def Shinohara1(retI = False):
""" no = 12: Shinohara1
{ y(0) = p*p*p*p*p - 10.*p*p*p*q*q + 5.*p*q*q*q*q
- 2.*p*p*p*p + 12.*p*p*q*q - 2.*q*q*q*q
+ 10.*p*p*p - 30.*p*q*q - 9.*p + 3.
{ y(1) = q*q*q*q*q - 10.*p*p*q*q*q + 5.*p*p*p*p*q
- 8.*p*p*p*q + 8.*p*q*q*q + 30.*p*p*q
-10.*q*q*q - 9.*q
true value = ?
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
p = x[0]
q= x[1]
y[0] = p*p*p*p*p - 10.*p*p*p*q*q + 5.*p*q*q*q*q\
- 2.*p*p*p*p + 12.*p*p*q*q - 2.*q*q*q*q\
+ 10.*p*p*p - 30.*p*q*q - 9.*p + 3.
y[1] = q*q*q*q*q - 10.*p*p*q*q*q + 5.*p*p*p*p*q\
- 8.*p*p*p*q + 8.*p*q*q*q + 30.*p*p*q\
-10.*q*q*q - 9.*q
if retI == True:
return np.matrix([[interval(-5.1, 5.)], [interval(-5., 5.1)]])
return y
def Shinohara3(retI = False):
""" no = 14: Shinohara3
{ y(0) = p*p*p - 2.*p*q + r + 0.75*p + 1.
{ y(1) = p*p*q - q*q - p*r +s + 0.75*q + 0.25
{ y(2) = p*p*r - p*s - q*r + t + 0.75*r + 0.75
{ y(3) = p*p*s - p*t - q*s + 0.75*s
{ y(4) = p*p*t - q*t + 0.75*t - 0.25
true value = ?
"""
y = [0.0 for i in range(5)]
x[0], x[1], x[2], x[3], x[4] = fd.oovars('x0', 'x1', 'x2', 'x3', 'x4')
p = x[0];
q = x[1];
r = x[2];
s = x[3];
t = x[4];
y[0] = p*p*p - 2.*p*q + r + 0.75*p + 1.
y[1] = p*p*q - q*q - p*r +s + 0.75*q + 0.25
y[2] = p*p*r - p*s - q*r + t + 0.75*r + 0.75
y[3] = p*p*s - p*t - q*s + 0.75*s
y[4] = p*p*t - q*t + 0.75*t - 0.25
if retI == True:
return np.matrix([[interval(-1.5, 2.)],\
[interval(-0.6, 3.)],\
[interval(-1.5, 2.5)],\
[interval(-0.5, 1.9)],\
[interval(-1., 1.)]])
return y
def solve(self, *args, **kw):
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
graph = self.graph # must be networkx instance
nodes = graph.nodes()
edges = graph.edges()
n = len(nodes)
node2index = dict([(node, i) for i, node in enumerate(nodes)])
index2node = dict([(i, node) for i, node in enumerate(nodes)])
import FuncDesigner as fd, openopt
x = fd.oovars(n, domain=bool)
objective = fd.sum(x)
startPoint = {x: [0] * n}
fixedVars = {}
includedNodes = getattr(kw, 'includedNodes', None)
if includedNodes is None:
includedNodes = getattr(self, 'includedNodes', ())
for node in includedNodes:
fixedVars[x[node2index[node]]] = 1
excludedNodes = getattr(kw, 'excludedNodes', None)
if excludedNodes is None:
excludedNodes = getattr(self, 'excludedNodes', ())
for node in excludedNodes:
fixedVars[x[node2index[node]]] = 0
if openopt.oosolver(solver).__name__ == 'interalg':
constraints = [
fd.NAND(x[node2index[i]], x[node2index[j]]) for i, j in edges
]
P = openopt.GLP
else:
constraints = [
x[node2index[i]] + x[node2index[j]] <= 1 for i, j in edges
]
P = openopt.MILP
p = P(objective,
startPoint,
constraints=constraints,
fixedVars=fixedVars,
goal='max')
for key, val in kw.items():
setattr(p, key, val)
r = p.solve(solver, **kw)
r.solution = [index2node[i] for i in range(n) if r.xf[x[i]] == 1]
r.ff = len(r.solution)
return r
def solve(self, *args, **kw):
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
graph = self.graph # must be networkx instance
nodes = graph.nodes()
edges = graph.edges()
n = len(nodes)
node2index = dict([(node, i) for i, node in enumerate(nodes)])
index2node = dict([(i, node) for i, node in enumerate(nodes)])
import FuncDesigner as fd, openopt
x = fd.oovars(n, domain=bool)
objective = fd.sum(x)
startPoint = {x:[0]*n}
fixedVars = {}
includedNodes = getattr(kw, 'includedNodes', None)
if includedNodes is None:
includedNodes = getattr(self, 'includedNodes', ())
for node in includedNodes:
fixedVars[x[node2index[node]]] = 1
excludedNodes = getattr(kw, 'excludedNodes', None)
if excludedNodes is None:
excludedNodes = getattr(self, 'excludedNodes', ())
for node in excludedNodes:
fixedVars[x[node2index[node]]] = 0
if openopt.oosolver(solver).__name__ == 'interalg':
constraints = [fd.NAND(x[node2index[i]], x[node2index[j]]) for i, j in edges]
P = openopt.GLP
else:
constraints = [x[node2index[i]]+x[node2index[j]] <=1 for i, j in edges]
P = openopt.MILP
p = P(objective, startPoint, constraints = constraints, fixedVars = fixedVars, goal = 'max')
for key, val in kw.items():
setattr(p, key, val)
r = p.solve(solver, **kw)
r.solution = [index2node[i] for i in range(n) if r.xf[x[i]] == 1]
r.ff = len(r.solution)
return r
def GE1(retI = False):
""" no = 10: GE1
{ -1/(1 + x1) + x2/(1 + x2) = 0
{ 1/(1 + x1) - x2/(x1 + x2) = 0
true value = ?
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = -1./(1. + x[0]) + x[1]/(1. + x[1])
y[1] = 1./(1. + x[0]) - x[1]/(x[0] + x[1])
if retI == True:
return np.matrix([[interval(0.01, 100.)], [interval(0.001, 100.)]])
#return np.matrix([[interval(0.1, 10.)], [interval(0.01, 11.)]])
return y
def sincos_function(retI = False):
""" no = 4: function including sine and cosine
{ sin(x1)*cos(x1) - x2 = 0
{ x1^2 - 6*x1 + 8 - x2 = 0
true value
(x1, x2) = (,), (,)
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = fd.sin(x[0]) * fd.cos(x[0]) - x[1]
y[1] = x[0] * x[0] - 6 * x[0] + 8 - x[1]
if retI == True:
return np.matrix([[interval(-6.1, 6.)], [interval(-6., 6.)]])
return y
def sample_function_1(retI = False):
""" no = 1: sample function 1
{ x1^2 - x2 = 0
{ (1/2)*x1 - x2 = 0
true value
(x1, x2) = (0, 0), (0.5, 0.25)
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0] * x[0] - x[1]
y[1] = 0.5 * x[0] - x[1]
if retI == True:
return np.matrix([[interval(-2.2, 2.1)], [interval(-1., 2.)]])
return y
def sin_function(retI = False):
""" no = 3: function including sin
{ (pi/2)*sin(x1) - x2 = 0
{ x1 - x2 = 0
true value
(x1, x2) = (0, 0), (1.57079633.., 1.57079633..), (-1.5709633.., -1.57079633..)
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
#y[0] = 1.57079633 * fd.sin(x[0]) - x[1]
y[0] = (np.pi/2) * fd.sin(x[0]) - x[1]
y[1] = x[0] - x[1]
if retI == True:
return np.matrix([[interval(-3.1, 3.)], [interval(-2., 2.)]])
return y
def sample_function_2(retI = False):
""" no = 2: sample function 2
{ x1^2 - x2 = 0
{ -x1^2 + 2*x1 - x2 = 0
true value
(x1, x2) = (0, 0), (1, 1)
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0] * x[0] - x[1]
y[1] = -x[0] * x[0] + 2 * x[0] - x[1]
if retI == True:
return np.matrix([[interval(-11., 10.)], [interval(-10., 11.)]])
