JBoss.orgCommunity Documentation

Chapter 5. Score Calculation

5.1. Score Terminology
5.1.1. What is a Score?
5.1.2. Score Constraint Signum (Positive or Negative)
5.1.3. Score Constraint Weight
5.1.4. Score Level
5.1.5. Pareto Scoring (AKA Multi-objective Optimization Scoring)
5.1.6. Combining Score Techniques
5.1.7. Score interface
5.1.8. Avoid Floating Point Numbers in Score Calculation
5.2. Choose a Score Definition
5.2.1. SimpleScore
5.2.2. HardSoftScore (Recommended)
5.2.3. HardMediumSoftScore
5.2.4. BendableScore
5.2.5. Implementing a Custom Score
5.3. Calculate the Score
5.3.1. Score Calculation Types
5.3.2. Easy Java Score Calculation
5.3.3. Incremental Java Score Calculation
5.3.4. Drools Score Calculation
5.3.5. InitializingScoreTrend
5.3.6. Invalid Score Detection
5.4. Score Calculation Performance Tricks
5.4.1. Overview
5.4.2. Average Calculation Count Per Second
5.4.3. Incremental Score Calculation (with Delta's)
5.4.4. Avoid Calling Remote Services During Score Calculation
5.4.5. Pointless Constraints
5.4.6. Built-in Hard Constraint
5.4.7. Other Score Calculation Performance Tricks
5.4.8. Score Trap
5.4.9. stepLimit Benchmark
5.4.10. Fairness Score Constraints
5.5. Explaining the Score: Using Score Calculation Outside the Solver

Sometimes a score constraint outranks another score constraint, no matter how many times the other is broken. In that case, those score constraints are in different levels. For example: a nurse cannot do 2 shifts at the same time (due to the constraints of physical reality), this outranks all nurse happiness constraints.

Most use cases have only 2 score levels: hard and soft. When comparing 2 scores, they are compared lexicographically: the first score level gets compared first. If those differ, the others score levels are ignored. For example: a score that breaks 0 hard constraints and 1000000 soft constraints is better than a score that breaks 1 hard constraint and 0 soft constraints.

Score levels often employ score weighting per level. In such case, the hard constraint level usually makes the solution feasible and the soft constraint level maximizes profit by weighting the constraints on price.

Don't use a big constraint weight when your business actually wants different score levels. That hack, known as score folding, is broken:

Note

Your business will probably tell you that your hard constraints all have the same weight, because they cannot be broken (so their weight does not matter). This is not true and it could create a score trap. For example in cloud balance: if a Computer has 7 CPU too little for its Processes, then it must be weighted 7 times as much as if it had only 1 CPU too little. This way, there is an incentive to move a Process with 6 CPU or less away from that Computer.

Three or more score levels are also supported. For example: a company might decide that profit outranks employee satisfaction (or visa versa), while both are outranked by the constraints of physical reality.

Note

To model fairness or load balancing, there is no need to use lots of score levels (even though Planner can handle many score levels).

Far less common is the use case of pareto optimization, which is also known under the more confusing term multi-objective optimization. In pareto scoring, score constraints are in the same score level, yet they are not weighted against each other. When 2 scores are compared, each of the score constraints are compared individually and the score with the most dominating score constraints wins. Pareto scoring can even be combined with score levels and score constraint weighting.

Consider this example with positive constraints, where we want to get the most apples and oranges. Since it's impossible to compare apples and oranges, we can't weight them against each other. Yet, despite that we can't compare them, we can state that 2 apples are better then 1 apple. Similarly, we can state that 2 apples and 1 orange are better than just 1 orange. So despite our inability to compare some Scores conclusively (at which point we declare them equal), we can find a set of optimal scores. Those are called pareto optimal.

Scores are considered equal far more often. It's left up to a human to choose the better out of a set of best solutions (with equal scores) found by Planner. In the example above, the user must choose between solution A (3 apples and 1 orange) and solution B (1 apple and 6 oranges). It's guaranteed that Planner has not found another solution which has more apples or more oranges or even a better combination of both (such as 2 apples and 3 oranges).

