def lp_model(cg: ComputationGraph,
agentsdef: Iterable[AgentDef],
footprint: Callable[[str], float],
capacity: Callable[[str], float],
route: Callable[[str, str], float],
msg_load: Callable[[str, str], float],
hosting_cost: Callable[[str, str], float]):
comp_names = [n.name for n in cg.nodes]
agt_names = [a.name for a in agentsdef]
pb = LpProblem('ilp_compref', LpMinimize)
# One binary variable xij for each (variable, agent) couple
xs = LpVariable.dict('x', (comp_names, agt_names), cat=LpBinary)
# One binary variable for computations c1 and c2, and agent a1 and a2
betas = {}
count = 0
for a1, a2 in combinations(agt_names, 2):
# Only create variables for couple c1, c2 if there is an edge in the
# graph between these two computations.
for l in cg.links:
# As we support hypergraph, we may have more than 2 ends to a link
for c1, c2 in combinations(l.nodes, 2):
count += 2
b = LpVariable('b_{}_{}_{}_{}'.format(c1, a1, c2, a2),
cat=LpBinary)
betas[(c1, a1, c2, a2)] = b
pb += b <= xs[(c1, a1)]
pb += b <= xs[(c2, a2)]
pb += b >= xs[(c2, a2)] + xs[(c1, a1)] - 1
b = LpVariable('b_{}_{}_{}_{}'.format(c1, a2, c2, a1),
cat=LpBinary)
betas[(c1, a2, c2, a1)] = b
pb += b <= xs[(c2, a1)]
pb += b <= xs[(c1, a2)]
pb += b >= xs[(c1, a2)] + xs[(c2, a1)] - 1
# Set objective: communication + hosting_cost
pb += _objective(xs, betas, route, msg_load, hosting_cost), \
'Communication costs and prefs'
# Adding constraints:
# Constraints: Memory capacity for all agents.
for a in agt_names:
pb += lpSum([footprint(i) * xs[i, a] for i in comp_names])\
<= capacity(a), \
'Agent {} capacity'.format(a)
# Constraints: all computations must be hosted.
for c in comp_names:
pb += lpSum([xs[c, a] for a in agt_names]) == 1, \
'Computation {} hosted'.format(c)
# solve using GLPK
status = pb.solve(solver=GLPK_CMD(keepFiles=1, msg=False,
options=['--pcost']))
if status != LpStatusOptimal:
raise ImpossibleDistributionException("No possible optimal"
" distribution ")
logger.debug('GLPK cost : %s', value(pb.objective))
# print('BETAS:')
# for c1, a1, c2, a2 in betas:
# print(' ', c1, a1, c2, a2, value(betas[(c1, a1, c2, a2)]))
#
# print('XS:')
# for c, a in xs:
# print(' ', c, a, value(xs[(c, a)]))
mapping = {}
for k in agt_names:
agt_computations = [i for i, ka in xs
if ka == k and value(xs[(i, ka)]) == 1]
# print(k, ' -> ', agt_computations)
mapping[k] = agt_computations
return mapping
def distribute_factors(
agents: Dict[str, AgentDef],
cg: ComputationGraph,
footprints: Dict[str, float],
mapping: Dict[str, List[str]],
msg_load: Callable[[str, str], float],
) -> Dict[str, List[str]]:
"""
Optimal distribution of factors on agents.
Parameters
----------
cg: computations graph
agents: dict
a dict {agent_name : AgentDef} containing all available agents
Returns
-------
a dict { agent_name: list of factor names}
"""
pb = LpProblem("ilp_factors", LpMinimize)
# build the inverse mapping var -> agt
inverse_mapping = {} # type: Dict[str, str]
for a in mapping:
inverse_mapping[mapping[a][0]] = a
# One binary variable xij for each (variable, agent) couple
factor_names = [n.name for n in cg.nodes if isinstance(n, FactorComputationNode)]
xs = LpVariable.dict("x", (factor_names, agents), cat=LpBinary)
logger.debug("Binary variables for factor distribution : %s", xs)
# Hard constraints: respect agent's capacity
for a in agents:
# Footprint of the variable this agent is already hosting:
v_footprint = footprints[mapping[a][0]]
pb += (
lpSum([footprints[fn] * xs[fn, a] for fn in factor_names])
<= (agents[a].capacity - v_footprint),
"Agent {} capacity".format(a),
)
# Hard constraints: all computations must be hosted.
for c in factor_names:
pb += lpSum([xs[c, a] for a in agents]) == 1, "Factor {} hosted".format(c)
# 1st objective : minimize communication costs:
comm = LpAffineExpression()
for (fn, an_f) in xs:
for vn in cg.neighbors(fn):
an_v = inverse_mapping[vn] # agt hosting neighbor var vn
comm += agents[an_f].route(an_v) * msg_load(vn, fn) * xs[(fn, an_f)]
# 2st objective : minimize hosting costs
hosting = lpSum([agents[a].hosting_cost(c) * xs[(c, a)] for c, a in xs])
# agregate the two objectives using RATIO_HOST_COMM
pb += lpSum([RATIO_HOST_COMM * comm, (1 - RATIO_HOST_COMM) * hosting])
# solve using GLPK and convert to mapping { agt_name : [factors names]}
status = pb.solve(solver=GLPK_CMD(keepFiles=1, msg=False, options=["--pcost"]))
if status != LpStatusOptimal:
raise ImpossibleDistributionException(
"No possible optimal distribution for factors"
)
logger.debug("GLPK cost : %s", value(pb.objective))
mapping = {} # type: Dict[str, List[str]]
for k in agents:
agt_computations = [i for i, ka in xs if ka == k and value(xs[(i, ka)]) == 1]
# print(k, ' -> ', agt_computations)
mapping[k] = agt_computations
logger.debug("Factors distribution : %s ", mapping)
return mapping