#return np.matrix([[interval(-10., 10.)], [interval(-10., 10.)]])
return y
def Duffing(retI = False):
""" no = 11: Duffing-equation
{ y(0) = -x(0) + B + 0.1 * x(1) + 0.75 * (x(0)*x(0)*x(0) + x(0) *x(1) * x(1))
{ y(1) = - x(1) + 0.1 * x(0) + 0.75 * (x(0)*x(0)*x(1) + x(1)*x(1)*x(1))
true value = 5?
"""
B = 0.
#B = 0.15
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = -1.*x[0] + B + 0.1*x[1] + 0.75*(x[0]*x[0]*x[0] + x[0]*x[1]*x[1])
y[1] = -1.*x[1] + 0.1*x[0] + 0.75*(x[0]*x[0]*x[1] + x[1]*x[1]*x[1])
if retI == True:
return np.matrix([[interval(-1e+8-1., 1e+8)], [interval(-1e+8, 1e+8+1.)]])
#return np.matrix([[interval(-1e+5-1., 1e+5)], [interval(-1e+5, 1e+5+1.)]])
return y
def Nosol(retI = False):
""" no = 9: No-solutions
{ x1^2 - x2 = 0
{ x1^2 - x2 + param
true value
(x1, x2) = None
"""
#param = 0.01
param = 0.001
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0]*x[0] - x[1]
y[1] = x[0]*x[0] - x[1] + param
if retI == True:
return np.matrix([[interval(-1., 1.)], [interval(-1., 1.)]])
return y
def default_function(retI = False):
""" no = 0: default function
{ x1^2 + x2^2 -1 = 0
{ x1 - x2 = 0
one true solution which sample function has is below:
x1 = x2 = (2^(1/2))/2
(=~ 0.70710678)
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0] * x[0] + x[1] * x[1] - 1
y[1] = x[0] - x[1]
if retI == True:
#return np.matrix([[interval(-1.1, 1.)], [interval(-1., 1.)]])
return np.matrix([[interval(-1., 1.)], [interval(-1., 1.)]])
return y
def badCond(retI = False):
""" no = 7: BadCond
{ x1^2 - x2 = 0
{ (1 - param) * x1^2 - x2 + param = 0
true value
(x1, x2) = (, ), (, )
"""
#param = 0.0000001
#param = 0.01
param = 0.001
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0]*x[0] - x[1]
y[1] = (1 - param)*x[0]*x[0] - x[1] + param
if retI == True:
return np.matrix([[interval(-10., 10.)], [interval(-10., 10.)]])
return y
def function_3_dim(retI = False):
""" no = 5: function of 3-dimention
{ x1 + x2 + x3 = 6
{ 3*x1 + 2*x2 -2*x3 = 1
{ 2*x1 - x2 + 3*x3 = 9
true value
(x1, x2, x3) = (1, 2, 3)
"""
y = [0.0 for i in range(3)]
x[0], x[1], x[2] = fd.oovars('x0', 'x1', 'x2')
y[0] = x[0] + x[1] + x[2] - 6
y[1] = 3*x[0] + 2*x[1] - 2*x[2] - 1
y[2] = 2*x[0] - x[1] + 3*x[2] - 9
if retI == True:
#return np.matrix([[interval(-1.1, 5.)], [interval(-1., 5.)], [interval(-1., 5.1)]])
return np.matrix([[interval(-50.1, 50.)], [interval(-50., 50.)], [interval(-50., 50.1)]])
return y
def Burden(retI = False):
""" no = 8: Burden
{ x1*(4 - 0.0003*x1 - 0.0004*x2) = 0
{ x2*(2 - 0.0002*x1 - 0.0001*x2) = 0
true value
(x1, x2) = ?
"""
#param = 0.0001
param = 0.1
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
y[0] = x[0]*(4. - 3.*param*x[0] - 4.*param*x[1])
y[1] = x[1]*(2. - 2.*param*x[0] - 1.*param*x[1])
if retI == True:
#return np.matrix([[interval(0., pow(10., 10))], [interval(0., pow(10., 10))]])
return np.matrix([[interval(-1., pow(10., 10))], [interval(0., pow(10., 10)+1)]])
return y
def function_3_dim_2(retI = False):
""" no = 6: function of 3-dimention
{ x1*x2 - 9 = 0
{ x2*x3 - 6 = 0
{ x3*x1 - 6 = 0
true value
(x1, x2, x3) = (3, 3, 2), (-3, -3, -2)
"""
y = [0.0 for i in range(3)]
x[0], x[1], x[2] = fd.oovars('x0', 'x1', 'x2')
y[0] = x[0] * x[1] - 9
y[1] = x[1] * x[2] - 6
y[2] = x[2] * x[0] - 6
if retI == True:
#return np.matrix([[interval(-6.1, 5.)], [interval(-5., 6.)], [interval(-6., 7.1)]])
#return np.matrix([[interval(-10.1, 15.)], [interval(-15., 20.)], [interval(-16., 10.1)]])
return np.matrix([[interval(-100, 100.)], [interval(-100., 100.)], [interval(-100., 100.)]])
return y
def automaticdiffertest():
#from FuncDesigner import *
a, b, c = fd.oovars('a', 'b', 'c')
f1, f2 = fd.sin(a) + fd.cos(b) - fd.log2(c) + fd.sqrt(b), fd.sum(c) + c * fd.cosh(b) / fd.arctan(a) + c[0] * c[1] + c[-1] / (a * c.size)
f3 = f1*f2 + 2*a + fd.sin(b) * (1+2*c.size + 3*f2.size)
f = 2*a*b*c + f1*f2 + f3 + fd.dot(a+c, b+c)
point = {a:1, b:2, c:[3, 4, 5]} # however, you'd better use numpy arrays instead of Python lists
print(f(point))
print(f.D(point))
print(f.D(point, a))
print(f.D(point, [b]))
print(f.D(point, fixedVars = [a, c]))
def Shinohara2(retI = False):
""" no = 13: Shinohara2
{ y(0) = p*p*p*p*p - 10.*p*p*p*q*q + 5.*p*q*q*q*q
- 3.*p*p*p*p + 18.*p*p*q*q - 3.*q*q*q*q
- 2.*p*p*p + 6.*p*q*q + 3.*p*p*q - q*q*q
+ 12.*p*p - 12.*q*q - 10.*p*q - 8.*p + 8.*q;
{ y(1) = 5.*p*p*p*p*q - 10.*p*p*q*q*q + q*q*q*q*q
- 12.*p*p*p*q + 12.*p*q*q*q - p*p*p + 3.*p*q*q
- 6.*p*p*q + 2.*q*q*q + 5.*p*p - 5.*q*q
+ 24.*p*q - 8.*p - 8.*q + 4.;
true value = ?
output:
0 = [[[-2.09868411349,-2.09868411345]]
[[-0.455089860584,-0.455089860541]]]
1 = [[[0.999999999995,1.0]]
[[-4.51311746098e-12,4.51285733701e-12]]]
2 = [[[0.0986841134678,0.0986841134678]]
[[0.455089860562,0.455089860562]]]
"""
y = [0.0 for i in range(2)]
x[0], x[1] = fd.oovars('x0', 'x1')
p = x[0]
q= x[1]
y[0] = p*p*p*p*p - 10.*p*p*p*q*q + 5.*p*q*q*q*q\
- 3.*p*p*p*p + 18.*p*p*q*q - 3.*q*q*q*q\
- 2.*p*p*p + 6.*p*q*q + 3.*p*p*q - q*q*q\
+ 12.*p*p - 12.*q*q - 10.*p*q - 8.*p + 8.*q
y[1] = 5.*p*p*p*p*q - 10.*p*p*q*q*q + q*q*q*q*q\
- 12.*p*p*p*q + 12.*p*q*q*q - p*p*p + 3.*p*q*q\
- 6.*p*p*q + 2.*q*q*q + 5.*p*p - 5.*q*q\
+ 24.*p*q - 8.*p - 8.*q + 4.
