I am coding an optimization problem. The model is giving infeasible solution. I want to check which constraint is giving infeasible solution. So far, I have checked online, but have not been able to come up with the solution to the problem. Can anyone help me? For example:in the code below, because of constraint 3 model is infeasible. How do I determine it from the solution? Thanks
from gurobipy import *
# Create a new model
m = Model("mip1")
# Create variables
x1 = m.addVar(vtype=GRB.INTEGER, name="x1")
x2 = m.addVar(vtype=GRB.INTEGER, name="x2")
# Integrate new variables
m.update()
# Set objective
m.setObjective(7*x1 + 2*x2, GRB.MAXIMIZE)
m.addConstr(-x1 + 2 * x2 <= 4, "constraint-0")
m.addConstr(5*x1 + x2 <= 20, "constraint-1")
m.addConstr(-2*x1 -2*x2 <= -7, "constraint-2")
m.addConstr(x1 <= -2, "constraint-3")
m.addConstr(x2 <= 4, "constraint-4")
m.optimize()
for v in m.getVars():
print('%s %g' % (v.varName, v.x))
print('Obj: %g' % m.objVal)
an exemple :
from gurobipy import *
# Create a new model
m = Model("mip1")
# Create variables
x1= m.addVar(lb=0,ub=62,vtype=GRB.INTEGER,name="x1")
x2 = m.addVar(lb=0,ub=50, vtype=GRB.INTEGER,name="x2")
m.update()
m.addConstr(-x1 + 2*x2 <= 4, "constraint-0")
m.addConstr(5*x1 + x2 <= 20, "constraint-1")
m.addConstr(-2*x1 -2*x2 <= -25, "constraint-2")
m.addConstr(x1 <= 2, "constraint-3")
#m.addConstr(x2 <= 50, "constraint-4")
m.update()
# Set objective
m.setObjective(7*x1 + 2*x2, GRB.MAXIMIZE)
m.update()
m.optimize()
status = m.status
if status == GRB.Status.OPTIMAL:
for v in m.getVars():
print('%s %g' % (v.varName, v.x))
print('Obj: %g' % m.objVal)
elif status == GRB.Status.INFEASIBLE:
print('Optimization was stopped with status %d' % status)
# do IIS
m.computeIIS()
for c in m.getConstrs():
if c.IISConstr:
print('%s' % c.constrName)
Related
I am trying to get all solutions for a Mixed Integer program through ortools. I have two lists x and y of size 4. I want to get all solutions which satisfy sum(x) = 4 * sum(y). I created a function which takes list of past solutions as input and returns next solution. I am able to get only 2 solutions even though there are more. What am I doing wrong here?
I am expecting the following solutions
Solution 1:
xs1 = [0,0,0,0], ys1 = [0,0,0,0]
Solution 2:
xs2 = [4,0,0,0], ys2 = [1,0,0,0]
Solution 3:
xs3 = [0,4,0,0], ys3 = [1,0,0,0]
Solution 4:
xs4 = [0,0,4,0], ys4 = [0,0,1,0]
and soon on
from ortools.linear_solver import pywraplp
def opt(xs, ys):
solver = pywraplp.Solver.CreateSolver('SCIP')
infinity = solver.infinity()
