain_edges = []
matching_chains = []
matching_edges = pair_edges + ndd_chain_edges
if cfg.cardinality_restriction is not None:
if len(matching_edges) > cfg.cardinality_restriction:
raise Warning(
"cardinality restriction is violated: restriction = %d edges, matching uses %d edges"
% (cfg.cardinality_restriction, len(matching_edges))
)
cycles_used = [c for c, v in zip(cycles, cycle_vars) if v.x > 0.5]
cycle_obj = [c for c in cycle_list if c.grb_var.x > 0.5]
sol = OptSolution(
ip_model=m,
cycles=cycles_used,
cycle_obj=cycle_obj,
chains=matching_chains,
digraph=cfg.digraph,
edge_success_prob=cfg.edge_success_prob,
chain_restriction=cfg.chain_restriction,
cycle_restriction=cfg.cycle_restriction,
cycle_cap=cfg.max_chain,
chain_cap=cfg.max_cycle,
cardinality_restriction=cfg.cardinality_restriction,
)
sol.add_matching_edges(cfg.ndds)
kidney_utils.check_validity(
sol, cfg.digraph, cfg.ndds, cfg.max_cycle, cfg.max_chain
)
return cycle_obj, matching_chains
