Drools Planner User Guide

The above solution is wrong because queens A1 and B0 can attack each other (as can queens B0 and D0). Removing queen B0 would respect the "no 2 queens can attack each other" constraint, but would break the "place n queens" constraint.

All the constraints have been met, so the solution is correct. Note that most n queens puzzles have multiple correct solutions. We 'll focus on finding a single correct solution for a given n, not on finding the number of possible correct solutions for a given n.

The Drools Planner implementation has not been optimized because it functions as a beginner example. Nevertheless, it can easily handle 64 queens.

When 2 queens share the same column, row or diagonal line, such as (*) and (**), they can attack each other.

A single NQueens instance contains a list of all Queen instances. It is the Solution implementation which will be supplied to, solved by and retrieved from the Solver. Notice that in the 4 queens example, NQueens's getN() method will always return 4.

Geoffrey De Smet (the Drools Planner lead) finished 4th in the International Timetabling Competition 2007's examination track with a very early version of Drools Planner. Many improvements have been made since then.

Notice that we've split up the exam concept into an Exam class and a Topic class. The Exam instances change during solving (this is the planning entity class), when they get another period or room property. The Topic, Period and Room instances never change during solving (these are problem facts, just like some other classes).

The solve() method can take a long time (depending on the problem size and the solver configuration). The Solver will remember (actually clone) the best solution it encounters during its solving. Depending on a number factors (including problem size, how time the Solver has, the solver configuration, ...), that best solution will be a feasible or even an optimal solution.

A move can have a small or large impact. In the above example, the move of queen C0 to C2 is a small move. Some moves are the same move type. These are some possibilities for move types in n queens:

Because we have decided that all queens will be on the board at all times and each queen has an appointed column (for performance reasons), only the first 2 move types are usable in our example. Furthermore, we 're only using the first move type in the example because we think it gives the best performance, but you are welcome to prove us wrong.

Each of your move types will be an implementation of the Move interface:

public interface Move {


    boolean isMoveDoable(EvaluationHandler evaluationHandler);


    Move createUndoMove(EvaluationHandler evaluationHandler);


    void doMove(EvaluationHandler evaluationHandler);


}

Let's take a look at the Move implementation for 4 queens which moves a queen to a different row:

public class RowChangeMove implements Move {


    private Queen queen;

    private Row toRow;


    public RowChangeMove(Queen queen, Row toRow) {

        this.queen = queen;

        this.toRow = toRow;

    }


    // ... see below


}

An instance of RowChangeMove moves a queen from its current row to a different row.

Drools Planner calls the doMove(WorkingMemory) method to do a move. The Move implementation must notify the working memory of any changes it does on the solution facts:

    public void doMove(WorkingMemory workingMemory) {

        FactHandle queenHandle = workingMemory.getFactHandle(queen);

        queen.setRow(toRow);

        workingMemory.update(queenHandle, queen); // after changes are made

    }

You need to call the workingMemory.update(FactHandle, Object) method after modifying the fact. Note that you can alter multiple facts in a single move and effectively create a big move (also known as a coarse-grained move).

Drools Planner automatically filters out non doable moves by calling the isDoable(WorkingMemory) method on a move. A non doable move is:

In the n queens example, a move which moves the queen from its current row to the same row isn't doable:

    public boolean isMoveDoable(WorkingMemory workingMemory) {

        return !ObjectUtils.equals(queen.getRow(), toRow);

    }

Because we won't generate a move which can move a queen outside the board limits, we don't need to check it. A move that is currently not doable can become doable on a later solution.

Each move has an undo move: a move (usually of the same type) which does the exact opposite. In the above example the undo move of C0 to C2 would be the move C2 to C0. An undo move can be created from a move, but only before the move has been done on the current solution.

    public Move createUndoMove(WorkingMemory workingMemory) {

        return new RowChangeMove(queen, queen.getRow());

    }

Notice that if C0 would have already been moved to C2, the undo move would create the move C2 to C2, instead of the move C2 to C0.

The local search solver can do and undo a move more than once, even on different (successive) solutions.

