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 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 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 unbounded(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
0 <= w
maximize obj = x + 4*y + 9*z + w
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
c4: w >= 0
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "unbounded"
obj.maximize = True
# names
cols = prob.cols
for i in range(4):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
cols[3].name = "w"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0, 1), (1, 1)]))
rows.add(yaposib.vec([(0, 1), (2, 1)]))
rows.add(yaposib.vec([(1, -1), (2, 1)]))
rows.add(yaposib.vec([(3, 1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7
rows[2].upperbound = 7
rows[3].lowerbound = 0
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
rows[3].name = "c4"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
prob.obj[3] = 1
return prob
def unbounded(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
0 <= w
maximize obj = x + 4*y + 9*z + w
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
c4: w >= 0
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "unbounded"
obj.maximize = True
# names
cols = prob.cols
for i in range(4):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
cols[3].name = "w"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0,1),(1,1)]))
rows.add(yaposib.vec([(0,1),(2,1)]))
rows.add(yaposib.vec([(1,-1),(2,1)]))
rows.add(yaposib.vec([(3,1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7
rows[2].upperbound = 7
rows[3].lowerbound = 0
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
rows[3].name = "c4"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
prob.obj[3] = 1
return prob
def mip(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
minimize obj = x + 4*y + 9*z
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7.5
z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "mip"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# integer variables
cols[2].integer = True
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0,1),(1,1)]))
rows.add(yaposib.vec([(0,1),(2,1)]))
rows.add(yaposib.vec([(1,-1),(2,1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7.5
rows[2].upperbound = 7.5
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
return prob
def mip(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
minimize obj = x + 4*y + 9*z
such that:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7.5
z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "mip"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# integer variables
cols[2].integer = True
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0, 1), (1, 1)]))
rows.add(yaposib.vec([(0, 1), (2, 1)]))
rows.add(yaposib.vec([(1, -1), (2, 1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7.5
rows[2].upperbound = 7.5
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
return prob
def integer_infeasible(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z <= 10
no objective
constraints:
c1: x+y <= 5.2
c2: x+z >= 10.3
c3: -y+z == 7.4
x, y, z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "integer_infeasible"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# integer variables
for col in cols:
col.integer = True
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
cols[2].upperbound = 10
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0,1),(1,1)]))
rows.add(yaposib.vec([(0,1),(2,1)]))
rows.add(yaposib.vec([(1,-1),(2,1)]))
# constraints bounds
rows[0].upperbound = 5.2
rows[1].lowerbound = 10.3
rows[2].lowerbound = 7.4
rows[2].upperbound = 7.4
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
return prob
def integer_infeasible(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z <= 10
no objective
constraints:
c1: x+y <= 5.2
c2: x+z >= 10.3
c3: -y+z == 7.4
x, y, z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "integer_infeasible"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# integer variables
for col in cols:
col.integer = True
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
cols[2].upperbound = 10
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0, 1), (1, 1)]))
rows.add(yaposib.vec([(0, 1), (2, 1)]))
rows.add(yaposib.vec([(1, -1), (2, 1)]))
# constraints bounds
rows[0].upperbound = 5.2
rows[1].lowerbound = 10.3
rows[2].lowerbound = 7.4
rows[2].upperbound = 7.4
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
return prob
def feasability_only(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
no objective
constraints:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7.5
