def solve_sat(expression):
if len(expression) == 0: return [] # Trivial case. Otherwise count vars.
numvars = max([max([abs(v) for v in clause]) for clause in expression])
lp = yaposib.Problem(
yaposib.available_solvers()[0]) # Construct an empty linear program.
for i in range(2 * numvars):
col = lp.cols.add(yaposib.vec(
[])) # As many columns as there are literals.
col.lowerbound = 0.0 # Literal must be between false and true.
col.upperbound = 1.0
def lit2col(lit): # Function to compute column index.
return [2 * (-lit) - 1, 2 * lit - 2][lit > 0]
for i in xrange(1, numvars + 1): # Ensure "oppositeness" of literals.
row = lp.rows.add(yaposib.vec([(lit2col(i), 1.0), (lit2col(-i), 1.0)]))
row.lowerbound = row.upperbound = 1.0 # Must sum to exactly 1.
for clause in expression: # Ensure "trueness" of each clause.
row = lp.rows.add(yaposib.vec([(lit2col(lit), 1.0) for lit in clause]))
row.lowerbound = 1.0 # At least one literal must be true.
lp.solve() # Try to solve the relaxed problem.
if lp.status != 'optimal':
return None # If no relaxed solution, no exact sol.
for col in lp.cols:
col.integer = True
lp.solveMIP() # Try to solve this integer problem.
if lp.status != 'optimal': return None
return [lp.cols[i].solution > 0.99 for i in range(0, len(lp.cols), 2)]
def __init__(
self,
mip=True,
msg=True,
timeLimit=None,
epgap=None,
solverName=None,
**solverParams
):
"""
Initializes the yaposib solver.
@param mip: if False the solver will solve a MIP as
an LP
@param msg: displays information from the solver to
stdout
@param timeLimit: not supported
@param epgap: not supported
@param solverParams: not supported
"""
LpSolver.__init__(self, mip, msg)
if solverName:
self.solverName = solverName
else:
self.solverName = yaposib.available_solvers()[0]
def halfint_correlation_clustering(similarity):
"""Wacky MIP-based half-int constrained correlation clustering."""
lp = yaposib.Problem(yaposib.available_solvers()[0]) # Define the linear program.
items = len(similarity) # Get the number of items.
lp.obj.maximize = True # Set as maximization.
for i in range((items*(items-1))/2):
lp.cols.add(yaposib.vec([])) # Each item pair has a var.
for j in xrange(items):
for i in xrange(j):
index = pair2index(i, j) # Get the index for this pair.
lp.cols[index].lowerbound = 0 # Each variable in range 0 to 1.
lp.cols[index].upperbound = 2 # Each variable in range 0 to 1.
lp.cols[index].integer = True # This should be integral.
lp.obj[index]=similarity[j][i]/2 # If 1, this much added to obj.
for k in xrange(items): # For all triples of items, we
for j in xrange(k): # want to add in constraints to
jk = pair2index(j,k) # enforce respect for the
for i in xrange(j): # triangle inequality.
ij, ik = pair2index(i,j), pair2index(i,k)
# We want Xij >= Xik + Xjk - 1.
# That is, we want 1 >= Xik + Xjk - Xij.
# Add constraints to enforce this!
lp.rows.add(yaposib.vec([(ij, 1), (ik, 1), (jk,-1)]))
lp.rows.add(yaposib.vec([(ij, 1), (ik,-1), (jk, 1)]))
lp.rows.add(yaposib.vec([(ij,-1), (ik, 1), (jk, 1)]))
for row in lp.rows: # For each row.
row.upperbound = 2 # Each row is <= 1.
lp.solveMIP() # Find the basic solution.
labels = [[lp.cols[pair2index(i,j)].solution/2 for i in xrange(j)]
for j in xrange(items)]
return lp.obj.value, labels
def halfint_correlation_clustering(similarity):
"""Wacky MIP-based half-int constrained correlation clustering."""
