A

Road

to

Trouble

When

programming

in

Java,

you

generally

have

[

collections

|http://docs.oracle.com/javase/tutorial/collections/]

of

objects,

as

previously discussed

[

here

|http://docs.oracle

.

com/javase/tutorial/collections/].

Often,

you

want

to

create

a

variable

(or

constraint)

for

element

of

a

collection.

A

*

bad

*

approach

is

illustrated

below:

{

Code Block
} Set<String> stringCollection = makeSomeStrings();//assume this is defined elsewhere IloCplex cplex = new IloCplex(); String[] stringToIndex = new String[stringCollection.size()]; IloIntVar[] variablesToIndex = cplex.boolVarArray(stringCollection.size()); int i = 0; for(String s: stringCollection){ stringToIndex[i++] = s; } {code}

Then

given

a

String

from

the

collection,

we

could

access

the

corresponding

IloIntVar,

and

with

an

IloIntVar,

we

would

access

the

corresponding

String,

with

the

following

snippets

{

Code Block

} public IloIntVar getVariableForString(String s, String[] stringToIndex, IloIntVar[] variablesToIndex){ for(int i = 0; i < stringToIndex.length; i++){ if(stringToIndex[i].equals(s)){ return variablesToIndex[i]; } } return null; } public String getStringForVariable(IloIntVar v, String[] stringToIndex, IloIntVar[] variablesToIndex){ for(int i = 0; i < variablesToIndex.length; i++){ if(variablesToIndex[i] == v){ return stringToIndex[i]; } } return null; } {code}

There

are

several

reasons

to

be

concerned

with

this.

* For {mathinline}n{mathinline}

• For

  Mathinline

  variables,

• access

• time

• takes

  Mathinline

  .
• We are maintaining two data structures and an index by hand, which leave a lot of room for programmer error
• We cannot add new variables at a later date

We can eliminate any chance of an indexing error and improve our access time to

Mathinline

by replacing our two arrays by two HashMaps, e.g.

Code Block

{mathinline}O(n){mathinline}. * We are maintaining two data structures and an index by hand, which leave a lot of room for programmer error * We cannot add new variables at a later date We can eliminate any chance of an indexing error and improve our access time to {mathinline}O(1){mathinline} by replacing our two arrays by two [HashMaps|http://docs.oracle.com/javase/6/docs/api/java/util/HashMap.html], e.g. {code} Set<String> stringCollection = makeSomeStrings();//assume this is defined elsewhere IloCplex cplex = new IloCplex(); Map<String,IloIntVar> stringToVariable = new HashMap<String,IloIntVar>(); Map<IloIntVar,String> variableToString = new HashMap<IloIntVar,String>(); for(String s: stringCollection){ IloIntVar v = cplex.boolVar(); stringToVariable.put(s,v); variableToString.put(v,s); } {code}

However,

we

are

still

maintaining

two

separate

data

structures

which

we

need

to

keep

synchronized,

which

is

asking

for

trouble.

h1. Good Style

Good Style

Instead,

we

use

Guava's

special

data

structure,

the

ImmutableBiMap

,

which

will

maintain

two

HashMaps

for

us

(and

as

a

bonus,

prevent

any

accidental

modifications

once

we

build

the

map).

The

following

methods

can

be

found

in

Util.java

in

your

project:

}
public static <T> ImmutableBiMap<T,IloIntVar> makeBinaryVariables(IloCplex cplex, Iterable<T> set) throws IloException{
	Builder<T,IloIntVar> ans = ImmutableBiMap.builder();
	for(T t: set){
		ans.put(t, cplex.boolVar());
	}
	return ans.build();
}
{code}

Now

the

unfortunate

code

from

before

can

be

replaced

by

}
Set<String> stringCollection = makeSomeStrings();//assume this is defined elsewhere
IloCplex cplex = new IloCplex();
ImmutableBiMap<String,IloIntVar> stringVarBiMap = Util.makeBinaryVariables(cplex,stringCollection);
for(String s: stringCollection){
  stringVarMap.put(s,cplex.boolVar());
}

public IloIntVar getVariableForString(String s, ImmutableBiMap<String,IloIntVar> stringVarBiMap){
  return stringVarBiMap.get(s);
}
public String getStringForVariable(IloIntVar v, ImmutableBiMap<String,IloIntVar> stringVarBiMap){
  return stringVarBiMap.inverse().get(v);
}
{code}

{code}
public static <T> IloLinearIntExpr integerSum(IloCplex cplex, 
		BiMap<T,IloIntVar> variables, Iterable<T> set, 
		Function<? super T,Integer> coefficients) throws IloException{
	IloLinearIntExpr sum = cplex.linearIntExpr();
	for(T t: set){
		sum.addTerm(variables.get(t), coefficients.

There are a few additional methods in the class Util for creating IloLinearIntExpr objects and IloLinearNumExpr objects designed to keep your code organized and error free. They use another Guava class, Function, (see here for Javadoc). The idea of a Function<F,T> is simple, they take in any object of type F and produce some object of type T. Functions are a little clunky to make (a weakness of Java), but fortunately you won't have to make many. The follwing static functions are also found in Util

While the final function actually has nothing to do with CPLEX, it will often be useful when using CPLEX.

Simple Example Revisited

Recall the IP we modeled with CPLEX in the previous section:

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

Lets design a more scalable implementation using our new methods. Finish the method exercise2() from WarmUps.java, which currently reads

public static void exerciseTwo(apply(t));
	}
	return sum;
}
public static <T> IloLinearIntExpr integerSum(IloCplex cplex, 
		BiMap<T,IloIntVar> variables, Iterable<T> set) throws IloException{
	return integerSum(cplex,variables,set,unity);
}

private static Function<Object,Integer> unityList<String> varNames = Arrays.asList("x","y","z");
	Map<String,Integer> weightsMap = new Function<ObjectHashMap<String,Integer>(){;
	@Override
	public Integer apply(Object arg0) {
		return 1;
	}};
{code}
weightsMap.put("x",1);
	weightsMap.put("y",2);
	weightsMap.put("z",3);
	Function<String,Integer> weights = Functions.forMap(weightsMap);
	IloCplex cplex = new IloCplex();
	//write code here!
}

The functionality should be the same as exercise1(). Modify the main method to test your code.