Thursday, April 24, 2008

Solving the Examination problem part 2: score function

This is the second part in a blog series about drools-solver and the Examination problem. If you haven't done so, read Solving the Examination problem: Domain diagram first.

Each possible solution has a score. Before we try to find the best solution, we need a way to calculate the score of a solution. And that's where the drools rule engine comes into play.

So the current working solution is asserted into the working memory (based on it's getFacts() method) and a number of score rules are fired upon it. Generally, each (hard or soft) constraint translates into a single score rule.

For example, this is the score rule to penalize all exams for which the period duration doesn't suffice.
// More time required during a period than available in that period.
rule "periodDurationTooShort"
// Any exam who's duration is longer that it's period duration ...
$exam : Exam(eval(topicDuration > periodDuration));
// ... is penalized hard.
insertLogical(new IntConstraintOccurrence("periodDurationTooShort", ConstraintType.NEGATIVE_HARD,

Of course, some rules are more complicated, like the score rule to penalize all conflicting exams in a row:
// Two exams in a row which share students
rule "twoExamsInARow"
// When 2 in row exams are penalized, ...
$institutionalWeighting : InstitutionalWeighting(twoInARowPenality != 0);

// ..., any 2 exams that share students ...
$topicConflict : TopicConflict($leftTopic : leftTopic, $rightTopic : rightTopic);

// ... of which the periods ...
$leftExam : Exam(topic == $leftTopic, $leftPeriod : period);
$rightExam : Exam(topic == $rightTopic, $rightPeriod : period);

// ... occur on the same day ...
eval($leftPeriod.getDayIndex() == $rightPeriod.getDayIndex());

// ... and are successive, ...
eval(Math.abs($leftPeriod.getPeriodIndex() - $rightPeriod.getPeriodIndex()) == 1);
// ..., are penalized softly.
insertLogical(new IntConstraintOccurrence("twoExamsInARow", ConstraintType.NEGATIVE_SOFT,
$topicConflict.getStudentSize() * $institutionalWeighting.getTwoInARowPenality(),
$leftExam, $rightExam));

Using the drools rule engine to calculate the score has a bunch of advantages:
  • The constraint score rules are easier to implement, once you get the hang of the DRL pattern syntax.

  • The implementations of the constraints are isolated from each other.
    So adding extra constraints is easy and scalable.

  • If the working solution changes into an adjacent solution (for example due to a solver move), drools does forward-chaining. This means you get delta based score calculation without any effort. That's a huge performance boost without breaking a sweat.

Now that we know how to calculate the score of solution, we can recognize a good solution. In a next blog we 'll take a look at finding the best solution we can find out of 10^5761 possible solutions.