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 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 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