lp = yaposib.Problem(
yaposib.available_solvers()[0]) # Define the linear program.
items = len(similarity) # Get the number of items.
lp.obj.maximize = True # Set as maximization.
for i in range((items * (items - 1)) / 2):
lp.cols.add(yaposib.vec([])) # Each item pair has a var.
for j in xrange(items):
for i in xrange(j):
index = pair2index(i, j) # Get the index for this pair.
lp.cols[index].lowerbound = 0 # Each variable in range 0 to 1.
lp.cols[index].upperbound = 2 # Each variable in range 0 to 1.
lp.cols[index].integer = True # This should be integral.
lp.obj[
index] = similarity[j][i] / 2 # If 1, this much added to obj.
for k in xrange(items): # For all triples of items, we
for j in xrange(k): # want to add in constraints to
jk = pair2index(j, k) # enforce respect for the
for i in xrange(j): # triangle inequality.
ij, ik = pair2index(i, j), pair2index(i, k)
# We want Xij >= Xik + Xjk - 1.
# That is, we want 1 >= Xik + Xjk - Xij.
# Add constraints to enforce this!
lp.rows.add(yaposib.vec([(ij, 1), (ik, 1), (jk, -1)]))
lp.rows.add(yaposib.vec([(ij, 1), (ik, -1), (jk, 1)]))
lp.rows.add(yaposib.vec([(ij, -1), (ik, 1), (jk, 1)]))
for row in lp.rows: # For each row.
row.upperbound = 2 # Each row is <= 1.
lp.solveMIP() # Find the basic solution.
labels = [[lp.cols[pair2index(i, j)].solution / 2 for i in xrange(j)]
for j in xrange(items)]
return lp.obj.value, labels
def test_duals_and_slacks(self):
for solver in yaposib.available_solvers():
prob = duals_and_slacks(solver)
yaposibTestCheck(prob, ["optimal"], sol=[4, -1, 6],
reducedcosts=[0, 12, 0], duals=[0, 1, 8],
#slacks=[2, 0, 0]
)
def hamiltonian(edges):
node2colnums = {} # Maps node to col indices of incident edges.
for colnum, edge in enumerate(edges):
n1, n2 = edge
node2colnums.setdefault(n1, []).append(colnum)
node2colnums.setdefault(n2, []).append(colnum)
print node2colnums
lp = yaposib.Problem(yaposib.available_solvers()[0]) # A new empty linear program
for i in range(len(edges)):
col = lp.cols.add(yaposib.vec([])) # A struct var for each edge
col.integer = True # Make integer, not continuous
col.lowerbound = 0 # Make binary, not continuous
col.upperbound = 1 # Make binary, not continuous
# For each node, select at least 1 and at most 2 incident edges.
for edge_column_nums in node2colnums.values():
row = lp.rows.add(yaposib.vec([(cn, 1.0) for cn in edge_column_nums]))
row.lowerbound = 1
row.upperbound = 2
# We should select exactly (number of nodes - 1) edges total
row = lp.rows.add(yaposib.vec([(cn, 1.0) for cn in
range(len(lp.cols))]))
row.lowerbound = row.upperbound = len(node2colnums)-1
lp.solve()
if lp.status != 'optimal': return None # If no relaxed sol., no exact sol.
# Return the edges whose associated struct var has value 1.
return [edge for edge, col in zip(edges, lp.cols) if col.solution > 0.99]
def test_duals_and_slacks(self):
for solver in yaposib.available_solvers():
prob = duals_and_slacks(solver)
yaposibTestCheck(
prob,
["optimal"],
sol=[4, -1, 6],
reducedcosts=[0, 12, 0],
duals=[0, 1, 8],
#slacks=[2, 0, 0]
)
def maxflow(capgraph, s, t):
node2rnum = {} # Map non-source/sink nodes to row num.
