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Cream is a class library helping Java programmers to develop intelligent programs requiring constraint satisfaction or optimization on finite domains. The followings are features of Cream.
There is nothing special for installation. Please unzip the zip file you can obtained from the web page, then you are ready to run example programs in examples directory as follows.
java -classpath .:../cream.jar FourColor
java -classpath .;..\cream.jar FourColor
This section describes how to use Cream step-by-step. Consider an old Japanese elementary school problem:
To solve this problem in Cream, firstly you need to create a constraint network (an instance of Network class) consisting of variables and constraints over those variables.There are some cranes and tortoises. They are 7 in total, and their legs are 20 in total. How many cranes and tortoises are there?
Network net = new Network();Secondly, please declare and create variables for numbers of cranes (that is, x) and tortoises (that is, y).
IntVariable x = new IntVariable(net); IntVariable y = new IntVariable(net);These variables are added to the constraint network by the constructor. Thirdly, please describe constraint conditions over those variables, that is x >= 0, y >= 0, x + y == 7, and 2x + 4y == 20. First two conditions can be written in Cream as follows.
x.ge(0); y.ge(0);These constraints are also added to the same constraint network which the variables belong. It is possible to write them (but lengthy) as follows.
new IntComparison(net, IntComparison.GE, x, 0); new IntComparison(net, IntComparison.GE, y, 0);The latter two conditions x + y == 7 and 2x + 4y == 20 can be written simply as follows.
x.add(y).equals(7); x.multiply(2).add(y.multiply(4)).equals(20);It is possible to rewrite them as follows.
// 7 == x + y new IntArith(net, IntArith.ADD, 7, x, y); // t1 == x * 2 IntVariable t1 = new IntVariable(net); new IntArith(net, IntArith.MULTIPLY, t1, x, 2); // t2 == y * 4 IntVariable t2 = new IntVariable(net); new IntArith(net, IntArith.MULTIPLY, t2, y, 4); // 20 == t1 + t2 new IntArith(net, IntArith.ADD, 20, t1, t2);Now, pass the constraint network to DefaultSolver to solve the problem by constraint propagation and backtracking.
Solver solver = new DefaultSolver(net);You can get a solution from the solver as follows.
Solution solution = solver.findFirst();This code only finds the first solution, but it is sufficient in this case. To get values of the variables in the solution, getIntValue methods can be used.
int xv = solution.getIntValue(x); int yv = solution.getIntValue(y);The following is the whole program.
/* * @(#)FirstStep.java */ import jp.ac.kobe_u.cs.cream.*; public class FirstStep { public static void main(String args[]) { // Create a constraint network Network net = new Network(); // Declare variables IntVariable x = new IntVariable(net); IntVariable y = new IntVariable(net); // x >= 0 x.ge(0); // y >= 0 y.ge(0); // x + y == 7 x.add(y).equals(7); // 2x + 4y == 20 x.multiply(2).add(y.multiply(4)).equals(20); // Solve the problem Solver solver = new DefaultSolver(net); Solution solution = solver.findFirst(); int xv = solution.getIntValue(x); int yv = solution.getIntValue(y); System.out.println("x = " + xv + ", y = " + yv); } }The same program is in examples directory. You can compile and execute it as follows.
javac -classpath .:../cream.jar FirstStep.java java -classpath .:../cream.jar FirstStep
javac -classpath .;..\cream.jar FirstStep.java java -classpath .;..\cream.jar FirstStep
If you want to find all solutions, you can use coroutining facility or SolutionHandler interface described in the next subsection. The previous example program can be rewritten as follows.
Solver solver = new DefaultSolver(net); for (solver.start(); solver.waitNext(); solver.resume()) { Solution solution = solver.getSolution(); int xv = solution.getIntValue(x); int yv = solution.getIntValue(y); System.out.println("x = " + xv + ", y = " + yv); } solver.stop();The start() method starts the solver in a new thread, and immediately returns to the caller. The waitNext() method is used to wait the next solution. It returns true if the next solution is found, and returns false if there are no more solutions. The getSolution() method returns the solution. The solver is suspended when the solution is found, and it resumes the execution when the resume() method is called. The stop() method should be called so that the solver thread is disposed cleanly. The invocation of the stop() method during the search results in the abortion of the solver execution.
SolutionHandler can be used to find all solutions. The previous example program can be rewritten as follows.
Solver solver = new DefaultSolver(net); solver.findAll(new FirstStepHandler(x, y));The findAll(SolutionHandler handler) invokes solved method of the handler for each solution and at the end of the solver execution. The following is an example implementation of the SolutionHandler.
class FirstStepHandler implements SolutionHandler { IntVariable x; IntVariable y; public FirstStepHandler(IntVariable x, IntVariable y) { this.x = x; this.y = y; } public synchronized void solved(Solver solver, Solution solution) { if (solution != null) { int xv = solution.getIntValue(x); int yv = solution.getIntValue(y); System.out.println("x = " + xv + ", y = " + yv); } } }Another way is the use of start(SolutionHandler handler) method. It starts the solver in a new thread, and immediately returns to the caller. You can wait the end of the solver execution by join() method.
Solver solver = new DefaultSolver(net); solver.start(new FirstStepHandler(x, y)); /* other jobs can be performed in parallel */ solver.join();
Above mentioned methods (findFirst, findAll, and start) have optional argument for specifying timeout in milliseconds.
The following is an outline of a program to find the optimal solution by complete search.
// set the objective variable net.setObjective(v); // set the solver to find the minimal value Solver solve = new DefaultSolver(net, Solver.MINIMIZE); for (solver.start(); solver.waitNext(); solver.resume()) { // find the next better solution Solution solution = solver.getSolution(); ..... } solver.stop(); // get the best solution Solution solution = solver.getBestSolution();The method getBestSolution always return the best solution up to now.
Currently, Cream can solve a problem by local search when the problem involves Serialized constraints.
Serialized(Variable[] s, int[] d)
All intervals [s_{i}, s_{i}+d_{i}-1] are not overlapped each other
net.setObjective(v); long timeout = 60000; Solver solve = new SASearch(net, Solver.MINIMIZE); for (solver.start(timeout); solver.waitNext(); solver.resume()) { // find the next neighbor solution Solution solution = solver.getSolution(); ..... } solver.stop(); // get the best solution Solution solution = solver.getBestSolution();
Solver solver1 = new SASearch((Network).net.clone(), Solver.MINIMIZE); Solver solver2 = new TabooSearch((Network).net.clone(), Solver.MINIMIZE); Solver[] solvers = { solver1, solver2 }; Solver solver = new ParallelSolver(solvers); for (solver.start(timeout); solver.waitNext(); solver.resume()) { Solution solution = solver.getSolution(); ..... } solver.stop(); Solution solution = solver.getBestSolution();
Cream was developed as a part of HECS (HEterogeneous Constraint Solver) system which was supported in part by METI and IPA (The Information-technology Promotion Agency) under grant of 2002 Exploratory Software Project and 2003 Exploratory Software Project. Some improvement ideas of Cream are obtained through the discussion with Mr. Kino, a project manager of IPA Exploratory Software Project and also a developer of K-Prolog and ICS in Java.