What is PuLP

A Python package that solves linear programming problems. https://code.google.com/p/pulp-or/ https://pythonhosted.org/PuLP/index.html

A linear programming problem is an optimization problem in which an objective function and constraints are expressed by a linear expression. For example

Find a combination of quantities that maximizes profits when making a fixed quantity of several products with different costs and profits.
Solve the puzzle

Is one of the linear programming problems.

Since it was introduced at PyConJP 2014, when I investigated how to use it, It's pretty easy to use, so I summarized it.

Installation method

sudo pip install pulp

procedure

Create a linear programming problem object

This expresses all the problems. For the constructor, choose the name of the problem and whether to minimize or maximize the objective function.

import pulp
problem = pulp.LpProblem('Problem Name', pulp.LpMinimize) #When minimizing
problem = pulp.LpProblem('Problem Name', pulp.LpMaximize) #When maximizing

Create a variable object

Create variables for use in linear programming. There are two ways to make it. You will often use 2 when you have a large number of variables.

(1) Make one by one

pulp.LpVariable('name', 0, 1, 'Continuous')

Variables are in order from the front

Variable name
Minimum value of variable
Maximum value of variable
Variable type. 'Continuous' for floats,'Integer' for integers,'Binary' for binary variables

With this code, you can generate a variable with a variable name that takes a continuous value from 0 to 1.

(2) Pass the list and make it all together

var = pulp.LpVariable.dicts('VAR', ([1,2,3], ['a', 'b']), 0, 1, 'Continuous')

Variables are in order from the front

Variable name prefix
Tuple of a list of postfix variable names
Minimum value of variable
Maximum value of variable
Variable type

3-5 is the same as before.

When this code is executed, it takes continuous values with a minimum value of 0 and a maximum value of 1, You can get a dictionary with the variables VAR_1_a, VAR_1_b, VAR_2_a, .... The access method is var [1] ['a'] like this. This will be used in a future article.

Create an objective function

Create an expression using variables and add it to the Mathematical Planning Problem object ** This is amazing.

For example, if you want to maximize the sum of ʻaandb`

import pulp

problem = pulp.LpProblem('test', pulp.LpMinimize)
a = pulp.LpVariable('a', 0, 1)
b = pulp.LpVariable('b', 0, 1)
problem += a + b

If you print the problem in this state, the problem will be displayed.

test:
MINIMIZE
1*a + 1*b + 0
VARIABLES
a <= 1 Continuous
b <= 1 Continuous

Create constraints

Make a comparison using variables and ** add it to a mathematical planning problem object ** This is also great.

For example, for the variables ʻaandb`

ʻa` is greater than or equal to 0
b is 0.1 or more
The sum of ʻaandb` is 0.5 When you want to create a constraint

problem += a >= 0
problem += b >= 0.1
problem += a + b == 0.5

Only the anti-inequality sign (<=, =>) could be used.

solve

problem.solve()

only this.

Depending on the constraints, it may not be possible to solve it, so if you want to know the result,

status = problem.solve()
print pulp.LpStatus[status]

OK if Optimal appears in

Get the result.

You can get the value by calling the value method of the variable added to the problem.

Summary

import pulp

problem = pulp.LpProblem('sample', pulp.LpMinimize)

a = pulp.LpVariable('a', 0, 1)
b = pulp.LpVariable('b', 0, 1)

problem += a + b

problem += a >= 0
problem += b >= 0.1
problem += a + b == 0.5

status = problem.solve()
print "Status", pulp.LpStatus[status]

print problem

print "Result"
print "a", a.value()
print "b", b.value()

Result is,

Status Optimal
sample:
MINIMIZE
1*a + 1*b + 0
SUBJECT TO
_C1: a >= 0

_C2: b >= 0.1

_C3: a + b = 0.5

VARIABLES
a <= 1 Continuous
b <= 1 Continuous

Result
a 0.4
b 0.1

[PYTHON] Getting started on how to solve linear programming problems with PuLP