if retI == True:
return np.matrix([[interval(-3.1, 3.)], [interval(-3., 3.1)]])
return y
def set_routine(p, *args, **kw):
if len(args) > 1:
p.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', p.solver)
import FuncDesigner as fd, openopt
is_interalg = openopt.oosolver(solver).__name__ == 'interalg'
graph = p.graph # must be networkx instance
nodes = graph.nodes()
edges = graph.edges()
n = len(nodes)
node2index = dict((node, i) for i, node in enumerate(nodes))
index2node = dict((i, node) for i, node in enumerate(nodes))
x = fd.oovars(n, domain=bool)
objective = fd.sum(x)
startPoint = {x:[0]*n}
fixedVars = {}
includedNodes = getattr(kw, 'includedNodes', None)
if includedNodes is None:
includedNodes = getattr(p, 'includedNodes', ())
for node in includedNodes:
fixedVars[x[node2index[node]]] = 1
excludedNodes = getattr(kw, 'excludedNodes', None)
if excludedNodes is None:
excludedNodes = getattr(p, 'excludedNodes', ())
for node in excludedNodes:
fixedVars[x[node2index[node]]] = 0
if p.probType == 'DSP':
constraints = []
engine = fd.OR if is_interalg else lambda List: fd.sum(List) >= 1
Engine = lambda d, n: engine([x[node2index[k]] for k in (list(d.keys())+[n])])
for node in nodes:
adjacent_nodes_dict = graph[node]
if len(adjacent_nodes_dict) == 0:
fixedVars[x[node2index[node]]] = 1
continue
constraints.append(Engine(adjacent_nodes_dict, node))
else:
constraints = \
[fd.NAND(x[node2index[i]], x[node2index[j]]) for i, j in edges] \
if is_interalg else \
[x[node2index[i]]+x[node2index[j]] <=1 for i, j in edges]
P = openopt.GLP if is_interalg else openopt.MILP
goal = 'min' if p.probType == 'DSP' else 'max'
p = P(objective, startPoint, constraints = constraints, fixedVars = fixedVars, goal = goal)
for key, val in kw.items():
setattr(p, key, val)
r = p.solve(solver, **kw)
r.solution = [index2node[i] for i in range(n) if r.xf[x[i]] == 1]
r.ff = len(r.solution)
return r
h = []
for i in range(n):
if i == j:
h.append(12+n/(i+1.0))
elif i == j + 1:
h.append(0)
elif j == i + 2:
h.append(0)
else:
h.append(15/((i+1)+0.1*(j+1)))
H.append(h)
#print H
#H = [[15,0,4.83871],
# [12.5,13.5,0],
# [0,6.52174,13]]
#print H
x = fd.oovars(n)
f = fd.dot(fd.dot(x, H), x)
startPoint = {x: np.zeros(n)}
constraints = []
constraints.append(x > np.zeros(n))
constraints.append(fd.sum(x) == 1)
p = QP(f, startPoint, constraints=constraints)
r = p.solve("qlcp")
x_opt = r(x)
print(math.sqrt(r.ff))
# problem
# http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html
def solve(self, *args, **kw):
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
if self.start is None and not self.returnToStart:
self.err('for returnToStart=False mode you should provide start, other cases are unimplemented yet')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
KW = self.__init_kwargs.copy()
KW.update(kw)
objective = KW.get('objective', self.objective)
if isinstance(objective, (list, tuple, set)):
nCriteria = len(self.objective)
if 3 * nCriteria != np.asarray(self.objective).size:
objective = [(objective[3*i], objective[3*i+1], objective[3*i+2]) for i in range(int(round(np.asarray(self.objective).size / 3)))]
if len(objective) == 1:
KW['fTol'], KW['goal'] = objective[0][1:]
else:
objective = [(self.objective, KW.get('fTol', getattr(self, 'fTol')), KW.get('goal', getattr(self, 'goal')))]
nCriteria = len(objective)
isMOP = nCriteria > 1
mainCr = objective[0][0]
import FuncDesigner as fd, openopt as oo
solverName = solver if type(solver) == str else solver.__name__
is_interalg = solverName == 'interalg'
is_glp = solverName == 'sa'
if is_glp:
assert nCriteria == 1, 'you cannot solve multiobjective tsp by the solver'
is_interalg_raw_mode = is_interalg and KW.get('dataHandling', oo.oosolver(solver).dataHandling) in ('auto','raw')
KW.pop('objective', None)
P = oo.MOP if nCriteria > 1 else oo.GLP if is_interalg else oo.MILP if not is_glp else oo.GLP
import networkx as nx
graph = self.graph # must be networkx Graph instance
init_graph_is_directed = graph.is_directed()
init_graph_is_multigraph = graph.is_multigraph()
if not init_graph_is_multigraph or not init_graph_is_directed:
graph = nx.MultiDiGraph(graph) #if init_graph_is_directed else nx.MultiGraph(graph)
nodes = graph.nodes()
edges = graph.edges()
n = len(nodes)
m = len(edges)
node2index = dict([(node, i) for i, node in enumerate(nodes)])
# TODO: implement MOP with interalg_gdp mode (requires interpolation interval analysis for non-monotone funcs)
interalg_gdp = 1
if not is_interalg:# or isMOP:
# !!!!!!!!!!!!! TODO: add handling of MOP with interalg_gdp?
interalg_gdp = 0
if interalg_gdp:
x = []
edge_ind2x_ind_val = {}
else:
pass
#x = fd.oovars(m, domain=bool)
#cr_values = dict([(obj[0], []) for obj in objective])
cr_values = {}
constraints = []
EdgesDescriptors, EdgesCoords = [], []
