def init_matchable(self):
"""initialize the property matchable for each edge in the graph. matchable = True means the edge can be included
in any matching (i.e., it's in at least one cycle or chain)"""
# initialize all edges to be not-matchable
for e in self.all_edge_list:
e.matchable = False
cycles = self.graph.find_cycles(self.cycle_cap)
cycle_list = []
# all edges in a cycle are matchable
for c in cycles:
c_obj = Cycle(c)
c_obj.add_edges(self.graph.es)
cycle_list.append(c_obj)
for e in c_obj.edges:
e.matchable = True
# all NDDEdges are matchable
for n in self.altruists:
for e in n.edges:
e.matchable = True
# all pair-pair edges that are within chain distance are matchable
dists_from_ndd = kidney_utils.get_dist_from_nearest_ndd(
self.graph, self.altruists
)
for e in self.all_edge_list:
if dists_from_ndd[e.src.id] <= self.chain_cap - 1:
e.matchable = True
if self.logger is not None:
self.logger.info(
f"matchable edges: {len([e for e in self.all_edge_list if e.matchable])} (out of {len(self.all_edge_list)} total)"
)
def add_chain_vars_and_constraints(digraph, ndds, max_chain, m, vtx_to_vars, store_edge_positions=False):
"""Add the IP variables and constraints for chains in PICEF and HPIEF'.
Args:
ndds: a list of NDDs in the instance
max_chain: the chain cap
m: The Gurobi model
vtx_to_vars: A list such that for each Vertex v in the Digraph,
vtx_to_vars[v.id] will contain the Gurobi variables representing
edges pointing to v.
store_edge_positions: if this is True, then an attribute grb_edge_positions
will be added to edges that have associated Gurobi variables.
edge.grb_edge_positions[i] will indicate the position of the edge respresented
by edge.grb_vars[i]. (default: False)
"""
if max_chain > 0:
for v in digraph.vs:
v.grb_vars_in = [[] for i in range(max_chain - 1)]
v.grb_vars_out = [[] for i in range(max_chain - 1)]
for ndd in ndds:
ndd_edge_vars = []
for e in ndd.edges:
edge_var = m.addVar(vtype=GRB.BINARY)
e.edge_var = edge_var
ndd_edge_vars.append(edge_var)
vtx_to_vars[e.target_v.id].append(edge_var)
if max_chain > 1:
e.target_v.grb_vars_in[0].append(edge_var)
m.update()
m.addConstr(quicksum(ndd_edge_vars) <= 1)
dists_from_ndd = kidney_utils.get_dist_from_nearest_ndd(digraph, ndds)
# Add pair->pair edge variables, indexed by position in chain
for e in digraph.es:
e.grb_vars = []
if store_edge_positions:
e.grb_var_positions = []
for i in range(max_chain - 1):
if dists_from_ndd[e.src.id] <= i + 1:
edge_var = m.addVar(vtype=GRB.BINARY)
e.grb_vars.append(edge_var)
if store_edge_positions:
e.grb_var_positions.append(i + 1)
vtx_to_vars[e.tgt.id].append(edge_var)
e.src.grb_vars_out[i].append(edge_var)
if i < max_chain - 2:
e.tgt.grb_vars_in[i + 1].append(edge_var)
m.update()
# At each chain position, sum of edges into a vertex must be >= sum of edges out
for i in range(max_chain - 1):
for v in digraph.vs:
m.addConstr(quicksum(v.grb_vars_in[i]) >= quicksum(v.grb_vars_out[i]))
def add_chain_vars_and_constraints(digraph, ndds, max_chain, m, vtx_to_vars,
store_edge_positions=False):
"""Add the IP variables and constraints for chains in PICEF and HPIEF'.