To implement pareto scoring in Planner, implement a custom ScoreDefinition and Score (and replace the BestSolutionRecaller). Future versions will provide out-of-the-box support.

Note

A pareto Score's compareTo method is not transitive because it does a pareto comparison. For example: having 2 apples is greater than 1 apple. 1 apple is equal to 1 orange. Yet, 2 apples are not greater than 1 orange (but actually equal). Pareto comparison violates the contract of the interface java.lang.Comparable's compareTo method, but Planner's systems are pareto comparison safe, unless explicitly stated otherwise in this documentation.

Each Score implementation also has a ScoreDefinition implementation. For example: SimpleScore is defined by SimpleScoreDefinition.

An easy way to implement your score calculation in Java.

Just implement one method of the interface EasyScoreCalculator:

public interface EasyScoreCalculator<Sol extends Solution> {

    Score calculateScore(Sol solution);
   
}

For example in n queens:

public class NQueensEasyScoreCalculator implements EasyScoreCalculator<NQueens> {

    public SimpleScore calculateScore(NQueens nQueens) {
        int n = nQueens.getN();
        List<Queen> queenList = nQueens.getQueenList();
        
        int score = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                Queen leftQueen = queenList.get(i);
                Queen rightQueen = queenList.get(j);
                if (leftQueen.getRow() != null && rightQueen.getRow() != null) {
                    if (leftQueen.getRowIndex() == rightQueen.getRowIndex()) {
                        score--;
                    }
                    if (leftQueen.getAscendingDiagonalIndex() == rightQueen.getAscendingDiagonalIndex()) {
                        score--;
                    }
                    if (leftQueen.getDescendingDiagonalIndex() == rightQueen.getDescendingDiagonalIndex()) {
                        score--;
                    }
                }
            }
        }
        return SimpleScore.valueOf(score);
    }

}

Configure it in your solver configuration:

  <scoreDirectorFactory>
    <scoreDefinitionType>...</scoreDefinitionType>
    <easyScoreCalculatorClass>org.optaplanner.examples.nqueens.solver.score.NQueensEasyScoreCalculator</easyScoreCalculatorClass>
  </scoreDirectorFactory>

Alternatively, build a EasyScoreCalculator instance at runtime and set it with the programmatic API:

    solverFactory.getSolverConfig().getScoreDirectorFactoryConfig.setEasyScoreCalculator(easyScoreCalculator);

A way to implement your score calculation incrementally in Java.

Implement all the methods of the interface IncrementalScoreCalculator and extend the class AbstractIncrementalScoreCalculator:

public interface IncrementalScoreCalculator<Sol extends Solution> {

    void resetWorkingSolution(Sol workingSolution);

    void beforeEntityAdded(Object entity);

    void afterEntityAdded(Object entity);

    void beforeVariableChanged(Object entity, String variableName);

    void afterVariableChanged(Object entity, String variableName);

    void beforeEntityRemoved(Object entity);

    void afterEntityRemoved(Object entity);

    Score calculateScore();
    
}

For example in n queens:

public class NQueensAdvancedIncrementalScoreCalculator extends AbstractIncrementalScoreCalculator<NQueens> {

    private Map<Integer, List<Queen>> rowIndexMap;
    private Map<Integer, List<Queen>> ascendingDiagonalIndexMap;
    private Map<Integer, List<Queen>> descendingDiagonalIndexMap;

    private int score;

    public void resetWorkingSolution(NQueens nQueens) {
        int n = nQueens.getN();
        rowIndexMap = new HashMap<Integer, List<Queen>>(n);
        ascendingDiagonalIndexMap = new HashMap<Integer, List<Queen>>(n * 2);
        descendingDiagonalIndexMap = new HashMap<Integer, List<Queen>>(n * 2);
        for (int i = 0; i < n; i++) {
            rowIndexMap.put(i, new ArrayList<Queen>(n));
            ascendingDiagonalIndexMap.put(i, new ArrayList<Queen>(n));
            descendingDiagonalIndexMap.put(i, new ArrayList<Queen>(n));
            if (i != 0) {
                ascendingDiagonalIndexMap.put(n - 1 + i, new ArrayList<Queen>(n));
                descendingDiagonalIndexMap.put((-i), new ArrayList<Queen>(n));
            }
        }
        score = 0;
        for (Queen queen : nQueens.getQueenList()) {
            insert(queen);
        }
    }