# mb rework it by successors etc?
Funcs = {}
Cons = KW.pop('constraints', [])
if type(Cons) not in (list, tuple):
Cons = [Cons]
usedValues = getUsedValues(Cons)
usedValues.update(getUsedValues([obj[0] for obj in objective]))
MainCr = mainCr if type(mainCr) in (str, np.str_) else list(usedValues)[0]
isMainCrMin = objective[0][2] in ('min', 'minimum')
node_out_edges_num = []
for node in nodes:
Edges = graph[node]
node_out_edges_num.append(len(Edges))
out_nodes = Edges.keys()
if len(out_nodes) == 0:
self.err('input graph has node %s that does not lead to any other node; solution is impossible' % node)
if init_graph_is_multigraph and not isMOP and type(mainCr) in [str, np.str_]:
W = {}
for out_node in out_nodes:
ww = list(Edges[out_node].values())
for w in ww:
tmp = W.get(out_node, None)
if tmp is None:
W[out_node] = w
continue
th = tmp[mainCr]
w_main_cr_val = w[mainCr]
if isMainCrMin == (th > w_main_cr_val):
W[out_node] = w
Out_nodes, W = np.array(list(W.keys())), np.array(list(W.values()))
else:
W = np.hstack([list(Edges[out_node].values()) for out_node in out_nodes])
Out_nodes = np.hstack([[out_node] * len(Edges[out_node]) for out_node in out_nodes])
if interalg_gdp:
rr = np.array([w[MainCr] for w in W])
if isMainCrMin:
rr = -rr
elif objective[0][2] not in ('max', 'maximum'):
self.err('unimplemented for fixed value goal in TSP yet, only min/max is possible for now')
ind = rr.argsort()
W = W[ind]
Out_nodes = Out_nodes[ind]
lc = 0
for i, w in enumerate(W):
if interalg_gdp:
edge_ind2x_ind_val[len(EdgesCoords)] = (len(x), lc)
lc += 1
EdgesCoords.append((node, Out_nodes[i]))
EdgesDescriptors.append(w)
for key, val in w.items():
# for undirected:
#if node2index[key] < node2index[out_node]: continue
Val = val if self.returnToStart or node != self.start else 0
if key in cr_values:
cr_values[key].append(Val)
else:
cr_values[key] = [Val]
if interalg_gdp:
x.append(fd.oovar(domain = np.arange(lc)))
m = len(EdgesCoords) # new value
if is_glp:
if type(mainCr) not in (str, np.str_):
self.err('for the solver "sa" only text name objectives are implemented (e.g. "time", "price")')
if init_graph_is_multigraph:
self.err('the solver "sa" cannot handle multigraphs yet')
if len(Cons) != 0:
self.err('the solver "sa" cannot handle constrained TSP yet')
M = np.empty((n, n))
M.fill(np.nan)
Cr_values = np.array(cr_values[mainCr])
isMax = objective[0][-1] in ('max', 'maximum')
if isMax:
Cr_values = -Cr_values
for i, w in enumerate(EdgesDescriptors):
node_in, node_out = EdgesCoords[i]
M[node_in, node_out] = Cr_values[i]
S = np.abs(Cr_values).sum() + 1.0
# TODO: check it
M[np.isnan(M)] = S
prob = P(lambda x: 0, np.zeros(n), iprint = 1)
prob.f = lambda x: np.nan if not hasattr(prob, 'ff') else (prob.ff if isMax else -prob.ff)
prob.M = dict([((i, j), M[i, j]) for i in range(n) for j in range(n) if i != j])
r = prob.solve(solver, **KW)
xf = [nodes[j] for j in np.array(r.xf, int)]
r.nodes = xf#.tolist()
if self.start is not None:
j = r.nodes.index(self.start)
r.nodes = r.nodes[j:] + r.nodes[:j]
if self.returnToStart:
r.nodes += [r.nodes[0]]
r.edges = [(r.nodes[i], r.nodes[i+1]) for i in range(n-1)]
r.Edges = [(r.nodes[i], r.nodes[i+1], graph[r.nodes[i]][r.nodes[i+1]][0]) for i in range(n-1)]
if self.returnToStart:
r.edges.append((r.nodes[-2], r.nodes[0]))
print(r.nodes[-1], r.nodes[0], type(r.nodes[-1]), type(r.nodes[0]), graph[2])
r.Edges.append((r.nodes[-2], r.nodes[0], graph[r.nodes[-2]][r.nodes[0]][0]))
#r.xf = r.xk = r.nodes
# TODO: Edges
return r
#TODO: fix ooarray lb/ub
#u = np.array([1] + [fd.oovar(lb=2, ub=n) for i in range(n-1)])
u = fd.hstack((1, fd.oovars(n-1, lb=2, ub=n)))
for i in range(1, u.size):
u[i]('u' + str(i))
if is_interalg_raw_mode:
for i in range(n-1):
u[1+i].domain = np.arange(2, n+1)
if interalg_gdp:
assert len(x) == n
x = fd.ooarray(x)
# TODO: remove it when proper enum implementation in FD engine will be done
for i in range(n):
x[i]._init_domain = x[i].domain
constraints.append(x[i]-x[i]._init_domain[-1] <= 0)
x[i].domain = np.arange(int(2 ** np.ceil(np.log2(node_out_edges_num[i]))))
# for i in range(n-1):
# u[1+i]._init_domain = u[1+i].domain
# constraints.append(u[1+i]-u[1+i]._init_domain[-1] <= 0)
# u[1+i].domain = np.arange(u[1+i]._init_domain[0], u[1+i]._init_domain[0]+int(2 ** np.ceil(np.log2(u[1+i]._init_domain[-1]-u[1+i]._init_domain[0]+1))))
# u[1+i].ub = u[1+i].domain[-1]
else:
x = fd.oovars(m, domain=bool) # new m value
for i in range(x.size):
x[i]('x'+str(i))
# if init_graph_is_directed:
dictFrom = dict([(node, []) for node in nodes])
dictTo = dict([(node, []) for node in nodes])
for i, edge in enumerate(EdgesCoords):
From, To = edge
dictFrom[From].append(i)
dictTo[To].append(i)
engine = fd.XOR
# number of outcoming edges = 1
if not interalg_gdp:
for node, edges_inds in dictFrom.items():
# !!!!!!!!!! TODO for interalg_raw_mode: and if all edges have sign similar to goal
if 1 and is_interalg_raw_mode:
c = engine([x[j] for j in edges_inds])
else:
nEdges = fd.sum([x[j] for j in edges_inds])
c = nEdges >= 1 if self.allowRevisit else nEdges == 1
constraints.append(c)
# number of incoming edges = 1
for node, edges_inds in dictTo.items():
if len(edges_inds) == 0:
self.err('input graph has node %s that has no edge from any other node; solution is impossible' % node)
if interalg_gdp:
x_inds, x_vals = [], []
for elem in edges_inds:
x_ind, x_val = edge_ind2x_ind_val[elem]
x_inds.append(x_ind)
x_vals.append(x_val)
c = engine([(x[x_ind] == x_val)(tol = 0.5) for x_ind, x_val in zip(x_inds, x_vals)])
else:
if 1 and is_interalg_raw_mode and engine == fd.XOR:
c = engine([x[j] for j in edges_inds])
else:
nEdges = fd.sum([x[j] for j in edges_inds])
c = nEdges >= 1 if self.allowRevisit else nEdges == 1
constraints.append(c)
# MTZ
for i, (I, J) in enumerate(EdgesCoords):
ii, jj = node2index[I], node2index[J]
if ii != 0 and jj != 0:
if interalg_gdp:
x_ind, x_val = edge_ind2x_ind_val[i]
c = fd.ifThen((x[x_ind] == x_val)(tol=0.5), u[ii] - u[jj] <= - 1.0)
elif is_interalg_raw_mode:
c = fd.ifThen(x[i], u[ii] - u[jj] <= - 1.0)#u[jj] - u[ii] >= 1)
else:
c = u[ii] - u[jj] + 1 <= (n-1) * (1-x[i])
constraints.append(c)
# handling objective(s)
FF = []
for optCrName in usedValues:
tmp = cr_values.get(optCrName, [])
if len(tmp) == 0:
self.err('seems like graph edgs have no attribute "%s" to perform optimization on it' % optCrName)
elif len(tmp) != m:
self.err('for optimization creterion "%s" at least one edge has no this attribute' % optCrName)
if interalg_gdp:
F = []
lc = 0
for X in x:
domain = X._init_domain
vals = [tmp[i] for i in range(lc, lc + domain.size)]
lc += domain.size
#F = sum(x)
#F.append(fd.interpolator(domain, vals, k=1, s=0.00000001)(X))
F.append(fd.interpolator(domain, vals, k=1)(X))
#print(domain, vals)
F = fd.sum(F)
else:
F = fd.sum(x*tmp)
Funcs[optCrName] = F
for obj in objective:
FF.append((Funcs[obj[0]] if type(obj[0]) in (str, np.str_) else obj[0](Funcs), obj[1], obj[2]))
for c in Cons:
tmp = c(Funcs)
if type(tmp) in (list, tuple, set):
constraints += list(tmp)
else:
constraints.append(tmp)
startPoint = {x:[0]*(m if not interalg_gdp else n)}
startPoint.update(dict([(U, i+2) for i, U in enumerate(u[1:])]))
p = P(FF if isMOP else FF[0][0], startPoint, constraints = constraints)#, fixedVars = fixedVars)
for param in ('start', 'returnToStart'):
KW.pop(param, None)
r = p.solve(solver, **KW)
if P != oo.MOP:
r.ff = p.ff
if interalg_gdp:
x_ind_val2edge_ind = dict([(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()])
SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in [x_ind_val2edge_ind[(ind, x[ind](r))] for ind in range(n)]]
else:
SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in range(m) if r.xf[x[i]] == 1]