# x and y are integer non-negative variables.
n = 4
M = 20
x = [0]* n
y = [0]* n
w = [[0]* n]*len(xs)
δ = [[0]* n]*len(xs)
for i in range(0,n):
x[i] = solver.IntVar(0, 20, 'x'+str(i))
y[i] = solver.IntVar(0, 20, 'y'+str(i))
for j in range(len(xs)):
w[j][i] = solver.IntVar(0, 20, 'zp'+str(j)+ '-' + str(i))
δ[j][i] = solver.IntVar(0, 1, 'δ'+str(j)+ '-' + str(i))
for j in (range(len(xs))):
for i in range(0,n):
solver.Add((w[j][i] - x[i] + xs[j][i]) >=0)
solver.Add((w[j][i] - x[i] + xs[j][i]) <= M*(1-δ[j][i]))
solver.Add((w[j][i] + x[i] - xs[j][i]) >=0)
solver.Add((w[j][i] + x[i] - xs[j][i]) <= M*δ[j][i])
for j in range(len(xs)):
solver.Add(solver.Sum([w[j][i] for i in range(0,n)]) >= 1)
solver.Add(solver.Sum([x[i] for i in range(0, n)]) - 4 * solver.Sum([y[i] for i in range(0, n)]) == 0)
solver.Minimize(solver.Sum([x[i] for i in range(0, n)]))
status = solver.Solve()
if status == pywraplp.Solver.OPTIMAL:
solver_x = [0]*n
solver_y = [0]*n
for i in range(0,n):
solver_x[i] = x[i].solution_value()
solver_y[i] = y[i].solution_value()
return ([solver_x, solver_y, solver.Objective().Value()])
else:
print('No Solution')
return ([[0], [0]], -1)
psx = [[0,0,0,0], [0,4,0,0]]
psy = [[0,0,0,0], [1,0,0,0]]
ns = opt(psx, psy)
print(ns)
Output:
No Solution
([[0], [0]], -1)
Reference:
Finding multiple solutions to general integer linear programs
How to write constraints for sum of absolutes
If you have a pure integer programming model, you can use the CP-SAT solver which allows you to print all the solutions [See this].
I am trying to use the linprog in python to solve this problem:
# Minimize = (0.035*x1) + (0.015*x2) + (0.025*x3)
# x1+x2+x3=1.2
# 0<=x1<=0.7
# 0<=x2<=0.3
# 0<=x3<=0.5
c = [0.035, 0.015, 0.025] #objective function
A_eq = [[1, 1, 1]]
b = [1.2]
lb = (0, 0, 0)
up = (0.7, 0.3, 0.5)
from scipy.optimize import linprog
linprog(c, A_ub=None, b_ub=None, A_eq=A_eq, b_eq=b, bounds=[lb,up], method='interior-point', callback=None, options=None, x0=None)
However I am getting an error could you help me with that?
thanks a lot!
You sholud define correctly the bounds for each variable in the same order as the coefficients. In this case, they’re between zero and some number:
# Minimize = (0.035*x1) + (0.015*x2) + (0.025*x3)
# x1+x2+x3=1.2
# 0<=x1<=0.7
# 0<=x2<=0.3
# 0<=x3<=0.5
c = [0.035, 0.015, 0.025] #objective function
A_eq = [[1, 1, 1]]
b = [1.2]
x1_b = (0, 0.7)
x2_b = (0, 0.3)
x3_b = (0, 0.5)
from scipy.optimize import linprog
linprog(c, A_ub=None, b_ub=None, A_eq=A_eq, b_eq=b, bounds=[x1_b, x2_b,x3_b], method='interior-point', callback=None, options=None, x0=None)
I wanna get all integer solutions in a limited time, is it possible?
This is a linear, integer constraint satisfaction problem, which can be solved efficiently by OR Tools' CP-SAT. I've modified their example to solve your problem in Python:
from ortools.sat.python import cp_model
class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
"""Print intermediate solutions."""
def __init__(self, variables):
cp_model.CpSolverSolutionCallback.__init__(self)
self.__variables = variables
self.__solution_count = 0
def on_solution_callback(self):
self.__solution_count += 1
for v in self.__variables:
print('%s=%i' % (v, self.Value(v)), end=' ')
print()
def solution_count(self):
return self.__solution_count
def SearchForAllSolutionsSampleSat():
"""Showcases calling the solver to search for all solutions."""