A move must implement the equals() and hashcode() methods. 2 moves which make the same change on a solution, must be equal.

    public boolean equals(Object o) {

        if (this == o) {

            return true;

        } else if (o instanceof RowChangeMove) {

            RowChangeMove other = (RowChangeMove) o;

            return new EqualsBuilder()

                    .append(queen, other.queen)

                    .append(toRow, other.toRow)

                    .isEquals();

        } else {

            return false;

        }

    }


    public int hashCode() {

        return new HashCodeBuilder()

                .append(queen)

                .append(toRow)

                .toHashCode();

    }

In the above example, the Queen class uses the default Object equal() and hashcode() implementations. Notice that it checks if the other move is an instance of the same move type. This is important because a move will be compared to a move with another move type if you're using more then 1 move type.

It's also recommended to implement the toString() method as it allows you to read Drools Planner's logging more easily:

    public String toString() {

        return queen + " => " + toRow;

    }

Now that we can make a single move, let's take a look at generating moves.

As you can see, not all the moves are doable. At the starting solution we have 12 doable moves (n * (n - 1)), one of which will be move which changes the starting solution into the next solution. Notice that the number of possible solutions is 256 (n ^ n), much more that the amount of doable moves. Don't create a move to every possible solution. Instead use moves which can be sequentially combined to reach every possible solution.

It's highly recommended that you verify all solutions are connected by your move set. This means that by combining a finite number of moves you can reach any solution from any solution. Otherwise you're already excluding solutions at the start. Especially if you're using only big moves, you should check it. Just because big moves outperform small moves in a short test run, it doesn't mean that they will outperform them in a long test run.

You can mix different move types. Usually you're better off preferring small (fine-grained) moves over big (course-grained) moves because the score delta calculation will pay off more. However, as the traveling tournament example proves, if you can remove a hard constraint by using a certain set of big moves, you can win performance and scalability. Try it yourself: run both the simple (small moves) and the smart (big moves) version of the traveling tournament example. The smart version evaluates a lot less unfeasible solutions, which enables it to outperform and outscale the simple version.

Move generation currently happens with a MoveFactory:

public class NQueensMoveFactory extends CachedMoveListMoveFactory {


    public List<Move> createMoveList(Solution solution) {

        NQueens nQueens = (NQueens) solution;

        List<Move> moveList = new ArrayList<Move>();

        for (Queen queen : nQueens.getQueenList()) {

            for (int y : nQueens.getRowList()) {

                moveList.add(new YChangeMove(queen, y));

            }

        }

        return moveList;

    }


}

But we might be making move generation part of the DRL's in the future.

Because the move B0 to B3 has the highest score (-3), it is picked as the next step. Notice that C0 to C3 (not shown) could also have been picked because it also has the score -3. If multiple moves have the same highest score, one is picked randomly, in this case B0 to B3.

The step is made and from that new solution, the local search solver tries all the possible moves again, to decide the next step after that. It continually does this in a loop, and we get something like this:

Notice that the local search solver doesn't use a search tree, but a search path. The search path is highlighted by the green arrows. At each step it tries all possible moves, but unless it's the step, it doesn't investigate that solution further. This is one of the reasons why local search is very scalable.

As you can see, the local search solver solves the 4 queens problem by starting with the starting solution and make the following steps sequentially:

If we turn on DEBUG logging for the category org.drools.planner, then those steps are shown into the log:

INFO  Solver started: time spend (0), score (-6), new best score (-6), random seed (0).
DEBUG     Step index (0), time spend (20), score (-3), new best score (-3), accepted move size (12) for picked step (1 @ 0 => 3).
DEBUG     Step index (1), time spend (31), score (-1), new best score (-1), accepted move size (12) for picked step (0 @ 0 => 1).
DEBUG     Step index (2), time spend (40), score (0), new best score (0), accepted move size (12) for picked step (3 @ 0 => 2).
INFO  Phase local search finished: step total (3), time spend (41), best score (0).
INFO  Solved: time spend (41), best score (0), average calculate count per second (1780).

Notice that the logging uses the toString() method of our Move implementation: 1 @ 0 => 3.

The local search solver solves the 4 queens problem in 3 steps, by evaluating only 37 possible solutions (3 steps with 12 moves each + 1 starting solution), which is only fraction of all 256 possible solutions. It solves 16 queens in 31 steps, by evaluating only 7441 out of 18446744073709551616 possible solutions. Note: with construction heurstistics it's even a lot more efficient.