if len(SolutionEdges) == 0:
r.nodes = r.edges = r.Edges = []
return r
S = dict([(elem[0], elem) for elem in SolutionEdges])
SE = [SolutionEdges[0]]
for i in range(len(SolutionEdges)-1):
SE.append(S[SE[-1][1]])
SolutionEdgesCoords = [(elem[0], elem[1]) for elem in SE]
nodes = [edge[1] for edge in SolutionEdgesCoords]
if self.start is not None:
shift_ind = nodes.index(self.start)
nodes = nodes[shift_ind:] + nodes[:shift_ind]
if self.returnToStart:
nodes.append(nodes[0])
edges = SolutionEdgesCoords[1:] + [SolutionEdgesCoords[0]]
Edges = SE[1:] + [SE[0]]
if self.start is not None:
edges, Edges = edges[shift_ind:] + edges[:shift_ind], Edges[shift_ind:] + Edges[:shift_ind]
if not self.returnToStart:
edges, Edges = edges[:-1], Edges[:-1]
r.nodes, r.edges, r.Edges = nodes, edges, Edges
else:
r.solution = 'for MOP see r.solutions instead of r.solution'
tmp_c, tmp_v = r.solutions.coords, r.solutions.values
# if interalg_gdp:
# x_ind_val2edge_ind = dict([(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()])
# SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in [x_ind_val2edge_ind[(ind, x[ind](r))] for ind in range(n)]]
# else:
# SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in range(m) if r.xf[x[i]] == 1]
if interalg_gdp: # default for MOP
x_ind_val2edge_ind = dict([(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()])
r.solutions = MOPsolutions([[(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in [x_ind_val2edge_ind[(ind, x[ind](Point))] for ind in range(n)]] for Point in r.solutions])
else:# non-default
r.solutions = MOPsolutions([[(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in range(m) if Point[x[i]] == 1] for Point in r.solutions])
r.solutions.values = tmp_v
return r
def solve(self, *args, **kw):
import FuncDesigner as fd, openopt as oo
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
KW = self.__init_kwargs.copy()
KW.update(kw)
items = self.items
n = len(items)
objective = KW.get('objective', self.objective)
if isinstance(objective, (list, tuple, set)):
nCriteria = len(self.objective)
if 3 * nCriteria != np.asarray(self.objective).size:
objective = [
(objective[3 * i], objective[3 * i + 1],
objective[3 * i + 2]) for i in range(
int(round(np.asarray(self.objective).size / 3)))
]
if len(objective) == 1:
KW['fTol'], KW['goal'] = objective[0][1:]
else:
objective = [(self.objective, KW.get('fTol', getattr(self,
'fTol')),
KW.get('goal', getattr(self, 'goal')))]
nCriteria = len(objective)
isMOP = nCriteria > 1
#mainCr = objective[0][0]
solverName = solver if type(solver) == str else solver.__name__
is_interalg = solverName == 'interalg'
is_glp = False #solverName == 'sa'
if is_glp:
assert nCriteria == 1, 'you cannot solve multiobjective KSP by the solver'
#is_interalg_raw_mode = is_interalg and KW.get('dataHandling', oo.oosolver(solver).dataHandling) in ('auto','raw')
KW.pop('objective', None)
P = oo.MOP if nCriteria > 1 else oo.GLP if is_interalg else oo.MILP if not is_glp else oo.GLP
x = fd.oovars(n, domain=bool)
requireCount = False
for i, obj in enumerate(items):
if 'n' in obj:
x[i].domain = np.arange(obj['n'] + 1) if is_interalg else int
x[i].ub = obj['n']
x[i].lb = 0
requireCount = True
#cr_values = dict([(obj[0], []) for obj in objective])
constraints = []
Funcs = {}
Cons = KW.pop('constraints', [])
if type(Cons) not in (list, tuple):
Cons = [Cons]
usedValues = getUsedValues(Cons)
usedValues.update(getUsedValues([obj[0] for obj in objective]))
cr_values = {}
for val in usedValues:
if val == 'nItems':
cr_values[val] = 1
else:
cr_values[val] = [obj[val] for obj in items]
# MainCr = mainCr if type(mainCr) in (str, np.str_) else list(usedValues)[0]
#
# isMainCrMin = objective[0][2] in ('min', 'minimum')
# handling objective(s)
FF = []
for optCrName in usedValues:
F = fd.sum(x * cr_values[optCrName])
Funcs[optCrName] = F
for obj in objective:
FF.append((Funcs[obj[0]](obj[0]) if type(obj[0]) in (str, np.str_)
else obj[0](Funcs), obj[1], obj[2]))
for c in Cons:
tmp = c(Funcs)
if type(tmp) in (list, tuple, set):
constraints += list(tmp)
else:
constraints.append(tmp)
startPoint = {x: [0] * n}
p = P(FF if isMOP else FF[0][0], startPoint,
constraints=constraints) #, fixedVars = fixedVars)
if not isMOP:
p.goal = self.goal
r = p.solve(solver, **KW)
if P != oo.MOP:
r.ff = p.ff
if isMOP:
#assert not requireCount, 'MOP with nItem > 1 is unimplemented yet'
r.solution = 'for MOP see r.solutions instead of r.solution'
#tmp_c, tmp_v = r.solutions.coords, r.solutions.values
if len(r.solutions):
S = []
for s in r.solutions:
tmp = [((i, int(s[x[i]])) if requireCount else i)
for i in range(n) if s[x[i]] >= 1]
if 'name' in items[0]:
tmp = [
(items[i]['name'], k) for i, k in tmp
] if requireCount else [items[i]['name'] for i in tmp]
S.append(dict(tmp) if requireCount else tmp)
Vals = dict([(ff[0].name, r.solutions.values[:, i])
for i, ff in enumerate(FF)])
Dicts = [s.copy() for s in S]
for v in usedValues:
if v != 'nItems':
for i, d in enumerate(Dicts):
d[v] = Vals[v][i]
r.solutions = MOPsolutions(Dicts)
r.solutions.coords = S
r.solutions.values = Vals
else:
tmp = [((i, int(r.xf[x[i]])) if requireCount else i)
for i in range(n) if r.xf[x[i]] >= 1]
if 'name' in items[0]:
tmp = [(items[i]['name'], k) for i, k in tmp
] if requireCount else [items[i]['name'] for i in tmp]
r.xf = dict(tmp) if requireCount else tmp
return r
def solve(self, *args, **kw):
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
if self.start is None and not self.returnToStart:
self.err(
'for returnToStart=False mode you should provide start, other cases are unimplemented yet'
)
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
KW = self.__init_kwargs.copy()
KW.update(kw)
objective = KW.get('objective', self.objective)
if isinstance(objective, (list, tuple, set)):
nCriteria = len(self.objective)
if 3 * nCriteria != np.asarray(self.objective).size:
objective = [
(objective[3 * i], objective[3 * i + 1],
objective[3 * i + 2]) for i in range(
int(round(np.asarray(self.objective).size / 3)))
]
if len(objective) == 1:
KW['fTol'], KW['goal'] = objective[0][1:]
else:
objective = [(self.objective, KW.get('fTol', getattr(self,
'fTol')),
KW.get('goal', getattr(self, 'goal')))]
nCriteria = len(objective)
isMOP = nCriteria > 1
mainCr = objective[0][0]
import FuncDesigner as fd, openopt as oo
solverName = solver if type(solver) == str else solver.__name__
is_interalg = solverName == 'interalg'
is_glp = solverName == 'sa'
if is_glp:
assert nCriteria == 1, 'you cannot solve multiobjective tsp by the solver'
is_interalg_raw_mode = is_interalg and KW.get(
'dataHandling',
oo.oosolver(solver).dataHandling) in ('auto', 'raw')
KW.pop('objective', None)
P = oo.MOP if nCriteria > 1 else oo.GLP if is_interalg else oo.MILP if not is_glp else oo.GLP
import networkx as nx
graph = self.graph # must be networkx Graph instance
init_graph_is_directed = graph.is_directed()
init_graph_is_multigraph = graph.is_multigraph()
if not init_graph_is_multigraph or not init_graph_is_directed:
graph = nx.MultiDiGraph(
graph) #if init_graph_is_directed else nx.MultiGraph(graph)
nodes = graph.nodes()
edges = graph.edges()
n = len(nodes)
m = len(edges)
node2index = dict([(node, i) for i, node in enumerate(nodes)])
# TODO: implement MOP with interalg_gdp mode (requires interpolation interval analysis for non-monotone funcs)
interalg_gdp = 1
if not is_interalg: # or isMOP:
# !!!!!!!!!!!!! TODO: add handling of MOP with interalg_gdp?
interalg_gdp = 0
if interalg_gdp:
x = []
edge_ind2x_ind_val = {}
else:
pass
#x = fd.oovars(m, domain=bool)
#cr_values = dict([(obj[0], []) for obj in objective])
cr_values = {}
constraints = []
EdgesDescriptors, EdgesCoords = [], []