    public void beforeEntityAdded(Object entity) {
        // Do nothing
    }

    public void afterEntityAdded(Object entity) {
        insert((Queen) entity);
    }

    public void beforeVariableChanged(Object entity, String variableName) {
        retract((Queen) entity);
    }

    public void afterVariableChanged(Object entity, String variableName) {
        insert((Queen) entity);
    }

    public void beforeEntityRemoved(Object entity) {
        retract((Queen) entity);
    }

    public void afterEntityRemoved(Object entity) {
        // Do nothing
    }

    private void insert(Queen queen) {
        Row row = queen.getRow();
        if (row != null) {
            int rowIndex = queen.getRowIndex();
            List<Queen> rowIndexList = rowIndexMap.get(rowIndex);
            score -= rowIndexList.size();
            rowIndexList.add(queen);
            List<Queen> ascendingDiagonalIndexList = ascendingDiagonalIndexMap.get(queen.getAscendingDiagonalIndex());
            score -= ascendingDiagonalIndexList.size();
            ascendingDiagonalIndexList.add(queen);
            List<Queen> descendingDiagonalIndexList = descendingDiagonalIndexMap.get(queen.getDescendingDiagonalIndex());
            score -= descendingDiagonalIndexList.size();
            descendingDiagonalIndexList.add(queen);
        }
    }

    private void retract(Queen queen) {
        Row row = queen.getRow();
        if (row != null) {
            List<Queen> rowIndexList = rowIndexMap.get(queen.getRowIndex());
            rowIndexList.remove(queen);
            score += rowIndexList.size();
            List<Queen> ascendingDiagonalIndexList = ascendingDiagonalIndexMap.get(queen.getAscendingDiagonalIndex());
            ascendingDiagonalIndexList.remove(queen);
            score += ascendingDiagonalIndexList.size();
            List<Queen> descendingDiagonalIndexList = descendingDiagonalIndexMap.get(queen.getDescendingDiagonalIndex());
            descendingDiagonalIndexList.remove(queen);
            score += descendingDiagonalIndexList.size();
        }
    }

    public SimpleScore calculateScore() {
        return SimpleScore.valueOf(score);
    }

}

Configure it in your solver configuration:

  <scoreDirectorFactory>
    <scoreDefinitionType>...</scoreDefinitionType>
    <incrementalScoreCalculatorClass>org.optaplanner.examples.nqueens.solver.score.NQueensAdvancedIncrementalScoreCalculator</incrementalScoreCalculatorClass>
  </scoreDirectorFactory>

Optionally, to explain a score with ScoreDirector.getConstraintMatchTotals() or to get better output when the IncrementalScoreCalculator is corrupted in FAST_ASSERT or FULL_ASSERT environmentMode, implement also the ConstraintMatchAwareIncrementalScoreCalculator interface:

public interface ConstraintMatchAwareIncrementalScoreCalculator<Sol extends Solution> {

    void resetWorkingSolution(Sol workingSolution, boolean constraintMatchEnabled);

    Collection<ConstraintMatchTotal> getConstraintMatchTotals();
    
}

There are several ways to define where your score rules live.

A ScoreHolder instance is asserted into the KieSession as a global called scoreHolder. Your score rules need to (directly or indirectly) update that instance.

global SimpleScoreHolder scoreHolder;

rule "multipleQueensHorizontal"
    when
        Queen($id : id, row != null, $i : rowIndex)
        Queen(id > $id, rowIndex == $i)
    then
        scoreHolder.addConstraintMatch(kcontext, -1);
end

// multipleQueensVertical is obsolete because it is always 0

rule "multipleQueensAscendingDiagonal"
    when
        Queen($id : id, row != null, $i : ascendingDiagonalIndex)
        Queen(id > $id, ascendingDiagonalIndex == $i)
    then
        scoreHolder.addConstraintMatch(kcontext, -1);
end

rule "multipleQueensDescendingDiagonal"
    when
        Queen($id : id, row != null, $i : descendingDiagonalIndex)
        Queen(id > $id, descendingDiagonalIndex == $i)
    then
        scoreHolder.addConstraintMatch(kcontext, -1);
end

Most use cases will also weigh their constraint types or even their matches differently, by using a specific weight for each constraint match.