z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "feasability_only"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# integer variables
cols[2].integer = True
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0,1),(1,1)]))
rows.add(yaposib.vec([(0,1),(2,1)]))
rows.add(yaposib.vec([(1,-1),(2,1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7.5
rows[2].upperbound = 7.5
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
return prob
def duals_and_slacks(solver):
"""
returns the following problem
0 <= x <= 5
-1 <= y <= 1
0 <= z
Minimize obj = x + 4 y + 9 z
constraints:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "duals_and_slacks"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 5
cols[1].upperbound = 1
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0,1),(1,1)]))
rows.add(yaposib.vec([(0,1),(2,1)]))
rows.add(yaposib.vec([(1,-1),(2,1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7
rows[2].upperbound = 7
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
return prob
def duals_and_slacks(solver):
"""
returns the following problem
0 <= x <= 5
-1 <= y <= 1
0 <= z
Minimize obj = x + 4 y + 9 z
constraints:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "duals_and_slacks"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 5
cols[1].upperbound = 1
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0, 1), (1, 1)]))
rows.add(yaposib.vec([(0, 1), (2, 1)]))
rows.add(yaposib.vec([(1, -1), (2, 1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7
rows[2].upperbound = 7
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
# obj
prob.obj[0] = 1
prob.obj[1] = 4
prob.obj[2] = 9
return prob
def feasability_only(solver):
"""
returns the following problem
0 <= x <= 4
-1 <= y <= 1
0 <= z
no objective
constraints:
c1: x+y <= 5
c2: x+z >= 10
c3: -y+z == 7.5
z integer
"""
prob = yaposib.Problem(solver)
obj = prob.obj
obj.name = "feasability_only"
obj.maximize = False
# names
cols = prob.cols
for i in range(3):
cols.add(yaposib.vec([]))
cols[0].name = "x"
cols[1].name = "y"
cols[2].name = "z"
# lowerbounds
for col in cols:
col.lowerbound = 0
cols[1].lowerbound = -1
# upperbounds
cols[0].upperbound = 4
cols[1].upperbound = 1
# integer variables
cols[2].integer = True
# constraints
rows = prob.rows
rows.add(yaposib.vec([(0, 1), (1, 1)]))
rows.add(yaposib.vec([(0, 1), (2, 1)]))
rows.add(yaposib.vec([(1, -1), (2, 1)]))
# constraints bounds
rows[0].upperbound = 5
rows[1].lowerbound = 10
rows[2].lowerbound = 7.5
rows[2].upperbound = 7.5
# constraints names
rows[0].name = "c1"
rows[1].name = "c2"
rows[2].name = "c3"
return prob
def buildSolverModel(self, lp):
"""
Takes the pulp lp model and translates it into a yaposib model
"""
log.debug("create the yaposib model")
lp.solverModel = yaposib.Problem(self.solverName)
prob = lp.solverModel
prob.name = lp.name
log.debug("set the sense of the problem")
if lp.sense == constants.LpMaximize:
prob.obj.maximize = True
log.debug("add the variables to the problem")
for var in lp.variables():
col = prob.cols.add(yaposib.vec([]))
col.name = var.name
if not var.lowBound is None:
col.lowerbound = var.lowBound
if not var.upBound is None:
col.upperbound = var.upBound
if var.cat == constants.LpInteger:
col.integer = True
prob.obj[col.index] = lp.objective.get(var, 0.0)
var.solverVar = col
log.debug("add the Constraints to the problem")
for name, constraint in lp.constraints.items():
row = prob.rows.add(
yaposib.vec(
[
(var.solverVar.index, value)
for var, value in constraint.items()
]
)
)
if constraint.sense == constants.LpConstraintLE:
row.upperbound = -constraint.constant
elif constraint.sense == constants.LpConstraintGE:
row.lowerbound = -constraint.constant
elif constraint.sense == constants.LpConstraintEQ:
row.upperbound = -constraint.constant
row.lowerbound = -constraint.constant
else:
raise PulpSolverError("Detected an invalid constraint type")
row.name = name
constraint.solverConstraint = row
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 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 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) ]
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
prob.cols[0].upperbound = 4
prob.cols[1].upperbound = 1
# constraints
prob.rows.add(yaposib.vec([(0,1),(1,1)]))
prob.rows.add(yaposib.vec([(0,1),(2,1)]))
prob.rows.add(yaposib.vec([(1,-1),(2,1)]))
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
prob.cols[0].upperbound = 4
prob.cols[1].upperbound = 1
# constraints
prob.rows.add(yaposib.vec([(0, 1), (1, 1)]))
prob.rows.add(yaposib.vec([(0, 1), (2, 1)]))
prob.rows.add(yaposib.vec([(1, -1), (2, 1)]))