# Creates the model.
model = cp_model.CpModel()
p = [1, 2, 3, 4]
ceq = 30
cgeq = 2
N = len(p)
# Creates the variables
x = [model.NewIntVar(0, 100, f'x{i}') for i in range(N)]
# Create the constraints.
model.Add(sum([xi*pi for xi, pi in zip(x, p)]) == ceq)
model.Add(sum(x) >= cgeq)
# Create a solver and solve.
solver = cp_model.CpSolver()
solution_printer = VarArraySolutionPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
print('Status = %s' % solver.StatusName(status))
print('Number of solutions found: %i' % solution_printer.solution_count())
SearchForAllSolutionsSampleSat()
I am trying to run a simple linear regression using PyMC3. The below code is a snippet:
import numpy as np
from pymc3 import Model, sample, Normal, HalfCauchy
import pymc3 as pm
X = np.arange(500).reshape(500, 1)
y = np.random.normal(0, 5, [500, 1]) + X
with Model() as multiple_regression_model:
beta = Normal('beta', mu=0, sd=1000, shape=2)
sigma = HalfCauchy('sigma', 1000)
y_hat = beta[0] + X * beta[1]
exp = Normal('y', y_hat, sigma=sigma, observed=y)
with multiple_regression_model:
trace = sample(1000, tune=1000)
trace['beta'].mean(axis=0)
The above code runs in about 6 seconds and gives reasonable estimates for the betas ([-0.19646408, 1.00053091])
But when I try to use the dot product, things get really bad:
X = np.arange(500).reshape(500, 1)
y = np.random.normal(0, 5, [500, 1]) + X
X_aug_np = np.squeeze(np.dstack((np.ones((500, 1)), X)))
with Model() as multiple_regression_model:
beta = Normal('beta', mu=0, sd=1000, shape=2)
sigma = HalfCauchy('sigma', 1000)
y_hat = pm.math.dot(X_aug_np, beta)
exp = Normal('y', y_hat, sigma=sigma, observed=y)
with multiple_regression_model:
trace = sample(1000, tune=1000)
trace['beta'].mean(axis=0)
Now the code finished in 56 seconds and the estimates are totally off ([249.52363555, -0.0000481 ]).
I thought using dot product will make things faster. Why is it behaving this way? Am I doing something wrong here?
This is a subtle shape and broadcasting bug: if you change the shape of beta to (2, 1), then it works.
To see why, I renamed the two models and tidied the code a bit:
import numpy as np
import pymc3 as pm
X = np.arange(500).reshape(500, 1)
y = np.random.normal(0, 5, [500, 1]) + X
X_aug_np = np.squeeze(np.dstack((np.ones((500, 1)), X)))
with pm.Model() as basic_model:
beta = pm.Normal('beta', mu=0, sd=1000, shape=2)
sigma = pm.HalfCauchy('sigma', 1000)
y_hat = beta[0] + X * beta[1]
exp = pm.Normal('y', y_hat, sigma=sigma, observed=y)
with pm.Model() as matmul_model:
beta = pm.Normal('beta', mu=0, sd=1000, shape=(2, 1))
sigma = pm.HalfCauchy('sigma', 1000)
y_hat = pm.math.dot(X_aug_np, beta)
exp = pm.Normal('y', y_hat, sigma=sigma, observed=y)
How would you have found that out? Since it looked like the models were the same, but they were not sampling similarly, I ran
print(matmul_model.check_test_point())
print(basic_model.check_test_point())
which computes the log probability of the variables at a sensible default. This did not match up, so I checked exp.tag.test_value.shape, and found out it was (500, 500), when I expected it to be (500, 1). Shape handling is super hard in probabilistic programming, and this happened because exp broadcasts y_hat, sigma, and y together.
As an added problem, I could not get matmul_model to sample on my machine, without setting cores=1, chains=4.