Here's an example from CurriculumCourse, where assigning a Lecture to a Room which is missing 2 seats is weighted equally bad as having 1 isolated Lecture in a Curriculum:

global HardSoftScoreHolder scoreHolder;

// RoomCapacity: For each lecture, the number of students that attend the course must be less or equal
// than the number of seats of all the rooms that host its lectures.
// Each student above the capacity counts as 1 point of penalty.
rule "roomCapacity"
    when
        $room : Room($capacity : capacity)
        $lecture : Lecture(room == $room, studentSize > $capacity, $studentSize : studentSize)
    then
        scoreHolder.addSoftConstraintMatch(kcontext, ($capacity - $studentSize));
end

// CurriculumCompactness: Lectures belonging to a curriculum should be adjacent
// to each other (i.e., in consecutive periods).
// For a given curriculum we account for a violation every time there is one lecture not adjacent
// to any other lecture within the same day.
// Each isolated lecture in a curriculum counts as 2 points of penalty.
rule "curriculumCompactness"
    when
        ...
    then
        scoreHolder.addSoftConstraintMatch(kcontext, -2);
end

The InitializingScoreTrend specifies how the Score will change as more and more variables are initialized (while the already initialized variables don't change). Some optimization algorithms (such Construction Heuristics and Exhaustive Search) run faster if they have such information.

For for the Score (or each score level separately), specify a trend:

  • ANY (default): Initializing an extra variable can change the score positively or negatively. Gives no performance gain.

  • ONLY_UP (rare): Initializing an extra variable can only change the score positively. Implies that:

    • There are only positive constraints

    • And initializing the next variable can not unmatch a positive constraint that was matched by a previous initialized variable.

  • ONLY_DOWN: Initializing an extra variable can only change the score negatively. Implies that:

    • There are only negative constraints

    • And initializing the next variable can not unmatch a negative constraint that was matched by a previous initialized variable.

Most use cases only have negative constraints. Many of those have an InitializingScoreTrend that only goes down:

  <scoreDirectorFactory>
    <scoreDefinitionType>HARD_SOFT</scoreDefinitionType>
    <scoreDrl>.../cloudBalancingScoreRules.drl</scoreDrl>
    <initializingScoreTrend>ONLY_DOWN</initializingScoreTrend>
  </scoreDirectorFactory>

Alternatively, you can also specify the trend for each score level separately:

  <scoreDirectorFactory>
    <scoreDefinitionType>HARD_SOFT</scoreDefinitionType>
    <scoreDrl>.../cloudBalancingScoreRules.drl</scoreDrl>
    <initializingScoreTrend>ONLY_DOWN/ONLY_DOWN</initializingScoreTrend>
  </scoreDirectorFactory>

Put the environmentMode in FULL_ASSERT (or FAST_ASSERT) to detect corruption in the incremental score calculation. For more information, see the section about environmentMode. However, that will not verify that your score calculator implements your score constraints as your business actually desires.

A piece of incremental score calculator code can be difficult to write and to review. Assert its correctness by using a different implementation (for example a EasyScoreCalculator) to do the assertions triggered by the environmentMode. Just configure the different implementation as a assertionScoreDirectorFactory:

  <environmentMode>FAST_ASSERT</environmentMode>
  ...
  <scoreDirectorFactory>
    <scoreDefinitionType>...</scoreDefinitionType>
    <scoreDrl>org/optaplanner/examples/nqueens/solver/nQueensScoreRules.drl</scoreDrl>
    <assertionScoreDirectorFactory>
      <easyScoreCalculatorClass>org.optaplanner.examples.nqueens.solver.score.NQueensEasyScoreCalculator</easyScoreCalculatorClass>
    </assertionScoreDirectorFactory>
  </scoreDirectorFactory>

This way, the scoreDrl will be validated by the EasyScoreCalculator.