for nfrom, nto, cap in capgraph:
if nfrom != s and nfrom != t:
node2rnum.setdefault(nfrom, len(node2rnum))
if nto != s and nto != t:
node2rnum.setdefault(nto, len(node2rnum))
lp = yaposib.Problem(yaposib.available_solvers()[0]) # Empty LP instance.
for i in range(len(capgraph)):
lp.cols.add(yaposib.vec([])) # As many columns cap-graph edges.
mat = [] # Will hold constraint matrix entries.
for colnum, (nfrom, nto, cap) in enumerate(capgraph):
lp.cols[colnum].lowerbound = 0 # Flow along edge bounded by capacity.
lp.cols[
colnum].upperbound = cap # Flow along edge bounded by capacity.
if nfrom == s:
lp.obj[colnum] = 1.0 # Flow from source increases flow value
elif nto == s:
lp.obj[colnum] = -1.0 # Flow to source decreases flow value
if nfrom in node2rnum: # Flow from node decreases its net flow
mat.append((node2rnum[nfrom], colnum, -1.0))
if nto in node2rnum: # Flow to node increases its net flow
mat.append((node2rnum[nto], colnum, 1.0))
lp.obj.maximize = True # Want source s max flow maximized.
for row_nr in range(len(node2rnum)):
to_add = [(j, coef) for i, j, coef in mat if i == row_nr]
row = lp.rows.add(yaposib.vec(to_add))
row.lowerbound = row.upperbound = 0 # Net flow for non-source/sink is 0.
lp.solve() # This should work unless capgraph bad.
return [
(nfrom, nto, col.solution) # Return edges with assigned flow.
for col, (nfrom, nto, cap) in zip(lp.cols, capgraph)
]
def test_HotStart(self):
"""
Tests the hotstart feature.
1) solve, get a hotstart
2) wipe and resolve, knowing a hotstart now exists
3) wipe and unmark the hotstart, resolve again
"""
for solver in yaposib.available_solvers():
prob = continuous(solver)
prob.solve()
yaposibTestCheck(prob, ["optimal"], sol = [4.0, -1.0, 6.0, 0.0])
wipe_solution(prob)
prob.markHotStart()
#time = -clock()
prob.solve()
#time += clock()
yaposibTestCheck(prob, ["optimal"], sol = [4.0, -1.0, 6.0, 0.0])
wipe_solution(prob)
prob.unmarkHotStart()
prob.solve()
yaposibTestCheck(prob, ["optimal"], sol = [4.0, -1.0, 6.0, 0.0])
def test_HotStart(self):
"""
Tests the hotstart feature.
1) solve, get a hotstart
2) wipe and resolve, knowing a hotstart now exists
3) wipe and unmark the hotstart, resolve again
"""
for solver in yaposib.available_solvers():
prob = continuous(solver)
prob.solve()
yaposibTestCheck(prob, ["optimal"], sol=[4.0, -1.0, 6.0, 0.0])
wipe_solution(prob)
prob.markHotStart()
#time = -clock()
prob.solve()
#time += clock()
yaposibTestCheck(prob, ["optimal"], sol=[4.0, -1.0, 6.0, 0.0])
wipe_solution(prob)
prob.unmarkHotStart()
prob.solve()
yaposibTestCheck(prob, ["optimal"], sol=[4.0, -1.0, 6.0, 0.0])
def test_writeLp(self):
lpfile = ["\Problem name: ",
"",
"Minimize",
"OBJROW: x + 4 y + 9 z",
"Subject To",
"c1: x + y <= 5",
"c2: x + z >= 10",
"c3: - y + z = 7",
"c4: w >= 0",
"Bounds",
" 0 <= x <= 4",
" -1 <= y <= 1",
"End",]
for solver in yaposib.available_solvers():
prob = continuous(solver)
prob.writeLp("debug")
with open("debug.lp", "r") as f:
for line, ref in zip(f, lpfile):
if line.strip() != ref.strip():
error_msg = "\t%s != %s" % (line.strip(), ref.strip())
raise yaposib.YaposibError(error_msg)
def maxflow(capgraph, s, t):
node2rnum = {} # Map non-source/sink nodes to row num.
