flopt
A Python Flexible Modeler for Optimization Problems.
flopt is a modeling tool for optimization problems such as LP, QP, Ising, QUBO, etc.
flopt provides various functions for flexible and easy modeling.
Users can also solve modeled problems with several solvers to obtain optimal or good solutions.

documentation | tutorial | case studies
Install
PyPI
pip install flopt
GitHub
git clone https://github.com/flab-coder/flopt.git
cd flopt && python -m pip install .
Formulatable problems in flopt
- Linear Programming (LP)
- Quadratic Programming (QP)
- Ising
- Quadratic Unconstrainted Binary Programming (QUBO)
- Non-Linear problem
minimize 2*(3*a+b)*c**2 + 3
s.t a + b * c <= 3
0 <= a <= 1
1 <= b <= 2
c <= 3
- BlackBox problem
minimize simulator(a, b, c)
s.t 0 <= a <= 1
1 <= b <= 2
1 <= c <= 3
- Finding the best permutation problem (including TSP)
- Satisfiability problem (including MAX-SAT)
Available Solvers and Heuristic Algorithms
- CBC, CVXOPT, scipy.optimize(minimize, linprog, milp), Optuna
- Random Search, 2-Opt, Swarm Intelligence Search
Simple Example
You can write codes like PuLP application.
from flopt import Variable, Problem
a = Variable('a', lowBound=0, upBound=1, cat='Continuous')
b = Variable('b', lowBound=1, upBound=2, cat='Continuous')
c = Variable('c', upBound=3, cat='Continuous')
prob = Problem()
prob += 2 * (3*a+b) * c**2 + 3
prob += a + b * c <= 3
prob.solve(timelimit=0.5, msg=True)
print('obj value', prob.getObjectiveValue())
print('a', a.value())
print('b', b.value())
print('c', c.value())
In addition, you can represent any objective function by CustomExpression
from flopt import Variable, Problem, CustomExpression
a = Variable('a', lowBound=0, upBound=1, cat='Integer')
b = Variable('b', lowBound=1, upBound=2, cat='Continuous')
def user_func(a, b):
from math import sin, cos
return (0.7*a + 0.3*cos(b)**2 + 0.1*sin(b))*abs(a)
custom_obj = CustomExpression(func=user_func, args=[a, b])
prob = Problem(name='CustomExpression')
prob += custom_obj
prob.solve(timelimit=1, msg=True)
print('obj value', prob.getObjectiveValue())
In the case you solve TSP, Permutation Variable is useful.
from flopt import Variable, Problem, CustomExpression
N = 4
D = [[0,1,2,3],
[3,0,2,1],
[1,2,0,3],
[2,3,1,0]]
x = Variable('x', lowBound=0, upBound=N-1, cat='Permutation')
def tsp_dist(x):
distance = 0
for head, tail in zip(x, x[1:]+[x[0]]):
distance += D[head][tail]
return distance
tsp_obj = CustomExpression(func=tsp_dist, args=[x])
prob = Problem(name='TSP')
prob += tsp_obj
prob.solve(timelimit=10, msg=True)
print('obj value', prob.getObjectiveValue())
print('x', x.value())
Learning more