OptimJ is an extension of the Java with language support for writing optimization models and abstractions for bulk data processing. The extensions and the proprietary product implementing the extensions were developed by Ateji which went out of business in September 2011.^{[1]} OptimJ aims at providing a clear and concise algebraic notation for optimization modeling, removing compatibility barriers between optimization modeling and application programming tools, and bringing software engineering techniques such as objectorientation and modern IDE support to optimization experts.
OptimJ models are directly compatible with Java source code, existing Java libraries such as database access, Excel connection or graphical interfaces. OptimJ is compatible with development tools such as Eclipse, CVS, JUnit or JavaDoc. OptimJ is available free with the following solvers lp_solve, glpk, LP or MPS file formats and also supports the following commercial solvers: Gurobi, MOSEK, IBM ILOG CPLEX Optimization Studio.
Contents

Language concepts 1

The example of map coloring 2

ORspecific concepts 3

Models 3.1

Decision variables 3.2

Constraints 3.3

Objectives 3.4

Generalist concepts 4

Associative arrays 4.1

Extended initialization 4.2

Tuples 4.3

Ranges 4.4

Comprehensions 4.5

Development environment 5

OptimJ GUI and Rapid Prototyping 6

Supported solvers 7

External links 8

References 9
Language concepts
OptimJ combines concepts from objectoriented imperative languages with concepts from algebraic modeling languages for optimization problems. Here we will review the optimization concepts added to Java, starting with a concrete example.
The example of map coloring
The goal of a map coloring problem is to color a map so that regions sharing a common border have different colors. It can be expressed in OptimJ as follows.
package examples;
// a simple model for the mapcoloring problem
public model SimpleColoring solver lpsolve
{
// maximum number of colors
int nbColors = 4;
// decision variables hold the color of each country
var int belgium in 1 .. nbColors;
var int denmark in 1 .. nbColors;
var int germany in 1 .. nbColors;
// neighbouring countries must have a different color
constraints {
belgium != germany;
germany != denmark;
}
// a main entry point to test our model
public static void main(String[] args)
{
// instantiate the model
SimpleColoring m = new SimpleColoring();
// solve it
m.extract();
m.solve();
// print solutions
System.out.println("Belgium: " + m.value(m.belgium));
System.out.println("Denmark: " + m.value(m.denmark));
System.out.println("Germany: " + m.value(m.germany));
}
}
Readers familiar with Java will notice a strong similarity with this language. Indeed, OptimJ is a conservative extension of Java: every valid Java program is also a valid OptimJ program and has the same behavior.
This map coloring example also shows features specific to optimization that have no direct equivalent in Java, introduced by the keywords model
, var
, constraints
.
ORspecific concepts
Models
A model is an extension of a Java class that can contain not only fields and methods but also constraints and an objective function. It is introduced by the model
keyword and follows the same rules as class declarations. A nonabstract model must be linked to a solver, introduced by the keyword solver
. The capabilities of the solver will determine what kind of constraints can be expressed in the model, for instance a linear solver such as lp solve will only allow linear constraints.
public model SimpleColoring solver lpsolve
Decision variables
Imperative languages such as Java provide a notion of imperative variables, which basically represent memory locations that can be written to and read from.
OptimJ also introduces the notion of a decision variable, which basically represents an unknown quantity whose value one is searching. A solution to an optimization problem is a set of values for all its decision variables that respects the constraints of the problem—without decision variables, it would not possible to express optimization problems. The term "decision variable" comes from the optimization community, but decision variables in OptimJ are the same concept as logical variables in logical languages such as Prolog.
Decision variables have special types introduced by the keyword var
. There is a var
type for each possible Java type.
// a var type for a Java primitive type
var int x;
// a var type for a userdefined class
var MyClass y;
In the map coloring example, decision variables were introduced together with the range of values they may take.
var int germany in 1 .. nbColors;
This is just a shorthand equivalent to putting a constraint on the variable.
Constraints
Constraints express conditions that must be true in any solution of the problem. A constraint can be any Java boolean expression involving decision variables.
In the map coloring example, this set of constraints states that in any solution to the map coloring problem, the color of Belgium must be different from the color of Germany, and the color of Germany must be different from the color of Denmark.
constraints {
belgium != germany;
germany != denmark;
}
The operator !=
is the standard Java notequal operator.
Constraints typically come in batches and can be quantified with the forall
operator. For instance, instead of listing all countries and their neighbors explicitly in the source code, one may have an array of countries, an array of decision variables representing the color of each country, and an array boolean[][] neighboring
or a predicate (a boolean function) boolean isNeighbor()
.
constraints {
forall(Country c1 : countries, Country c2 : countries, :isNeighbor(c1,c2)) {
color[c1] != color[c2];
}
}
Country c1 : countries