for nfrom, nto, cap in capgraph:
if nfrom!=s and nfrom!=t:
node2rnum.setdefault(nfrom, len(node2rnum))
if nto!=s and nto!=t:
node2rnum.setdefault(nto, len(node2rnum))
lp = yaposib.Problem(yaposib.available_solvers()[0]) # Empty LP instance.
for i in range(len(capgraph)):
lp.cols.add(yaposib.vec([])) # As many columns cap-graph edges.
mat = [] # Will hold constraint matrix entries.
for colnum, (nfrom, nto, cap) in enumerate(capgraph):
lp.cols[colnum].lowerbound = 0 # Flow along edge bounded by capacity.
lp.cols[colnum].upperbound = cap # Flow along edge bounded by capacity.
if nfrom == s:
lp.obj[colnum] = 1.0 # Flow from source increases flow value
elif nto == s:
lp.obj[colnum] = -1.0 # Flow to source decreases flow value
if nfrom in node2rnum: # Flow from node decreases its net flow
mat.append((node2rnum[nfrom], colnum, -1.0))
if nto in node2rnum: # Flow to node increases its net flow
mat.append((node2rnum[nto], colnum, 1.0))
lp.obj.maximize = True # Want source s max flow maximized.
for row_nr in range(len(node2rnum)):
to_add = [(j, coef) for i, j, coef in mat if i == row_nr]
row = lp.rows.add(yaposib.vec(to_add))
row.lowerbound = row.upperbound = 0 # Net flow for non-source/sink is 0.
lp.solve() # This should work unless capgraph bad.
return [(nfrom, nto, col.solution) # Return edges with assigned flow.
for col, (nfrom, nto, cap) in zip(lp.cols, capgraph)]
def tsp(edges):
node2colnums = {} # Maps node to col indices of incident edges.
for colnum, edge in enumerate(edges):
n1, n2, cost = edge
node2colnums.setdefault(n1, []).append(colnum)
node2colnums.setdefault(n2, []).append(colnum)
lp = yaposib.Problem(yaposib.available_solvers()[0]) # A new empty linear program
for i in range(len(edges)):
col = lp.cols.add(yaposib.vec([])) # A struct var for each edge
col.integer = True # Make binary, not continuous
col.lowerbound = 0 # Either edge selected (1) or not (0)
col.upperbound = 1 # Either edge selected (1) or not (0)
lp.rows.add(len(node2colnums)+1) # Constraint for each node
lp.obj[:] = [e[-1] for e in edges] # Try to minimize the total costs.
lp.obj.maximize = False
# For each node, select two edges, i.e.., an arrival and a departure.
for edge_column_nums in node2colnums.values():
row = lp.rows.add(yaposib.vec([(cn, 1.0) for cn in edge_column_nums]))
row.lowerbound = row.upperbound = 2
# We should select exactly (number of nodes) edges total
row = lp.rows.add(yaposib.vec([(cn, 1.0) for cn in
range(len(lp.cols))]))
row.lowerbound = row.upperbound = len(node2colnums)
lp.solve()
if lp.status != 'optimal': return None # If no relaxed sol., no exact sol.
lp.solveMIP()
if lp.status != 'optimal': return None # Count not find integer solution!
