The

Java

Interface

to

CPLEX

The

use

of

CPLEX

in

Java

is

based

around

the

class

IloCplex

(documented

[

here

|http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r5/index.jsp?topic=%2Filog.odms.cplex.help%2Frefjavacplex%2Fhtml%2Filog%2Fcplex%2FIloCplex.html]

).

The

basic

idea

is

that

you

create

an

IloCplex

object

for

your

optimization

problem,

then

add

variables,

the

objective,

and

constraints

using

methods

in

the

class

IloCplex.

The

IloCplex

object

can

produce

[

IloNumVar

|http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r5/index.jsp?topic=%2Filog.odms.cplex.help%2Frefjavacplex%2Fhtml%2Filog%2Fconcert%2FIloNumVar.html]

objects

and

their

subclass

[

IloIntVar

|http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r5/index.jsp?topic=%2Filog.odms.cplex.help%2Frefjavacplex%2Fhtml%2Filog%2Fconcert%2FIloIntVar.html]

objects,

when

are

then

used

as

arguments

to

further

methods

from

IloCplex

to

make

the

objective

and

constraints.

The

IloCplex

interface

is

somewhat

pretty confusing.

It

is

very

large,

has

lots

of

redundant

methods,

and

has lots

of

methods

that

appear

to

be

the

same

but

produce

very

different

results.

We

now

summarize

the

methods

of

IloCplex

which

will

be

of

use

to

us:

||Name||Return Type||Arguments||Description|| |boolVar|IloIntVar| |Creates and returns a new Boolean variable (domain

Notice that the various numeric expressions are arguments for these functions. The inheritance relationship between the different classes of numeric expressions is a little complicated, but well designed. They are summarized in the chart below, with an arrow from interface A to interface B if A implements B (is a subinterface, like a subclass).

We will use a few methods from IloLinearIntExpr to build up sums.

The interface for IloLinearNumExpr is similar.

A Short Example

Suppose we want to solve the following IP in CPLEX:

 
\begin{aligned} 
&\min & x + 2y + 3z\\ 
&\text{subject to}& x + y + z &\geq 2\\ 
&& x,y,z &\in\{0,1\}
\end{aligned} 

In the file src/main/WarmUps.java, try to solve the above IP inside the method exerciseOne() and print out the values of the variables and the optimal solution. Then run the code. If you are on Linux or Mac, you will probably need to set a virtual machine argument as you did in the installation assignment. You can also look at the installation assignment if you need to see an example.

Reading Integer Variable Values from CPLEX

After solving an LP that is integral or an IP, you often want to query a variable and take some action if the variable has value 1.0, and another action if the variable has value 0.0. However, due to the nature of floating point arithmetic, there are often small rounding errors in the values produced by CPLEX. For example, to test if a variable is equal to zero, do not write

IloCplex cplex = new IloCplex();
IloIntVar var = cplex.boolVar();
//...
//solve some problem
//...
double val = cplex.getValue(var);
if(val == 0){
  //take some action
}

Instead, you need to allow for a small error, like so:

IloCplex cplex = new IloCplex();
IloIntVar var = cplex.boolVar();
//...
//solve some problem
//...
double val = cplex.getValue(var);
if(Math.abs(val) < 0.00001){
  //take some action
}

The level of numerical tolerance and a variety of methods to extract integer values up to a tolerance are provided for you with the following static methods from Util.java

Performance Issues Reading Variable Values from CPLEX

Consider the following piece of code you can find in your WarmUps.java:

	public static void testSpeed() throws IloException{
		IloCplex cplex = new IloCplex();
		IloIntVar[] variables = cplex.boolVarArray(2000000);
		cplex.addMaximize(cplex.sum(variables));
		cplex.solve();
		{			
			System.err.println("testing group access");
			long startTime = System.currentTimeMillis();
			double sum = 0;
			double[] vals = cplex.getValues(variables);
			for(int i = 0; i < vals.length; i++){
				sum+= vals[i];
			}
			long endTime = System.currentTimeMillis();
			System.err.println("group: " + (endTime-startTime));
			System.err.println(sum);
		}
		{
			System.err.println("testing individual access");
			long startTime = System.currentTimeMillis();
			double sum = 0;
			for(int i = 0; i < variables.length; i++){
				double val = cplex.getValue(variables[i]);
				sum+=val;
			}
			long endTime = System.currentTimeMillis();
			System.err.println("individual: " + (endTime-startTime));
			System.err.println(sum);
		}		
	}

It solves a very simple IP, then compares the amount of time to query the variables one at a time versus the amount of time needed to query all of the variables at once. Adjust the main method to run testSpeed() instead of exercise1(). The result should be surprising! On my machine, the group access took 23 milliseconds, while the individual access took 282 milliseconds, over ten times as long. If the variables were further wrapped in a BiMap (as suggested in the next section), the running time increases to over 500 milliseconds. If we are going to only read the values of the variables once, we wouldn't really care, as a typical IP with 2,000,000 variables takes much longer than half a second to solve. However, if instead we are querying the values of the variables at every node in the branch and bound tree to test for separation (as we will be soon), then these half seconds add up quickly. Know when to optimize.