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

|Do you know Java]

.

Often,

you

want

to

create

a

variable

(or

constraint)

for

element

of

a

collection.

A

*

bad

*

approach

is

illustrated

below:

}
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

}
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

  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}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.

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}

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:

 {mathinline} e \in \text{set}{mathinline} finds the variable {mathinline} x_e {mathinline} in variables and returns {mathinline} \sum_{e \in \text{set}} x_e{mathinline}|
|integerSum|IloLinearIntExpr|IloCplex cplex, BiMap<T,IloIntVar> variables, Iterable<T> set,Function<? super T,Integer> coefficients|For each {mathinline} e \in \text{set}{mathinline} finds the variable {mathinline} x_e {mathinline} in variables and {mathinline}c_e{mathinline} by applying coefficients to {mathinline}e{mathinline} and returns {mathinline} \sum_{e \in \text{set}} c_e x_e{mathinline}|

h1. Simple Example Revisited

Recall the IP we modeled with CPLEX in the previous section:
{mathdisplay} 
\begin{aligned} 
&\min & x + 2y + 3z\\ 
&\text{subject to}& x + y + z &\geq 2\\ 
&& x,y,z &\in\{0,1\} 
\end{aligned} 
{mathdisplay}

Lets

design

a

more

scalable

implementation

using

our

new

methods. Finish the method exercise2() from WarmUps.java, which currently reads

public static Tryvoid andexerciseTwo() finish the following stub.
{code}
throws IloException{
	List<String> varNames = Arrays.asList("x","y","z");
	Map<String,Integer> weightsMap = new HashMap<String,Integer>();
	weightsMap.put("x",1);
	weightsMap.put("y",2);
	weightsMap.put("z",3);
	Function<String,Integer> weights = Functions.forMap(weightsMap);
{code}
{toggle-cloak:id=GoodStyleSolution} _Solution_ 
{cloak:id=GoodStyleSolution|visible=false} 
{code}
ImmutableBiMap<String,IloIntVar> varMap = Util.makeBinaryVariables(cplex,varNames);
cplex.addGe(Util.integerSum(cplex,varMap,varNames),2);
cplex.addMinimize(Util.integerSum(cplex.varMap,varNames,weights));
{code}
{cloak}

	IloCplex cplex = new IloCplex();
	//write code here!
}

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