# mb rework it by successors etc?
Funcs = {}
Cons = KW.pop('constraints', [])
if type(Cons) not in (list, tuple):
Cons = [Cons]
usedValues = getUsedValues(Cons)
usedValues.update(getUsedValues([obj[0] for obj in objective]))
MainCr = mainCr if type(mainCr) in (str,
np.str_) else list(usedValues)[0]
isMainCrMin = objective[0][2] in ('min', 'minimum')
node_out_edges_num = []
for node in nodes:
Edges = graph[node]
node_out_edges_num.append(len(Edges))
out_nodes = Edges.keys()
if len(out_nodes) == 0:
self.err(
'input graph has node %s that does not lead to any other node; solution is impossible'
% node)
if init_graph_is_multigraph and not isMOP and type(mainCr) in [
str, np.str_
]:
W = {}
for out_node in out_nodes:
ww = list(Edges[out_node].values())
for w in ww:
tmp = W.get(out_node, None)
if tmp is None:
W[out_node] = w
continue
th = tmp[mainCr]
w_main_cr_val = w[mainCr]
if isMainCrMin == (th > w_main_cr_val):
W[out_node] = w
Out_nodes, W = np.array(list(W.keys())), np.array(
list(W.values()))
else:
W = np.hstack(
[list(Edges[out_node].values()) for out_node in out_nodes])
Out_nodes = np.hstack([[out_node] * len(Edges[out_node])
for out_node in out_nodes])
if interalg_gdp:
rr = np.array([w[MainCr] for w in W])
if isMainCrMin:
rr = -rr
elif objective[0][2] not in ('max', 'maximum'):
self.err(
'unimplemented for fixed value goal in TSP yet, only min/max is possible for now'
)
ind = rr.argsort()
W = W[ind]
Out_nodes = Out_nodes[ind]
lc = 0
for i, w in enumerate(W):
if interalg_gdp:
edge_ind2x_ind_val[len(EdgesCoords)] = (len(x), lc)
lc += 1
EdgesCoords.append((node, Out_nodes[i]))
EdgesDescriptors.append(w)
for key, val in w.items():
# for undirected:
#if node2index[key] < node2index[out_node]: continue
Val = val if self.returnToStart or node != self.start else 0
if key in cr_values:
cr_values[key].append(Val)
else:
cr_values[key] = [Val]
if interalg_gdp:
x.append(fd.oovar(domain=np.arange(lc)))
m = len(EdgesCoords) # new value
if is_glp:
if type(mainCr) not in (str, np.str_):
self.err(
'for the solver "sa" only text name objectives are implemented (e.g. "time", "price")'
)
if init_graph_is_multigraph:
self.err('the solver "sa" cannot handle multigraphs yet')
if len(Cons) != 0:
self.err('the solver "sa" cannot handle constrained TSP yet')
M = np.empty((n, n))
M.fill(np.nan)
Cr_values = np.array(cr_values[mainCr])
isMax = objective[0][-1] in ('max', 'maximum')
if isMax:
Cr_values = -Cr_values
for i, w in enumerate(EdgesDescriptors):
node_in, node_out = EdgesCoords[i]
M[node_in, node_out] = Cr_values[i]
S = np.abs(Cr_values).sum() + 1.0
# TODO: check it
M[np.isnan(M)] = S
prob = P(lambda x: 0, np.zeros(n), iprint=1)
prob.f = lambda x: np.nan if not hasattr(prob, 'ff') else (
prob.ff if isMax else -prob.ff)
prob.M = dict([((i, j), M[i, j]) for i in range(n)
for j in range(n) if i != j])
r = prob.solve(solver, **KW)
xf = [nodes[j] for j in np.array(r.xf, int)]
r.nodes = xf #.tolist()
if self.start is not None:
j = r.nodes.index(self.start)
r.nodes = r.nodes[j:] + r.nodes[:j]
if self.returnToStart:
r.nodes += [r.nodes[0]]
r.edges = [(r.nodes[i], r.nodes[i + 1]) for i in range(n - 1)]
r.Edges = [(r.nodes[i], r.nodes[i + 1],
graph[r.nodes[i]][r.nodes[i + 1]][0])
for i in range(n - 1)]
if self.returnToStart:
r.edges.append((r.nodes[-2], r.nodes[0]))
print(r.nodes[-1], r.nodes[0], type(r.nodes[-1]),
type(r.nodes[0]), graph[2])
r.Edges.append((r.nodes[-2], r.nodes[0],
graph[r.nodes[-2]][r.nodes[0]][0]))
#r.xf = r.xk = r.nodes
# TODO: Edges
return r
#TODO: fix ooarray lb/ub
#u = np.array([1] + [fd.oovar(lb=2, ub=n) for i in range(n-1)])
u = fd.hstack((1, fd.oovars(n - 1, lb=2, ub=n)))
for i in range(1, u.size):
u[i]('u' + str(i))
if is_interalg_raw_mode:
for i in range(n - 1):
u[1 + i].domain = np.arange(2, n + 1)
if interalg_gdp:
assert len(x) == n
x = fd.ooarray(x)
# TODO: remove it when proper enum implementation in FD engine will be done
for i in range(n):
x[i]._init_domain = x[i].domain
constraints.append(x[i] - x[i]._init_domain[-1] <= 0)
x[i].domain = np.arange(
int(2**np.ceil(np.log2(node_out_edges_num[i]))))
# for i in range(n-1):
# u[1+i]._init_domain = u[1+i].domain
# constraints.append(u[1+i]-u[1+i]._init_domain[-1] <= 0)
# u[1+i].domain = np.arange(u[1+i]._init_domain[0], u[1+i]._init_domain[0]+int(2 ** np.ceil(np.log2(u[1+i]._init_domain[-1]-u[1+i]._init_domain[0]+1))))
# u[1+i].ub = u[1+i].domain[-1]
else:
x = fd.oovars(m, domain=bool) # new m value
for i in range(x.size):
x[i]('x' + str(i))
# if init_graph_is_directed:
dictFrom = dict([(node, []) for node in nodes])
dictTo = dict([(node, []) for node in nodes])
for i, edge in enumerate(EdgesCoords):
From, To = edge
dictFrom[From].append(i)
dictTo[To].append(i)
engine = fd.XOR
# number of outcoming edges = 1
if not interalg_gdp:
for node, edges_inds in dictFrom.items():
# !!!!!!!!!! TODO for interalg_raw_mode: and if all edges have sign similar to goal
if 1 and is_interalg_raw_mode:
c = engine([x[j] for j in edges_inds])
else:
nEdges = fd.sum([x[j] for j in edges_inds])
c = nEdges >= 1 if self.allowRevisit else nEdges == 1
constraints.append(c)
# number of incoming edges = 1
for node, edges_inds in dictTo.items():
if len(edges_inds) == 0:
self.err(
'input graph has node %s that has no edge from any other node; solution is impossible'
% node)
if interalg_gdp:
x_inds, x_vals = [], []
for elem in edges_inds:
x_ind, x_val = edge_ind2x_ind_val[elem]
x_inds.append(x_ind)
x_vals.append(x_val)
c = engine([(x[x_ind] == x_val)(tol=0.5)
for x_ind, x_val in zip(x_inds, x_vals)])
else:
if 1 and is_interalg_raw_mode and engine == fd.XOR:
c = engine([x[j] for j in edges_inds])
else:
nEdges = fd.sum([x[j] for j in edges_inds])
c = nEdges >= 1 if self.allowRevisit else nEdges == 1
constraints.append(c)
# MTZ
for i, (I, J) in enumerate(EdgesCoords):
ii, jj = node2index[I], node2index[J]
if ii != 0 and jj != 0:
if interalg_gdp:
x_ind, x_val = edge_ind2x_ind_val[i]
c = fd.ifThen((x[x_ind] == x_val)(tol=0.5),
u[ii] - u[jj] <= -1.0)
elif is_interalg_raw_mode:
c = fd.ifThen(x[i],
u[ii] - u[jj] <= -1.0) #u[jj] - u[ii] >= 1)
else:
c = u[ii] - u[jj] + 1 <= (n - 1) * (1 - x[i])
constraints.append(c)
# handling objective(s)
FF = []
for optCrName in usedValues:
tmp = cr_values.get(optCrName, [])