is a generator: it iterates c1
over all the values in the collection countries
.
:isNeighbor(c1,c2)
is a filter: it keeps only the generated values for which the predicate is true (the symbol :
may be read as "if").
Assuming that the array countries
contains belgium
, germany
and denmark
, and that the predicate isNeighbor
returns true
for the couples (Belgium , Germany) and (Germany, Denmark), then this code is equivalent to the constraints block of the original map coloring example.
Objectives
Optionally, when a model describes an optimization problem, an objective function to be minimized or maximized can be stated in the model.
Generalist concepts
Generalist concepts are programming concepts that are not specific to OR problems and would make sense for any kind of application development. The generalist concepts added to Java by OptimJ make the expression of OR models easier or more concise. They are often present in older modeling languages and thus provide OR experts with a familiar way of expressing their models.
Associative arrays
While Java arrays can only be indexed by 0based integers, OptimJ arrays can be indexed by values of any type. Such arrays are typically called associative arrays or maps. In this example, the array age
contains the age of persons, identified by their name:
int[String] age;
The type int[String]
denoting an array of int
indexed by String
. Accessing OptimJ arrays using the standard Java syntax:
age["Stephan"] = 37;
x = age["Lynda"];
Traditionally, associative arrays are heavily used in the expression of optimization problems. OptimJ associative arrays are very handy when associated to their specific initialization syntax. Initial values can be given in intensional definition, as in:
int[String] age = {
"Stephan" > 37,
"Lynda" > 29
};
or can be given in extensional definition, as in:
int[String] length[String name : names] = name.length();
Here each of the entries length[i]
is initialized with names[i].length()
.
Extended initialization
Tuples
Tuples are ubiquitous in computing, but absent from most mainstream languages including Java. OptimJ provides a notion of tuple at the language level that can be very useful as indexes in combination with associative arrays.
(: int, String :) myTuple = new (: 3, "Three" :);
String s = myTuple#1;
Tuple types and tuple values are both written between (:
and :)
.
Ranges
Comprehensions
Comprehensions, also called aggregates operations or reductions, are OptimJ expressions that extend a given binary operation over a collection of values. A common example is the sum:
// the sum of all integers from 1 to 10
int k = sum { i  int i in 1 .. 10};
This construction is very similar to the bigsigma summation notation used in mathematics, with a syntax compatible with the Java language.
Comprehensions can also be used to build collections, such as lists, sets, multisets or maps:
// the set of all integers from 1 to 10
HashSet s = `hashSet(){ i  int i in 1 .. 10};
Comprehension expressions can have an arbitrary expression as target, as in:
// the sum of all squares of integers from 1 to 10
int k = sum { i*i  int i in 1 .. 10};
They can also have an arbitrary number of generators and filters:
// the sum of all f(i,j), for 0<=i<10, 1<=j<=10 and i!=j
int k = sum{ f(i,j)  int i : 10, int j : 1 .. 10, :i!=j }
Comprehension need not apply only to numeric values. Set or multisetbuilding comprehensions, especially in combination with tuples of strings, make it possible to express queries very similar to SQL database queries:
// select name from persons where age > 18
`multiSet(){ p.name  Person p : persons, :p.age > 18 }
In the context of optimization models, comprehension expressions provide a concise and expressive way to preprocess and clean the input data, and format the output data.
Development environment
OptimJ is available as an Eclipse plugin. The compiler implements a sourcetosource translation from OptimJ to standard Java, thus providing immediate compatibility with most development tools of the Java ecosystem.
OptimJ GUI and Rapid Prototyping
Since the OptimJ compiler knows about the structure of all data used in models, it is able to generate a structured graphical view of this data at compiletime. This is especially relevant in the case of associative arrays where the compiler knows the collections used for indexing the various dimensions.
The basic graphical view generated by the compiler is reminiscent of an OLAP cube. It can then be customized in many different ways, from simple coloring up to providing new widgets for displaying data elements.
The compilergenerated OptimJ GUI saves the OR expert from writing all the glue code required when mapping graphical libraries to data. It enables rapid prototyping, by providing immediate visual hints about the structure of data.
Another part of the OptimJ GUI reports in real time performance statistics from the solver. This information can be used for understanding performance problems and improving solving time. At this time, it is available only for lp_solve.
Supported solvers
OptimJ is available for free with the following solvers lp_solve, glpk, LP or MPS file formats and also supports the following commercial solvers: Gurobi, Mosek, IBM ILOG CPLEX Optimization Studio.
External links

The OptimJ language manual

OptimJ page

Free OptimJ download

OptimJ GUI
References

^ "Ateji is closed". Retrieved 20120111.

Rapid application development with OPTIMJ, a practitioner's experience report. David Gravot, Patrick Viry. EURO 2010 (Lisbon)

OptimJ used in an optimization model for mixedmodel assembly lines, University of Münster

OptimJ used in an Approximate SubgamePerfect Equilibrium Computation Technique for Repeated Games, Laval University
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.