# Return the edges whose associated struct var has value 1.
return [edge for edge, col in zip(edges, lp.cols) if col.value > 0.99]
def test_writeLp(self):
lpfile = [
"\Problem name: ",
"",
"Minimize",
"OBJROW: x + 4 y + 9 z",
"Subject To",
"c1: x + y <= 5",
"c2: x + z >= 10",
"c3: - y + z = 7",
"c4: w >= 0",
"Bounds",
" 0 <= x <= 4",
" -1 <= y <= 1",
"End",
]
for solver in yaposib.available_solvers():
prob = continuous(solver)
prob.writeLp("debug")
with open("debug.lp", "r") as f:
for line, ref in zip(f, lpfile):
if line.strip() != ref.strip():
error_msg = "\t%s != %s" % (line.strip(), ref.strip())
raise yaposib.YaposibError(error_msg)
def solve_sat(expression):
if len(expression)==0: return [] # Trivial case. Otherwise count vars.
numvars = max([max([abs(v) for v in clause]) for clause in expression])
lp = yaposib.Problem(yaposib.available_solvers()[0]) # Construct an empty linear program.
for i in range(2*numvars):
col = lp.cols.add(yaposib.vec([])) # As many columns as there are literals.
col.lowerbound = 0.0 # Literal must be between false and true.
col.upperbound = 1.0
def lit2col(lit): # Function to compute column index.
return [2*(-lit)-1,2*lit-2][lit>0]
for i in xrange(1, numvars+1): # Ensure "oppositeness" of literals.
row = lp.rows.add(yaposib.vec([(lit2col(i), 1.0), (lit2col(-i), 1.0)]))
row.lowerbound = row.upperbound = 1.0 # Must sum to exactly 1.
for clause in expression: # Ensure "trueness" of each clause.
row = lp.rows.add(yaposib.vec([(lit2col(lit), 1.0) for lit in clause]))
row.lowerbound = 1.0 # At least one literal must be true.
lp.solve() # Try to solve the relaxed problem.
if lp.status!='optimal': return None # If no relaxed solution, no exact sol.
for col in lp.cols:
col.integer = True
lp.solveMIP() # Try to solve this integer problem.
if lp.status != 'optimal': return None
return [lp.cols[i].solution > 0.99 for i in range(0, len(lp.cols), 2) ]
def test_isProvenOptimal(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
yaposibTestCheck(prob, ["optimal"], sol = [4.0, -1.0, 6.0, 0.0])
if (not prob.isProvenOptimal):
raise yaposib.YaposibError
def test_continuous_maximisation(self):
for solver in yaposib.available_solvers():
prob = continuous_maximisation(solver)
yaposibTestCheck(prob, ["optimal"], sol=[4.0, 1.0, 8.0, 0.0])
def test_isProvenDualInfeasible(self):
for solver in yaposib.available_solvers():
prob = unbounded(solver)
yaposibTestCheck(prob, ["infeasible"])
if (not prob.isProvenDualInfeasible):
raise yaposib.YaposibError
def test_mip(self):
for solver in yaposib.available_solvers():
prob = mip(solver)
yaposibTestCheck(prob, ["optimal"], [3.0, -0.5, 7.0],
solve_as_MIP = True)
def test_feasability_only(self):
for solver in yaposib.available_solvers():
prob = feasability_only(solver)
yaposibTestCheck(prob, ["optimal"])
def test_isDualObjectiveLimitReached(self):
for solver in yaposib.available_solvers():
prob = infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"])
if (not prob.isDualObjectiveLimitReached):
raise yaposib.YaposibError
def test_continuous_maximisation(self):
for solver in yaposib.available_solvers():
prob = continuous_maximisation(solver)
yaposibTestCheck(prob, ["optimal"], sol = [4.0, 1.0, 8.0, 0.0])
def test_relaxed_mip(self):
for solver in yaposib.available_solvers():
prob = mip(solver)
prob.obj.name = "relaxed_mip"
yaposibTestCheck(prob, ["optimal"], [3.5, -1, 6.5])
def test_isProvenOptimal(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
yaposibTestCheck(prob, ["optimal"], sol=[4.0, -1.0, 6.0, 0.0])
if (not prob.isProvenOptimal):
raise yaposib.YaposibError
def test_isProvenPrimalInfeasible(self):
for solver in yaposib.available_solvers():
