CPLEX Python API self-made manual LP edition

Motivation

I want to use CPLEX on Python, but there is only an English manual, and it is troublesome to check each one, so I have to write a Japanese manual myself. Please note that it is not exhaustive because it is for my own use. Also, it is assumed that the program will be written in jupyter notebook.

It is based on the following site. [Official CPLEX Python API Reference Manual] https://www.ibm.com/support/knowledgecenter/en/SSSA5P_12.8.0/ilog.odms.cplex.help/refpythoncplex/html/cplex-module.html

Reference article [Using IBM's optimized solver CPLEX in Python] https://qiita.com/leopardus/items/93cac0f97cb22151983a

environment

• MacBook Pro macOS Catalina
• Anaconda
• CPLEX_Studio1210 Academic Edition

LP (Linear Programming Problem)

This time, I will mainly describe what is necessary when solving LP (jupyter notebook format). Let's program using the following problem as an example. $ \begin{align} \max\ \ &2x_1+3x_2 \\\ \text{s.t.}\ \ &3x_1+2x_2 \leq 24 \\\ &x_1+2x_2 \leq 16 \\\ &x_1 \leq 6 \\\ &x_1 \geq 0,x_2 \geq 0 \end{align} $

Problem setting

import cplex

First, create an instance of the optimization problem.

lp = cplex.Cplex()

Now you have an empty problem with no data. Then set this problem to be an LP (Linear Programming Problem).

lp.set_problem_type(lp.problem_type.LP)

If you want to make an optimization problem other than LP, change the argument of the above function to lp.problem_type.MILP

lp.problem_type.It can be supported by using QP etc. This time it's LP

#### **`lp.problem_type.I am substituting LP.`**

Then specify whether to maximize or minimize the objective function. By default, it is "minimize", that is, it is a minimization problem, but this time it is set to "maximize" maximization.

lp.objective.set_sense(lp.objective.sense.maximize)

You don't have to, but give the problem a name.

lp.set_problem_name("test_lp")

Up to this point, the general settings for LP have been completed.

Variable setting

Next, set the variables.

lp.variables.add(names=["x1","x2"],lb=[0,0])

To add a new variable, use the above function called add, but the argument of add is obj lb ub types ` There are 6 types: `` names columns```. The explanation of each is as follows.

• obj
  Only when the objective function is linear, you can pass the coefficients of the variables of the objective function in a list. In this case, the objective function can be set by setting ```obj = [2,3] `` `.
• lb ub
  You can specify the lower bound (lb) and upper bound (ub) of the variable. By default, the lower limit is 0 and the upper limit is None.
• types
  You can specify the type of variable. The specification method is as follows. --Integer: `lp.variables.type.integer``` or 'I'``` --Binary variables: `` lp.variables.type.binary or `` `'B' --Continuous variables: lp.variables.type.continuous or `'C'``` --Half-integer: ``` lp.variables.type.semi_integer``` or'N'` --Semi-continuity: ``` lp.variables.type.semi_continuous``` or'S'`` `
  However, if you specify types, the problem type will be MIP even if you specify all variables consecutively. </ Font>
• names
  You can specify the name of the variable.
• columns
  It seems that you can set a constraint expression, but it seems complicated, so it is omitted.

lp.objective.set_linear("x1",2)
lp.objective.set_linear("x2",3)

lp.objective.set_linear([(0,2),(1,3)])

lp.linear_constraints.add(names=["C1","C2","C3"],
                       lin_expr=[cplex.SparsePair(ind=["x1","x2"],val=[3,2]),
                                 cplex.SparsePair(ind=["x1","x2"],val=[1,2]),
                                 cplex.SparsePair(ind=["x1","x2"],val=[1,0])],
                       senses=["L","L","L"],
                       rhs=[24,16,6])

lp.linear_constraints.add(names=["C1","C2","C3"],
                       lin_expr=[[["x1","x2"],[3,2]],
                                 [["x1","x2"],[1,2]],
                                 [["x1","x2"],[1,0]]],
                       senses=["L","L","L"],
                       rhs=[24,16,6])

lp.write("test.lp")

lp.solve()

print(lp.solution.get_status_string())

print(lp.solution.get_values())
print(lp.solution.get_objective_value())

import cplex

lp = cplex.Cplex()
lp.set_problem_type(lp.problem_type.LP)
lp.objective.set_sense(lp.objective.sense.maximize)
lp.set_problem_name("test_lp")

lp.variables.add(names=["x1","x2"],lb=[0.0,0.0])
lp.objective.set_linear([("x1",2),("x2",3)])
lp.linear_constraints.add(names=["C1","C2","C3"],
                       lin_expr=[[["x1","x2"],[3,2]],
                                 [["x1","x2"],[1,2]],
                                 [["x1","x2"],[1,0]]],
                       senses=["L","L","L"],
                       rhs=[24,16,6])

lp.write("test.lp")

lp.solve()
print(lp.solution.get_status_string())
print(lp.solution.get_values())
print(lp.solution.get_objective_value())