def _update(self, clique_data, parent=None):
for c in clique_data['cliques']:
self.cliques[c['name']] = v = self.model.variable(
c['name'],
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
for img, cmd in product(c['images'], c['commands']):
self.by_img_cmd[img,cmd].append(v)
self._obj.append(Expr.mul(float(c['time']), v))
if parent is not None:
self.model.constraint(
'c-%s-%s' % (c['name'], parent['name']),
Expr.sub(v, self.cliques[parent['name']]),
Domain.lessThan(0.0)
)
for child in c['children']:
self._update(child, c)
for inter in clique_data['intersections']:
self.model.constraint(
'iter-%d' % self._inter,
Expr.add([self.cliques[i] for i in inter]),
Domain.lessThan(1.0)
)
self._inter += 1
def solve(self, problem, saver):
# Construct model.
self.problem = problem
# Do recursive maximal clique detection.
self.clique_data = clique_data = problem.cliques()
self.model = model = Model()
if self.time is not None:
model.setSolverParam('mioMaxTime', 60.0 * int(self.time))
# Each image needs to run all its commands. This keep track of
# what variables run each command for each image.
self.by_img_cmd = by_img_cmd = defaultdict(list)
# Objective is the total cost of all the commands we run.
self._obj = []
# x[i,c] = 1 if image i incurs the cost of command c directly
self.x = x = {}
for img, cmds in problem.images.items():
for cmd in cmds:
name = 'x[%s,%s]' % (img, cmd)
x[name] = v = self.model.variable(
name,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
self._obj.append(Expr.mul(float(problem.commands[cmd]), v))
by_img_cmd[img,cmd].append(v)
# cliques[i] = 1 if clique i is used, 0 otherwise
self.cliques = {}
self._inter = 1
self._update(clique_data)
# Each image has to run each of its commands.
for img_cmd, vlist in by_img_cmd.items():
name = 'img-cmd-%s-%s' % img_cmd
self.model.constraint(
name,
Expr.add(vlist),
Domain.equalsTo(1.0)
)
model.objective('z', ObjectiveSense.Minimize, Expr.add(self._obj))
model.setLogHandler(sys.stdout)
model.acceptedSolutionStatus(AccSolutionStatus.Feasible)
model.solve()
# Translate the output of this to a schedule.
schedule = defaultdict(list)
self._translate(schedule, clique_data)
for name, v in x.items():
img, cmd = name.replace('x[','').replace(']','').split(',')
if v.level()[0] > 0.5:
schedule[img].append(cmd)
saver(schedule)
def solve(self, problem, saver):
# Construct model.
self.problem = problem
# Do recursive maximal clique detection.
self.clique_data = clique_data = problem.cliques()
self.model = model = Model()
if self.time is not None:
model.setSolverParam('mioMaxTime', 60.0 * int(self.time))
# Each image needs to run all its commands. This keep track of
# what variables run each command for each image.
self.by_img_cmd = by_img_cmd = defaultdict(list)
# Objective is the total cost of all the commands we run.
self._obj = []
# x[i,c] = 1 if image i incurs the cost of command c directly
self.x = x = {}
for img, cmds in problem.images.items():
for cmd in cmds:
name = 'x[%s,%s]' % (img, cmd)
x[name] = v = self.model.variable(name,
Domain.inRange(0.0, 1.0),
Domain.isInteger())
self._obj.append(Expr.mul(float(problem.commands[cmd]), v))
by_img_cmd[img, cmd].append(v)
# cliques[i] = 1 if clique i is used, 0 otherwise
self.cliques = {}
self._inter = 1
self._update(clique_data)
# Each image has to run each of its commands.
for img_cmd, vlist in by_img_cmd.items():
name = 'img-cmd-%s-%s' % img_cmd
self.model.constraint(name, Expr.add(vlist), Domain.equalsTo(1.0))
model.objective('z', ObjectiveSense.Minimize, Expr.add(self._obj))
model.setLogHandler(sys.stdout)
model.acceptedSolutionStatus(AccSolutionStatus.Feasible)
model.solve()