Instead of implementing a hard constraint, it can sometimes be built in. For example: If Lecture A should never be assigned to Room X, but it uses ValueRangeProvider on Solution, so the Solver will often try to assign it to Room X too (only to find out that it breaks a hard constraint). Use a ValueRangeProvider on the planning entity or filtered selection to define that Course A should only be assigned a Room different than X.

This can give a good performance gain in some use cases, not just because the score calculation is faster, but mainly because most optimization algorithms will spend less time evaluating unfeasible solutions. However, usually this not a good idea because there is a real risk of trading short term benefits for long term harm:

  • Many optimization algorithms rely on the freedom to break hard constraints when changing planning entities, to get out of local optima.

  • Both implementation approaches have limitations (feature compatiblity, disabling automatic performance optimizations, ...), as explained in their documentation.

Make sure that none of your score constraints cause a score trap. A trapped score constraint uses the same weight for different constraint matches, when it could just as easily use a different weight. It effectively lumps its constraint matches together, which creates a flatlined score function for that constraint. This can cause a solution state in which several moves need to be done to resolve or lower the weight of that single constraint. Some examples of score traps:

For example, consider this score trap. If the blue item moves from an overloaded computer to an empty computer, the hard score should improve. The trapped score implementation fails to do that:

The Solver should eventually get out of this trap, but it will take a lot of effort (especially if there are even more processes on the overloaded computer). Before they do that, they might actually start moving more processes into that overloaded computer, as there is no penalty for doing so.

There are several ways to deal with a score trap:

Not all score constraints have the same performance cost. Sometimes 1 score constraint can kill the score calculation performance outright. Use the Benchmarker to do a 1 minute run and check what happens to the average calculation count per second if you comment out all but 1 of the score constraints.

Some use cases have a business requirement to provide a fair schedule (usually as a soft score constraint), for example:

Implementing such a constraint can seem difficult (especially because there are different ways to formalize fairness), but usually the squared workload implementation behaves most desirable: for each employee/asset, count the workload w and subtract from the score.

As shown above, the squared workload implementation guarantees that if you select 2 employees from a given solution and make their distribution between those 2 employees fairer, then the resulting new solution will have a better overall score. Don't just use the difference from the average workload, as that can lead to unfairness, as demonstrated below.

Note

Instead of the squared workload, it's also possible to use the variance (squared difference to the average) or the standard deviation (square root of the variance). This has no effect on the score comparison, because the average won't change during planning. It's just more work to implement (because the average needs to be known) and trivially slower (because the calculation is a bit longer).

When the workload is perfect balanced, the user often likes to see a 0 score, instead of the distracting -34soft in the image above (for the last solution which is almost perfectly balanced). To nullify this, either add the average multiplied by the number of entities to the score or instead show the variance or standard deviation in the UI.

Other parts of your application, for example your webUI, might need to calculate the score too. Do that by reusing the ScoreDirectorFactory of the Solver to build a separate ScoreDirector for that webUI:

ScoreDirectorFactory scoreDirectorFactory = solver.getScoreDirectorFactory();
ScoreDirector guiScoreDirector = scoreDirectorFactory.buildScoreDirector();

Then use it when you need to calculate the Score of a Solution:

guiScoreDirector.setWorkingSolution(solution);
Score score = guiScoreDirector.calculateScore();

To explain in the GUI what entities are causing which part of the Score, get the ConstraintMatch objects from the ScoreDirector:

for (ConstraintMatchTotal constraintMatchTotal : guiScoreDirector.getConstraintMatchTotals()) {
    String constraintName = constraintMatchTotal.getConstraintName();
    Number weightTotal = constraintMatchTotal.getWeightTotalAsNumber();
    for (ConstraintMatch constraintMatch : constraintMatchTotal.getConstraintMatchSet()) {
        List<Object> justificationList = constraintMatch.getJustificationList();
        Number weight = constraintMatch.getWeightAsNumber();
        ...
    }
}

Note

Drools score calculation supports constraint matches automatically, but incremental Java score calculation requires requires implementing an extra interface (see that section).