I have a script as follows:
import numpy as np
import pandas as pd
import pdb
# conventions: W = fitness, A = affinity ; sex: 1=M, 0=F; alien: 1=alien,
# 0=native
# pop array order: W, A, sex, alien
def mkpop(n):
W = np.repeat(a=1, repeats=n)
A = np.random.normal(1, 0.1, size=n)
A[A < 0] = 0
alien = np.repeat(a=False, repeats=n)
sex = np.random.randint(0, 2, n)
pop = np.array([W, A, sex, alien])
pop = np.transpose(pop)
return pop
def migrate(pop, n=10, gParams=[1, 0.1]):
W = np.random.gamma(shape=gParams[0], scale=gParams[1], size=n)
A = np.repeat(1, n)
# 0 is native; 1 is alien
alien = np.repeat(True, n)
# 0 is female
sex = np.random.randint(0, 2, n)
popAlien = np.array([W, A, sex, alien])
popAlien = np.transpose(popAlien)
pop = np.vstack((pop, popAlien))
return pop
def mate(pop):
# split into male and female
f = pop[pop[:, 2] == 0]
m = pop[pop[:, 2] == 1]
# create transition matricies for native and alien mates
# m with native = m.!alien.transpose * f.alien
# negate alien
naLog = list(np.asarray(m[:, 3]) == False)
naPdMat = np.outer(naLog, f[:, 1])
# mate with alien = m.alien.transpose * affinity
alPdMat = np.outer(m[:, 3], f[:, 1])
# add transition matrices for probability density matrix
pdMat = alPdMat + naPdMat
# transition matrix is equal to the pd matrix / column sumso
colSums = np.sum(pdMat, axis=0)
pMat = pdMat / colSums
# select mates
def choice(x):
ch = np.random.choice(a=range(0, len(x)), p=x)
return ch
mCh = np.apply_along_axis(choice, 0, pMat)
mCh = m[mCh, :]
WMid = (f[:, 0] + mCh[:, 0]) / 2
AMid = (f[:, 1] + mCh[:, 1]) / 2
# assign fitness based on group affiliation; only native/alien matings have
# modified fitness
# reassign fitness and affinity based on group id and midparent vals
W1 = np.where(
(f[:, 3] == mCh[:, 3]) |
((f[:, 3] == 1) & (mCh[:, 3] == 0))
)
WMid[W1] = 1
# number of offspring is a poisson-distributed variable with lambda=2W
nOff = map(lambda x: np.random.poisson(lam=x), 2 * WMid)
# generate offspring
# expand list of nOff to numbers of offspring per pair
# realized offspring is index posisions of W and A vals to be replicated
# for offspring
# this can be rewritten to return a matrix of the appropriate length. This
# should work
midVals = np.array([WMid, AMid]).T
realOff = np.array([0, 0])
for i in range(0, len(nOff)):
sibs = np.repeat([np.array(midVals[i])], [nOff[i]], axis=0)
realOff = np.vstack((realOff, sibs))
offspring = np.delete(realOff, 0, 0)
sex = np.random.randint(0, 2, len(offspring))
alien = np.repeat(0, len(offspring))
otherStats = np.array([sex, alien]).T
offspring = np.hstack([offspring, otherStats])
return offspring # should return offspring
def sim(nInit, nGen=100, nAlien=10, gParams=[1, 0.1]):
gen = 0
pop = mkpop
stats = pd.DataFrame(columns=('gen', 'W', 'WMean', 'AMean', 'WVar', 'AVar'))
while gen < nGen:
pop = migrate(pop, nAlien, gParams)
offspring = mate(pop)
var = np.var(offspring, axis=0)
mean = np.mean(offspring, axis=0)
N = len(offspring)
W = N / nInit
genStats = N.append(W, gen, mean, var)
stats = stats.append(genStats)
print(N, gen)
gen = gen + 1
return stats
print mkpop(100)
print mate(mkpop(100))
#
sim(100, 100, 10, [1, 0.1])
Running this script, outputs NameError: name 'sim' is not defined. It is apparent from the commands before the final one that all the other functions defined within this script work without a hitch. I'm not sure what is going on here, and there is probably some very easy fix that I'm overlooking. Ctags recognizes this function just fine. It's entirely possibe that sim() doesn't actually work yet, as I haven't been able to debug it.
Your sim function defined in mate function scope so it's invisible to global scope. You need to fix your indentation for sim function