# Translate the output of this to a schedule.
schedule = defaultdict(list)
self._translate(schedule, clique_data)
for name, v in x.items():
img, cmd = name.replace('x[', '').replace(']', '').split(',')
if v.level()[0] > 0.5:
schedule[img].append(cmd)
saver(schedule)
def _update(self, clique_data, parent=None):
for c in clique_data['cliques']:
self.cliques[c['name']] = v = self.model.variable(
c['name'], Domain.inRange(0.0, 1.0), Domain.isInteger())
for img, cmd in product(c['images'], c['commands']):
self.by_img_cmd[img, cmd].append(v)
self._obj.append(Expr.mul(float(c['time']), v))
if parent is not None:
self.model.constraint(
'c-%s-%s' % (c['name'], parent['name']),
Expr.sub(v, self.cliques[parent['name']]),
Domain.lessThan(0.0))
for child in c['children']:
self._update(child, c)
for inter in clique_data['intersections']:
self.model.constraint('iter-%d' % self._inter,
Expr.add([self.cliques[i] for i in inter]),
Domain.lessThan(1.0))
self._inter += 1
#
# Image 2:
# x_2_a = 1
# x_2_b = 1
# x_2_c = 1
# x_2_d = 1
#
# Image 3:
# x_3_b = 1
# x_3_c = 1
# x_3_d = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Provide a variable for each image and command. This is 1 if the command
# is not run as part of a clique for the image.
x_1_a = m.variable('x_1_a', *binary)
x_1_b = m.variable('x_1_b', *binary)
x_2_a = m.variable('x_2_a', *binary)
x_2_b = m.variable('x_2_b', *binary)
x_2_c = m.variable('x_2_c', *binary)
x_2_d = m.variable('x_2_d', *binary)
x_3_b = m.variable('x_3_b', *binary)
x_3_c = m.variable('x_3_c', *binary)
x_3_d = m.variable('x_3_d', *binary)
#
# Images:
# w_1 = 0
# w_2 = 1
# w_3 = 1
#
# Commands:
# y_a = 0
# y_b = 1
# y_c = 1
# y_d = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Variables to determine if we include commands in the clique.
y_a = m.variable('y_a', *binary)
y_b = m.variable('y_b', *binary)
y_c = m.variable('y_c', *binary)
y_d = m.variable('y_d', *binary)
# Variables to determine if we include images in the clique.
w_1 = m.variable('w_1', *binary)
w_2 = m.variable('w_2', *binary)
w_3 = m.variable('w_3', *binary)
# Variables to enforce relationships between y and w decisions.
z_1_a = m.variable('z_1_a', *binary)
z_1_b = m.variable('z_1_b', *binary)
def solve(self, problem, saver):
# Construct model.
self.problem = problem
self.model = model = Model()
if self.time is not None:
model.setSolverParam('mioMaxTime', 60.0 * int(self.time))
# x[1,c] = 1 if the master schedule has (null, c) in its first stage
# x[s,c1,c2] = 1 if the master schedule has (c1, c2) in stage s > 1
x = {}
for s in problem.all_stages:
if s == 1:
# First arc in the individual image path.
for c in problem.commands:
x[1, c] = model.variable('x[1,%s]' % c, 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger())
else:
# Other arcs.
for c1, c2 in product(problem.commands, problem.commands):
if c1 == c2:
continue
x[s, c1, c2] = model.variable('x[%s,%s,%s]' % (s, c1, c2),
1, Domain.inRange(0.0, 1.0),
Domain.isInteger())
smax = max(problem.all_stages)
obj = [0.0]
# TODO: deal with images that do not have the same number of commands.
# t[s,c] is the total time incurred at command c in stage s
t = {}
for s in problem.all_stages:
for c in problem.commands:
t[s, c] = model.variable('t[%s,%s]' % (c, s), 1,
Domain.greaterThan(0.0))
if s == 1:
model.constraint(
't[1,%s]' % c,
Expr.sub(t[1, c],
Expr.mul(float(problem.commands[c]), x[1,
c])),
Domain.greaterThan(0.0))
else:
rhs = [0.0]
for c1, coeff in problem.commands.items():
if c1 == c:
continue
else:
rhs = Expr.add(
rhs, Expr.mulElm(t[s - 1, c1], x[s, c1, c]))
model.constraint('t[%s,%s]' % (s, c),
Expr.sub(t[1, c], rhs),
Domain.greaterThan(0.0))
# Objective function = sum of aggregate comand times
if s == smax:
obj = Expr.add(obj, t[s, c])
# y[i,1,c] = 1 if image i starts by going to c
# y[i,s,c1,c2] = 1 if image i goes from command c1 to c2 in stage s > 1
y = {}
for i, cmds in problem.images.items():
for s in problem.stages[i]:
if s == 1:
# First arc in the individual image path.
for c in cmds:
y[i, 1, c] = model.variable('y[%s,1,%s]' % (i, c), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger())
model.constraint('x_y[i%s,1,c%s]' % (i, c),
Expr.sub(x[1, c], y[i, 1, c]),
Domain.greaterThan(0.0))
else:
# Other arcs.
for c1, c2 in product(cmds, cmds):
if c1 == c2:
continue
y[i, s, c1, c2] = model.variable(
'y[%s,%s,%s,%s]' % (i, s, c1, c2), 1,
Domain.inRange(0.0, 1.0), Domain.isInteger())
model.constraint(
'x_y[i%s,s%s,c%s,c%s]' % (i, s, c1, c2),
Expr.sub(x[s, c1, c2], y[i, s, c1, c2]),
Domain.greaterThan(0.0))
for c in cmds:
# Each command is an arc destination exactly once.
arcs = [y[i, 1, c]]
for c1 in cmds:
if c1 == c:
continue
arcs.extend(
[y[i, s, c1, c] for s in problem.stages[i][1:]])
model.constraint('y[i%s,c%s]' % (i, c), Expr.add(arcs),
Domain.equalsTo(1.0))