if len(tmp) == 0:
self.err(
'seems like graph edgs have no attribute "%s" to perform optimization on it'
% optCrName)
elif len(tmp) != m:
self.err(
'for optimization creterion "%s" at least one edge has no this attribute'
% optCrName)
if interalg_gdp:
F = []
lc = 0
for X in x:
domain = X._init_domain
vals = [tmp[i] for i in range(lc, lc + domain.size)]
lc += domain.size
#F = sum(x)
#F.append(fd.interpolator(domain, vals, k=1, s=0.00000001)(X))
F.append(fd.interpolator(domain, vals, k=1)(X))
#print(domain, vals)
F = fd.sum(F)
else:
F = fd.sum(x * tmp)
Funcs[optCrName] = F
for obj in objective:
FF.append(
(Funcs[obj[0]] if type(obj[0]) in (str,
np.str_) else obj[0](Funcs),
obj[1], obj[2]))
for c in Cons:
tmp = c(Funcs)
if type(tmp) in (list, tuple, set):
constraints += list(tmp)
else:
constraints.append(tmp)
startPoint = {x: [0] * (m if not interalg_gdp else n)}
startPoint.update(dict([(U, i + 2) for i, U in enumerate(u[1:])]))
p = P(FF if isMOP else FF[0][0], startPoint,
constraints=constraints) #, fixedVars = fixedVars)
for param in ('start', 'returnToStart'):
KW.pop(param, None)
r = p.solve(solver, **KW)
if P != oo.MOP:
r.ff = p.ff
if interalg_gdp:
x_ind_val2edge_ind = dict([
(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()
])
SolutionEdges = [
(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i])
for i in
[x_ind_val2edge_ind[(ind, x[ind](r))] for ind in range(n)]
]
else:
SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1],
EdgesDescriptors[i]) for i in range(m)
if r.xf[x[i]] == 1]
if len(SolutionEdges) == 0:
r.nodes = r.edges = r.Edges = []
return r
S = dict([(elem[0], elem) for elem in SolutionEdges])
SE = [SolutionEdges[0]]
for i in range(len(SolutionEdges) - 1):
SE.append(S[SE[-1][1]])
SolutionEdgesCoords = [(elem[0], elem[1]) for elem in SE]
nodes = [edge[1] for edge in SolutionEdgesCoords]
if self.start is not None:
shift_ind = nodes.index(self.start)
nodes = nodes[shift_ind:] + nodes[:shift_ind]
if self.returnToStart:
nodes.append(nodes[0])
edges = SolutionEdgesCoords[1:] + [SolutionEdgesCoords[0]]
Edges = SE[1:] + [SE[0]]
if self.start is not None:
edges, Edges = edges[shift_ind:] + edges[:shift_ind], Edges[
shift_ind:] + Edges[:shift_ind]
if not self.returnToStart:
edges, Edges = edges[:-1], Edges[:-1]
r.nodes, r.edges, r.Edges = nodes, edges, Edges
else:
r.solution = 'for MOP see r.solutions instead of r.solution'
tmp_c, tmp_v = r.solutions.coords, r.solutions.values
# if interalg_gdp:
# x_ind_val2edge_ind = dict([(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()])
# SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in [x_ind_val2edge_ind[(ind, x[ind](r))] for ind in range(n)]]
# else:
# SolutionEdges = [(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i]) for i in range(m) if r.xf[x[i]] == 1]
if interalg_gdp: # default for MOP
x_ind_val2edge_ind = dict([
(elem[1], elem[0]) for elem in edge_ind2x_ind_val.items()
])
r.solutions = MOPsolutions([[
(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i])
for i in [
x_ind_val2edge_ind[(ind, x[ind](Point))]
for ind in range(n)
]
] for Point in r.solutions])
else: # non-default
r.solutions = MOPsolutions([[
(EdgesCoords[i][0], EdgesCoords[i][1], EdgesDescriptors[i])
for i in range(m) if Point[x[i]] == 1
] for Point in r.solutions])
r.solutions.values = tmp_v
return r
def solve(self, *args, **kw):
import FuncDesigner as fd, openopt as oo
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
KW = self.__init_kwargs.copy()
KW.update(kw)
items = self.items
n = len(items)
objective = KW.get('objective', self.objective)
if isinstance(objective, (list, tuple, set)):
nCriteria = len(self.objective)
if 3 * nCriteria != np.asarray(self.objective).size:
objective = [(objective[3*i], objective[3*i+1], objective[3*i+2]) for i in range(int(round(np.asarray(self.objective).size / 3)))]
if len(objective) == 1:
KW['fTol'], KW['goal'] = objective[0][1:]
else:
objective = [(self.objective, KW.get('fTol', getattr(self, 'fTol')), KW.get('goal', getattr(self, 'goal')))]
nCriteria = len(objective)
isMOP = nCriteria > 1
#mainCr = objective[0][0]
solverName = solver if type(solver) == str else solver.__name__
is_interalg = solverName == 'interalg'
is_glp = False#solverName == 'sa'
if is_glp:
assert nCriteria == 1, 'you cannot solve multiobjective KSP by the solver'
#is_interalg_raw_mode = is_interalg and KW.get('dataHandling', oo.oosolver(solver).dataHandling) in ('auto','raw')
KW.pop('objective', None)
P = oo.MOP if nCriteria > 1 else oo.GLP if is_interalg else oo.MILP if not is_glp else oo.GLP
x = fd.oovars(n, domain=bool)
requireCount = False
for i, obj in enumerate(items):
if 'n' in obj:
x[i].domain = np.arange(obj['n']+1) if is_interalg else int
x[i].ub = obj['n']
x[i].lb = 0
requireCount = True
#cr_values = dict([(obj[0], []) for obj in objective])
constraints = []
Funcs = {}
Cons = KW.pop('constraints', [])
if type(Cons) not in (list, tuple):
Cons = [Cons]
usedValues = getUsedValues(Cons)
usedValues.update(getUsedValues([obj[0] for obj in objective]))
cr_values = {}
for val in usedValues:
if val == 'nItems':
cr_values[val] = 1
else:
cr_values[val] = [obj[val] for obj in items]
# MainCr = mainCr if type(mainCr) in (str, np.str_) else list(usedValues)[0]
#
# isMainCrMin = objective[0][2] in ('min', 'minimum')
# handling objective(s)
FF = []
for optCrName in usedValues:
F = fd.sum(x * cr_values[optCrName])
Funcs[optCrName] = F
for obj in objective:
FF.append((Funcs[obj[0]](obj[0]) if type(obj[0]) in (str, np.str_) else obj[0](Funcs), obj[1], obj[2]))
for c in Cons:
tmp = c(Funcs)
if type(tmp) in (list, tuple, set):
constraints += list(tmp)
else:
constraints.append(tmp)
startPoint = {x:[0]*n}
p = P(FF if isMOP else FF[0][0], startPoint, constraints = constraints)#, fixedVars = fixedVars)
if not isMOP:
p.goal=self.goal
r = p.solve(solver, **KW)
if P != oo.MOP:
r.ff = p.ff
if isMOP:
#assert not requireCount, 'MOP with nItem > 1 is unimplemented yet'
r.solution = 'for MOP see r.solutions instead of r.solution'
#tmp_c, tmp_v = r.solutions.coords, r.solutions.values
if len(r.solutions):
S = []
for s in r.solutions:
tmp = [((i, int(s[x[i]])) if requireCount else i) for i in range(n) if s[x[i]]>=1]
if 'name' in items[0]:
tmp = [(items[i]['name'], k) for i, k in tmp] if requireCount else [items[i]['name'] for i in tmp]
S.append(dict(tmp) if requireCount else tmp)
Vals = dict([(ff[0].name, r.solutions.values[:, i]) for i, ff in enumerate(FF)])
Dicts = [s.copy() for s in S]
for v in usedValues:
if v != 'nItems':
for i, d in enumerate(Dicts):
d[v] = Vals[v][i]
r.solutions = MOPsolutions(Dicts)
r.solutions.coords = S
r.solutions.values = Vals
else:
tmp = [((i, int(r.xf[x[i]])) if requireCount else i) for i in range(n) if r.xf[x[i]]>=1]
if 'name' in items[0]:
tmp = [(items[i]['name'], k) for i, k in tmp] if requireCount else [items[i]['name'] for i in tmp]
r.xf = dict(tmp) if requireCount else tmp
return r
def solve(self, *args, **kw):
import FuncDesigner as fd, openopt as oo
if len(args) > 1:
self.err('''
incorrect number of arguments for solve(),
must be at least 1 (solver), other must be keyword arguments''')
solver = args[0] if len(args) != 0 else kw.get('solver', self.solver)
KW = self.__init_kwargs.copy()
KW.update(kw)
bins, items = self.bins, self.items
#n = len(items)
# objective = KW.get('objective', self.objective)
# if isinstance(objective, (list, tuple, set)):
# nCriteria = len(self.objective)
# if 3 * nCriteria != np.asarray(self.objective).size:
# objective = [(objective[3*i], objective[3*i+1], objective[3*i+2]) for i in range(int(round(np.asarray(self.objective).size / 3)))]
# if len(objective) == 1:
# KW['fTol'], KW['goal'] = objective[0][1:]
# else:
# objective = [(self.objective, KW.get('fTol', getattr(self, 'fTol')), KW.get('goal', getattr(self, 'goal')))]
nCriteria = 1#len(objective)
isMOP = nCriteria > 1
#mainCr = objective[0][0]
solverName = solver if type(solver) == str else solver.__name__
is_interalg = solverName == 'interalg'
is_glp = False#solverName == 'sa'
if is_glp:
assert nCriteria == 1, 'you cannot solve multiobjective KSP by the solver'
#is_interalg_raw_mode = is_interalg and KW.get('dataHandling', oo.oosolver(solver).dataHandling) in ('auto','raw')
KW.pop('objective', None)
P = oo.MOP if nCriteria > 1 else oo.GLP if is_interalg else oo.MILP if not is_glp else oo.GLP
item_numbers = [item.get('n', 1) for item in items]
nItemTypes = len(items)
nItems = sum(item_numbers)
Cons = KW.pop('constraints', [])
if type(Cons) not in (list, tuple):
Cons = [Cons]
Funcs = {}
usedValues = getUsedValues(Cons)
bins_keys = set(bins.keys())
for Set in (bins_keys, usedValues):
if 'n' in Set:
Set.remove('n')
UsedValues = usedValues.copy()
UsedValues.update(bins_keys)
cr_values = {}
for val in UsedValues:
if val == 'nItems':
cr_values[val] = 1
else:
cr_values[val] = [obj[val] for obj in items]
nBins = bins.get('n', -1)
if nBins == -1:
if len(UsedValues) == 1 and type(bins) == dict:
Tmp_items = sum(list(cr_values.values()[0]))
Tmp_bins = bins[list(UsedValues)[0]]
approx_n_bins = int(np.ceil((2.0 * Tmp_items) / Tmp_bins))
else:
approx_n_bins = nItems
nBins = approx_n_bins
X = fd.oovars(nBins * nItemTypes, domain=int, lb=0).view(np.ndarray).reshape(nItemTypes, nBins)
requireCount = False
for item in items:
if 'n' in item:
# x[i].domain = np.arange(obj['n']+1) if is_interalg else int
# x[i].ub = obj['n']
# x[i].lb = 0
requireCount = True
break
y = fd.oovars(nBins, domain = bool)('y')
aux_objective = fd.sum(y)
#cr_values = dict([(obj[0], []) for obj in objective])
# MainCr = mainCr if type(mainCr) in (str, np.str_) else list(usedValues)[0]
#
# isMainCrMin = objective[0][2] in ('min', 'minimum')
# handling objective(s)
# FF = []
for optCrName in UsedValues:
F = [fd.sum(X[:, j].view(fd.ooarray) * cr_values[optCrName]) for j in range(nBins)]
Funcs[optCrName] = F
FUNCS = [dict((optCrName, Funcs[optCrName][j]) for optCrName in UsedValues) for j in range(nBins)]
# for obj in objective:
# FF.append((Funcs[obj[0]](obj[0]) if type(obj[0]) in (str, np.str_) else obj[0](Funcs), obj[1], obj[2]))
constraints = []
# 1. Constraints from p.constraints
for c in Cons:
tmp = [c(F) for F in FUNCS]
constraints += tmp
# 2. Constraints from bins parameters
for k, v in bins.items():
if k != 'n':
constraints += [fd.sum(X[:, j].view(fd.ooarray) * cr_values[k]) <= v*y[j] for j in range(nBins)]
# 3. Number of items of type i from all bins equals to item_numbers[i]
constraints += [fd.sum(X[i].view(fd.ooarray)) == item_numbers[i] for i in range(nItemTypes)]
startPoint = dict((X[i, j], 0) for i in range(nItemTypes) for j in range(nBins))
startPoint[y] = [0]*nBins
p = P(aux_objective, startPoint, constraints = constraints)
# p = P(FF if isMOP else FF[0][0], startPoint, constraints = constraints)#, fixedVars = fixedVars)
if not isMOP:
p.goal=self.goal
r = p.solve(solver, **KW)
if P != oo.MOP:
r.ff = p.ff
if isMOP:
assert 0, 'unimplemented'
# #assert not requireCount, 'MOP with nItem > 1 is unimplemented yet'
# r.solution = 'for MOP see r.solutions instead of r.solution'
# #tmp_c, tmp_v = r.solutions.coords, r.solutions.values
# if len(r.solutions):
# S = []
# for s in r.solutions:
# tmp = [((i, int(s[x[i]])) if requireCount else i) for i in range(n) if s[x[i]]>=1]
# if 'name' in items[0]:
# tmp = [(items[i]['name'], k) for i, k in tmp] if requireCount else [items[i]['name'] for i in tmp]
# S.append(dict(tmp) if requireCount else tmp)
# Vals = dict([(ff[0].name, r.solutions.values[:, i]) for i, ff in enumerate(FF)])
#
# Dicts = [s.copy() for s in S]
# for v in usedValues:
# if v != 'nItems':
# for i, d in enumerate(Dicts):
# d[v] = Vals[v][i]
# r.solutions = MOPsolutions(Dicts)
# r.solutions.coords = S
# r.solutions.values = Vals
else:
if requireCount:
xf = [dict((item.get('name',i), int(r.xf[X[i, j]])) for i, item in enumerate(items) if r.xf[X[i, j]]>0) for j in range(nBins) if r.xf[y[j]]]
else:
xf = [tuple(item.get('name',i) for i, item in enumerate(items) if r.xf[X[i, j]]==1) for j in range(nBins) if r.xf[y[j]]]
r.values = dict((optCrName, tuple(sum(item[optCrName]*r.xf[X[i, j]] for i, item in enumerate(items)) for j in range(nBins) if r.xf[y[j]])) for optCrName in UsedValues)
r.xf = xf
# tmp = [((i, int(r.xf[x[i]])) if requireCount else i) for i in range(n) if r.xf[x[i]]>=1]
# if 'name' in items[0]:
# tmp = [(items[i]['name'], k) for i, k in tmp] if requireCount else [items[i]['name'] for i in tmp]
# r.xf = dict(tmp) if requireCount else tmp
return r