Args:
ndds: a list of NDDs in the instance
max_chain: the chain cap
m: The Gurobi model
vtx_to_vars: A list such that for each Vertex v in the Digraph,
vtx_to_vars[v.id] will contain the Gurobi variables representing
edges pointing to v.
store_edge_positions: if this is True, then an attribute grb_edge_positions
will be added to edges that have associated Gurobi variables.
edge.grb_edge_positions[i] will indicate the position of the edge respresented
by edge.grb_vars[i]. (default: False)
"""
if max_chain > 0:
for v in digraph.vs:
v.grb_vars_in = [[] for i in range(max_chain-1)]
v.grb_vars_out = [[] for i in range(max_chain-1)]
for ndd in ndds:
ndd_edge_vars = []
for e in ndd.edges:
edge_var = m.addVar(vtype=GRB.BINARY)
e.edge_var = edge_var
ndd_edge_vars.append(edge_var)
vtx_to_vars[e.target_v.id].append(edge_var)
if max_chain>1: e.target_v.grb_vars_in[0].append(edge_var)
m.update()
m.addConstr(quicksum(ndd_edge_vars) <= 1)
dists_from_ndd = kidney_utils.get_dist_from_nearest_ndd(digraph, ndds)
# Add pair->pair edge variables, indexed by position in chain
for e in digraph.es:
e.grb_vars = []
if store_edge_positions:
e.grb_var_positions = []
for i in range(max_chain-1):
if dists_from_ndd[e.src.id] <= i+1:
edge_var = m.addVar(vtype=GRB.BINARY)
e.grb_vars.append(edge_var)
if store_edge_positions:
e.grb_var_positions.append(i+1)
vtx_to_vars[e.tgt.id].append(edge_var)
e.src.grb_vars_out[i].append(edge_var)
if i < max_chain-2:
e.tgt.grb_vars_in[i+1].append(edge_var)
m.update()
# At each chain position, sum of edges into a vertex must be >= sum of edges out
for i in range(max_chain-1):
for v in digraph.vs:
m.addConstr(quicksum(v.grb_vars_in[i]) >= quicksum(v.grb_vars_out[i]))
def add_chain_vars_and_constraints(
digraph,
ndds,
use_chains,
max_chain,
m,
vtx_to_vars,
store_edge_positions=False,
add_o_vars=False,
num_o_vars=0,
check_edge_success=False,
):
"""Add the IP variables and constraints for chains in PICEF and HPIEF'.
Args:
ndds: a list of NDDs in the instance
use_chains: boolean: True if chains should be used
max_chain: the chain cap
m: The Gurobi model
vtx_to_vars: A list such that for each Vertex v in the Digraph,
vtx_to_vars[v.id] will contain the Gurobi variables representing
edges pointing to v.
store_edge_positions: if this is True, then an attribute grb_var_positions
will be added to edges that have associated Gurobi variables.
edge.grb_var_positions[i] will indicate the position of the edge respresented
by edge.grb_vars[i]. (default: False)
add_o_vars: (bool). specific to the heterogeneous edge success probability formulation. add o_vars and big_o_vars
properties to each edge, and add big_o_vars_in and big_o_vars_out properties to each vertex (analagous to
v.edges_in and v.edges_out. this requires that e.success_prob is set for each edge
num_o_vars: (int). if set to >1, then create this number of o and big_o variables, for the DRO-SAA formulation.
if this is set, each edge needs the property e.realizations - a binary vector of length num_o_vars
"""
if use_chains: # max_chain > 0:
for v in digraph.vs:
v.grb_vars_in = [[] for i in range(max_chain - 1)]
v.grb_vars_out = [[] for i in range(max_chain - 1)]
v.edges_in = [[] for i in range(max_chain - 1)]
v.edges_out = [[] for i in range(max_chain - 1)]
if add_o_vars:
if num_o_vars < 2:
v.big_o_vars_in = [[] for i in range(max_chain - 1)]
v.big_o_vars_out = [[] for i in range(max_chain - 1)]
else:
# v.big_o_vars[i][n] is the n^th instance of big_o_vars for the i^th edge position...
v.big_o_vars_in = [
[[] for j in range(num_o_vars)] for i in range(max_chain - 1)
]
v.big_o_vars_out = [
[[] for j in range(num_o_vars)] for i in range(max_chain - 1)
]
for ndd in ndds:
ndd_edge_vars = []
for e in ndd.edges:
edge_var = m.addVar(vtype=GRB.BINARY)
if check_edge_success:
if not e.success:
m.addConstr(edge_var == 0)
e.edge_var = edge_var
ndd_edge_vars.append(edge_var)
if add_o_vars:
if num_o_vars < 2:
e.o_var = m.addVar(lb=0, ub=(1 - e.success_prob))
e.big_o_var = m.addVar(lb=0, ub=(1 - e.success_prob))
m.addConstr(e.big_o_var <= e.edge_var)
m.addConstr(e.big_o_var <= e.o_var)
else:
e.o_vars = m.addVars(num_o_vars, lb=0, ub=1)
e.big_o_vars = m.addVars(num_o_vars, lb=0, ub=1)
for n in range(num_o_vars):
m.addConstr(e.big_o_vars[n] <= e.edge_var)
m.addConstr(e.big_o_vars[n] <= e.o_vars[n])
m.addConstr(e.o_vars[n] <= e.realizations[n])
vtx_to_vars[e.tgt.id].append(edge_var)
if max_chain > 1:
e.tgt.grb_vars_in[0].append(edge_var)
e.tgt.edges_in[0].append(e)
if add_o_vars:
if num_o_vars < 2:
e.tgt.big_o_vars_in[0].append(e.big_o_var)
else:
for n in range(num_o_vars):
e.tgt.big_o_vars_in[0][n].append(e.big_o_vars[n])
m.update()
m.addConstr(quicksum(ndd_edge_vars) <= 1)
dists_from_ndd = kidney_utils.get_dist_from_nearest_ndd(digraph, ndds)
# Add pair->pair edge variables, indexed by position in chain
# e.grb_var are the chain variables for each edge.
for e in digraph.es:
e.grb_vars = []
if add_o_vars:
if num_o_vars < 2:
e.o_vars = []
e.big_o_vars = []
else:
# e.o_vars[n][i] is the o-var for the n^th edge realization
e.o_vars = []
e.big_o_vars = []
if store_edge_positions:
e.grb_var_positions = []
for i in range(max_chain - 1):
if dists_from_ndd[e.src.id] <= i + 1:
edge_var = m.addVar(vtype=GRB.BINARY)
if check_edge_success:
if not e.success:
m.addConstr(edge_var == 0)
e.grb_vars.append(edge_var)
if add_o_vars:
if num_o_vars < 2:
o_var = m.addVar(lb=0, ub=(1 - e.success_prob))
big_o_var = m.addVar(lb=0, ub=(1 - e.success_prob))
e.o_vars.append(o_var)
e.big_o_vars.append(big_o_var)
m.addConstr(big_o_var <= edge_var)
m.addConstr(big_o_var <= o_var)
else:
o_vars = m.addVars(num_o_vars, lb=0, ub=1)
big_o_vars = m.addVars(num_o_vars, lb=0, ub=1)
e.o_vars.append(o_vars)
e.big_o_vars.append(big_o_vars)
for n in range(num_o_vars):
m.addConstr(big_o_vars[n] <= edge_var)
m.addConstr(big_o_vars[n] <= o_vars[n])
m.addConstr(o_vars[n] <= e.realizations[n])
if store_edge_positions:
e.grb_var_positions.append(i + 1)
vtx_to_vars[e.tgt.id].append(edge_var)
e.src.grb_vars_out[i].append(edge_var)
e.src.edges_out[i].append(e)
if add_o_vars:
if num_o_vars < 2:
e.src.big_o_vars_out[i].append(big_o_var)
else:
for n in range(num_o_vars):
e.src.big_o_vars_out[i][n].append(big_o_vars[n])
if i < max_chain - 2:
e.tgt.grb_vars_in[i + 1].append(edge_var)
e.tgt.edges_in[i + 1].append(e)
if add_o_vars:
if num_o_vars < 2:
e.tgt.big_o_vars_in[i + 1].append(big_o_var)
else:
for n in range(num_o_vars):
e.tgt.big_o_vars_in[i + 1][n].append(big_o_vars[n])
# m.update()
# At each chain position, sum of edges into a vertex must be >= sum of edges out
for i in range(max_chain - 1):
for v in digraph.vs:
m.addConstr(quicksum(v.grb_vars_in[i]) >= quicksum(v.grb_vars_out[i]))
if add_o_vars:
if num_o_vars < 2:
assert len(v.edges_out[i]) == len(v.big_o_vars_out[i])
m.addConstr(
quicksum(v.big_o_vars_in[i])
>= quicksum(
(1.0 / e.success_prob) * var
for e, var in zip(v.edges_out[i], v.big_o_vars_out[i])
)
)
else:
for n in range(num_o_vars):
m.addConstr(
quicksum(v.big_o_vars_in[i][n])
>= quicksum(v.big_o_vars_out[i][n])
)
m.update()