# Network balance equations (stages 2 to |stages|-1).
# Sum of arcs in = sum of arcs out.
for s in problem.stages[i][:len(problem.stages[i]) - 1]:
if s == 1:
arcs_in = [y[i, 1, c]]
else:
arcs_in = [y[i, s, c1, c] for c1 in cmds if c1 != c]
arcs_out = [y[i, s + 1, c, c2] for c2 in cmds if c2 != c]
model.constraint(
'y[i%s,s%s,c%s]' % (i, s, c),
Expr.sub(Expr.add(arcs_in), Expr.add(arcs_out)),
Domain.equalsTo(0.0))
model.objective('z', ObjectiveSense.Minimize, Expr.add(x.values()))
# model.objective('z', ObjectiveSense.Minimize, obj)
model.setLogHandler(sys.stdout)
model.acceptedSolutionStatus(AccSolutionStatus.Feasible)
model.solve()
# Create optimal schedule.
schedule = defaultdict(list)
for i, cmds in problem.images.items():
for s in problem.stages[i]:
if s == 1:
# First stage starts our walk.
for c in cmds:
if y[i, s, c].level()[0] > 0.5:
schedule[i].append(c)
break
else:
# After that we know what our starting point is.
for c2 in cmds:
if c2 == c:
continue
if y[i, s, c, c2].level()[0] > 0.5:
schedule[i].append(c2)
c = c2
break
saver(schedule)
def solve(self, problem, saver):
# Construct model.
self.problem = problem
self.model = model = Model()
if self.time is not None:
model.setSolverParam('mioMaxTime', 60.0 * int(self.time))
# x[1,c] = 1 if the master schedule has (null, c) in its first stage
# x[s,c1,c2] = 1 if the master schedule has (c1, c2) in stage s > 1
x = {}
for s in problem.all_stages:
if s == 1:
# First arc in the individual image path.
for c in problem.commands:
x[1,c] = model.variable(
'x[1,%s]' % c, 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
else:
# Other arcs.
for c1, c2 in product(problem.commands, problem.commands):
if c1 == c2:
continue
x[s,c1,c2] = model.variable(
'x[%s,%s,%s]' % (s,c1,c2), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
smax = max(problem.all_stages)
obj = [0.0]
# TODO: deal with images that do not have the same number of commands.
# t[s,c] is the total time incurred at command c in stage s
t = {}
for s in problem.all_stages:
for c in problem.commands:
t[s,c] = model.variable(
't[%s,%s]' % (c,s), 1,
Domain.greaterThan(0.0)
)
if s == 1:
model.constraint('t[1,%s]' % c,
Expr.sub(t[1,c], Expr.mul(float(problem.commands[c]), x[1,c])),
Domain.greaterThan(0.0)
)
else:
rhs = [0.0]
for c1, coeff in problem.commands.items():
if c1 == c:
continue
else:
rhs = Expr.add(rhs, Expr.mulElm(t[s-1,c1], x[s,c1,c]))
model.constraint('t[%s,%s]' % (s,c),
Expr.sub(t[1,c], rhs),
Domain.greaterThan(0.0)
)
# Objective function = sum of aggregate comand times
if s == smax:
obj = Expr.add(obj, t[s,c])
# y[i,1,c] = 1 if image i starts by going to c
# y[i,s,c1,c2] = 1 if image i goes from command c1 to c2 in stage s > 1
y = {}
for i, cmds in problem.images.items():
for s in problem.stages[i]:
if s == 1:
# First arc in the individual image path.
for c in cmds:
y[i,1,c] = model.variable(
'y[%s,1,%s]' % (i,c), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
model.constraint('x_y[i%s,1,c%s]' % (i,c),
Expr.sub(x[1,c], y[i,1,c]),
Domain.greaterThan(0.0)
)
else:
# Other arcs.
for c1, c2 in product(cmds, cmds):
if c1 == c2:
continue
y[i,s,c1,c2] = model.variable(
'y[%s,%s,%s,%s]' % (i,s,c1,c2), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
model.constraint('x_y[i%s,s%s,c%s,c%s]' % (i,s,c1,c2),
Expr.sub(x[s,c1,c2], y[i,s,c1,c2]),
Domain.greaterThan(0.0)
)
for c in cmds:
# Each command is an arc destination exactly once.
arcs = [y[i,1,c]]
for c1 in cmds:
if c1 == c:
continue
arcs.extend([y[i,s,c1,c] for s in problem.stages[i][1:]])
model.constraint('y[i%s,c%s]' % (i,c),
Expr.add(arcs),
Domain.equalsTo(1.0)
)