prob = infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"])
if (not prob.isProvenPrimalInfeasible):
raise yaposib.YaposibError
def test_available_solvers(self):
self.failIfEqual(yaposib.available_solvers(), [])
def test_feasability_only(self):
for solver in yaposib.available_solvers():
prob = feasability_only(solver)
yaposibTestCheck(prob, ["optimal"])
"""
builds the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
0 <= w
minimize obj = x + 4*y + 9*z
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
c4: w >= 0
"""
prob = yaposib.Problem(yaposib.available_solvers()[0])
prob.obj.name = "MyProblem"
prob.obj.maximize = False
# names
for i in range(4):
prob.cols.add(yaposib.vec([]))
prob.cols[0].name = "x"
prob.cols[1].name = "y"
prob.cols[2].name = "z"
prob.cols[3].name = "w"
# lowerbounds
for col in prob.cols:
col.lowerbound = 0
prob.cols[1].lowerbound = -1
# upperbounds
"""
builds the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
0 <= w
minimize obj = x + 4*y + 9*z
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
c4: w >= 0
"""
prob = yaposib.Problem(yaposib.available_solvers()[0])
prob.obj.name = "MyProblem"
prob.obj.maximize = False
# names
for i in range(4):
prob.cols.add(yaposib.vec([]))
prob.cols[0].name = "x"
prob.cols[1].name = "y"
prob.cols[2].name = "z"
prob.cols[3].name = "w"
# lowerbounds
for col in prob.cols:
col.lowerbound = 0
prob.cols[1].lowerbound = -1
# upperbounds
def test_isProvenPrimalInfeasible(self):
for solver in yaposib.available_solvers():
prob = infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"])
if (not prob.isProvenPrimalInfeasible):
raise yaposib.YaposibError
def test_isAbandoned(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
if (not prob.isAbandoned):
raise yaposib.YaposibError
def test_isProvenDualInfeasible(self):
for solver in yaposib.available_solvers():
prob = unbounded(solver)
yaposibTestCheck(prob, ["infeasible"])
if (not prob.isProvenDualInfeasible):
raise yaposib.YaposibError
def test_continuous(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
yaposibTestCheck(prob, ["optimal"], sol=[4.0, -1.0, 6.0, 0.0])
def test_continuous(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
yaposibTestCheck(prob, ["optimal"], sol = [4.0, -1.0, 6.0, 0.0])
def test_available_solvers(self):
self.failIfEqual(yaposib.available_solvers(), [])
def test_unbounded(self):
for solver in yaposib.available_solvers():
prob = unbounded(solver)
yaposibTestCheck(prob, ["infeasible"])
def test_mip(self):
for solver in yaposib.available_solvers():
prob = mip(solver)
yaposibTestCheck(prob, ["optimal"], [3.0, -0.5, 7.0],
solve_as_MIP=True)
def test_relaxed_mip(self):
for solver in yaposib.available_solvers():
prob = mip(solver)
prob.obj.name = "relaxed_mip"
yaposibTestCheck(prob, ["optimal"], [3.5, -1, 6.5])
def test_unbounded(self):
for solver in yaposib.available_solvers():
prob = unbounded(solver)
yaposibTestCheck(prob, ["infeasible"])
def test_integer_infeasible(self):
for solver in yaposib.available_solvers():
prob = integer_infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"], solve_as_MIP = True)
def test_isAbandoned(self):
for solver in yaposib.available_solvers():
prob = continuous(solver)
if (not prob.isAbandoned):
raise yaposib.YaposibError
def test_isDualObjectiveLimitReached(self):
for solver in yaposib.available_solvers():
prob = infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"])
if (not prob.isDualObjectiveLimitReached):
raise yaposib.YaposibError
def test_integer_infeasible(self):
for solver in yaposib.available_solvers():
prob = integer_infeasible(solver)
yaposibTestCheck(prob, ["infeasible", "limitreached"],
solve_as_MIP=True)