# Network balance equations (stages 2 to |stages|-1).
# Sum of arcs in = sum of arcs out.
for s in problem.stages[i][:len(problem.stages[i])-1]:
if s == 1:
arcs_in = [y[i,1,c]]
else:
arcs_in = [y[i,s,c1,c] for c1 in cmds if c1 != c]
arcs_out = [y[i,s+1,c,c2] for c2 in cmds if c2 != c]
model.constraint('y[i%s,s%s,c%s]' % (i,s,c),
Expr.sub(Expr.add(arcs_in), Expr.add(arcs_out)),
Domain.equalsTo(0.0)
)
model.objective('z', ObjectiveSense.Minimize, Expr.add(x.values()))
# model.objective('z', ObjectiveSense.Minimize, obj)
model.setLogHandler(sys.stdout)
model.acceptedSolutionStatus(AccSolutionStatus.Feasible)
model.solve()
# Create optimal schedule.
schedule = defaultdict(list)
for i, cmds in problem.images.items():
for s in problem.stages[i]:
if s == 1:
# First stage starts our walk.
for c in cmds:
if y[i,s,c].level()[0] > 0.5:
schedule[i].append(c)
break
else:
# After that we know what our starting point is.
for c2 in cmds:
if c2 == c:
continue
if y[i,s,c,c2].level()[0] > 0.5:
schedule[i].append(c2)
c = c2
break
saver(schedule)
def solve(self, problem, saver):
# Construct model.
self.problem = problem
self.model = model = Model()
if self.time is not None:
model.setSolverParam('mioMaxTime', 60.0 * int(self.time))
# x[i,s,c] = 1 if image i runs command c during stage s, 0 otherwise.
self.x = x = {}
for i, cmds in problem.images.items():
for s, c in product(problem.stages[i], cmds):
x[i,s,c] = model.variable(
'x[%s,%s,%s]' % (i,s,c), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
)
# y[ip,iq,s,c] = 1 if images ip & iq have a shared path through stage
# s by running command c during s, 0 otherwise.
y = {}
for (ip, iq), cmds in problem.shared_cmds.items():
for s, c in product(problem.shared_stages[ip, iq], cmds):
y[ip,iq,s,c] = model.variable(
'y[%s,%s,%s,%s]' % (ip,iq,s,c), 1,
Domain.inRange(0.0, 1.0),
Domain.isInteger()
# Domain.inRange(0.0, 1.0)
)
# TODO: need to remove presolved commands so the heuristic doesn't try them.
# TODO: Add a heuristic initial solution.
# TODO: Presolving
# Each image one command per stage, and each command once.
for i in problem.images:
for s in problem.stages[i]:
model.constraint('c1[%s,%s]' % (i,s),
Expr.add([x[i,s,c] for c in problem.images[i]]),
Domain.equalsTo(1.0)
)
for c in problem.images[i]:
model.constraint('c2[%s,%s]' % (i,c),
Expr.add([x[i,s,c] for s in problem.stages[i]]),
Domain.equalsTo(1.0)
)
# Find shared paths among image pairs.
for (ip, iq), cmds in problem.shared_cmds.items():
for s in problem.shared_stages[ip,iq]:
for c in cmds:
model.constraint('c3[%s,%s,%s,%s]' % (ip,iq,s,c),
Expr.sub(y[ip,iq,s,c], x[ip,s,c]),
Domain.lessThan(0.0)
)
model.constraint('c4[%s,%s,%s,%s]' % (ip,iq,s,c),
Expr.sub(y[ip,iq,s,c], x[iq,s,c]),
Domain.lessThan(0.0)
)
if s > 1:
lhs = Expr.add([y[ip,iq,s,c] for c in cmds])
rhs = Expr.add([y[ip,iq,s-1,c] for c in cmds])
model.constraint('c5[%s,%s,%s,%s]' % (ip,iq,s,c),
Expr.sub(lhs, rhs), Domain.lessThan(0.0)
)
if y:
obj = Expr.add(y.values())
else:
obj = 0.0
model.objective('z', ObjectiveSense.Maximize, obj)
model.setLogHandler(sys.stdout)
model.acceptedSolutionStatus(AccSolutionStatus.Feasible)
model.solve()
# Create optimal schedule.
schedule = defaultdict(list)
for i, stages in problem.stages.items():
for s in stages:
for c in problem.images[i]:
if x[i,s,c].level()[0] > 0.5:
schedule[i].append(c)
break
saver(schedule)
