Drools Planner Chtijug 2010

Ch’ti JUG Jboss Drools & Drools Planner 21 janvier 2010

Ch’ti JUG

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Ch’ti JUG Storeland pilote l’ensemble de votre supply chain étendue

Ch’ti JUG CYLANDE partenaire de la FFJ Le judo véhicule des valeurs Cylande a accompagné l’équipe de France de Judo à Pékin

Ch’ti JUG Une croissance résolument tournée vers l’international Lauréat du Prix PME France CHINE ACFCI / CCIFC

Ch’ti JUG Automated planning with Drools Planner Geoffrey De Smet Drools Planner lead "Do more with less."

Ch’ti JUG Agenda  Use cases of automated planning • N queens • Bin packaging • Employee shift rostering • Examination timetabling  Find the best solution • With Drools Planner  Calculate the score of a solution • With Drools

Ch’ti JUG N Queens: use case  Place n queens on a n-sized chess board  No 2 queens can attack each other

Ch’ti JUG N queens: partially solved  Score -1 for every 2 queens that can attack each other Score = -2

Ch’ti JUG N queens: an optimal solution Score = 0

Ch’ti JUG N queens: demo  Not optimized! • Hello world example  Not a real planning problem • I can make an optimal solution for any n queens without a computer • See Wikipedia

Ch’ti JUG

Ch’ti JUG NP complete  Yellow item goes in first (or last) • Why? • Not the largest size • Not the largest side • So why?  NP complete • A given solution can be verified fast • No efficient way to find a solution • Is there even a solution?

Ch’ti JUG Real world bin packaging  Not just 5 items • 1000+ items  Not just 1 container • 100+ containers • Different container types  More constraints... • Distribute weight evenly • Not all fireworks in the same container • ...

Ch’ti JUG

Ch’ti JUG Hard constraints  Hard constraints must be fulfilled  For example: • Ensure continuous service • At least 1 emergency nurse at any given time • Labor laws • Every 24 hours: at least 11 hours rest • Every 7 days: at least 35 hours rest • No shifts during approved vacation

Ch’ti JUG Soft constraints  Soft constraints should be fulfilled as much as possible • Only after the hard constraints are fulfilled  Each soft constraint is weighted  For example: • Fair night work assignment: weight 5 • Forward rotation: weight 10 • Nurse preferences: weight 1 • Ann dislikes Saturday night shifts • Beth dislikes Wednesday afternoon shifts

Ch’ti JUG Hard and soft score  Solution A B C  Hard constraints • 11 hours rest 1 0 0  Soft constraints • Fair night work assignment 0 1000 1 • Weight 5 • Nurse preferences 0 0 4000 • Weight 1  Total score -1H/0S 0H/-5000S 0H/-4005S • A<B<C • C is the best solution

Ch’ti JUG

Ch’ti JUG Hard constraints  Exam conflict: 2 exams that share students should not occur in the same period.  Room capacity: A room's seating capacity should suffice at all times.  Period duration: A period's duration should suffice for all of its exams.  Period related hard constraints should be fulfilled: • Coincidence: 2 exams should use the same period (but possibly another room). • Exclusion: 2 exams should not use the same period. • After: 1 exam should occur in a period after another exam's period.  Room related hard constraints should be fulfilled: • Exclusive: 1 exam should not have to share its room with any other exam.

Ch’ti JUG Soft constraints  2 exams in a row.  2 exams in a day.  Period spread: 2 exams that share students should be a number of periods apart.  Mixed durations: 2 exams that share a room should not have different durations.  Front load: Large exams should be scheduled earlier in the schedule.  Period penalty: Some periods have a penalty when used.  Room penalty: Some rooms have a penalty when used.

Ch’ti JUG Examination demo  International timetabling competition 2007 • Finished 4th (back then)  7 minutes • CPU depended  Real word test data  14 constraints • 7 hard constraints • 7 soft constraints

Ch’ti JUG Other use cases  Vehicle routing • Freight routing  Scheduling • Course, meeting, conference scheduling • Appointment and resource scheduling • Sport scheduling  Storage organizing  Machine queue planning  ...

Ch’ti JUG Why use Drools Planner?  Open source • ASL (business-friendly)  Maven-ready (JBoss repository)  Documentation • Reference manual • Examples  JBoss Drools community support • User mailing list, issue tracking, … • Blog & twitter (#droolsplanner)

Ch’ti JUG Brute force for (periodOfExam1 : periodList) { exam1.setPeriod(periodOfExam1); for (roomOfExam1 : roomList) { exam1.setRoom(roomOfExam1); for (periodOfExam2 : periodList) { exam2.setPeriod(periodOfExam2); for (roomOfExam2 : roomList) { exam2.setRoom(roomOfExam2); ... for (periodOfExamN : periodList) { examN.setPeriod(periodOfExamN); for (roomOfExamN : roomList) { examN.setRoom(roomOfExamN); Score score = calculateScore(solution); cloneIfScoreIsBetter(solution, score); } } } }…} }

Ch’ti JUG Needle in a haystack  How many possible solutions? • 1096 exams • 80 periods • 28 rooms  > habitants in Lille per km²? • 6 483 hab./km² Source: wikipedia

Ch’ti JUG Needle in a haystack  How many possible solutions? • 1096 exams • 80 periods • 28 rooms  > humans? • 7.000.000.000 humans Source: NASA (wikipedia)

Ch’ti JUG Needle in a haystack  How many possible solutions? • 1096 exams • 80 periods • 28 rooms  > minimum atoms in the observable universe? • 10^80 atoms Source: NASA and ESA (wikipedia)

Ch’ti JUG Needle in a haystack  How many possible solutions? • 1096 exams • 80 periods • 28 rooms  > atoms in the universe if every atom is a universe of atoms? • (10^80)^80 = 10^6400 Source: NASA and ESA (wikipedia)

Ch’ti JUG Do the math  1 exam • 80 periods and 28 rooms • 80 * 28 = 2240 ways to schedule 1 exam  2 exams • 2240 * 2240 = 5.017.600  3 exams • 2240 * 2240 * 2240 = 11.239.424.000  1096 exams • 2240 * 2240 * … * 2240 • 2240^1096 = a little over 10^3671

Ch’ti JUG A little over 10^3671  744437246744648820113833159531546214974276974551140513162882691 3469284310834499031050210214743407656244813085240442809855321 17872268184924364558999914849676314196976841658179857396613906 3492625485909685725897730184010924994541828672670138943325039 683048943713412274829614721695599636159777727101713768378004615 48701272177587402234891701308937790853816473943603349353332893 68078384002213161233225755719910067066354676237665251240673552 3153767499024677368278799816044299431500884240408977216982760 67946148250230917492054728443158872165054373936157659332956136 774730870081258025518405492389480888615900164269035398348299 0003805674675524102808572658937105740571173904119233244862828 53392817922617168734507604739703552080299261320457186755798353 7967203299588154666629888459837384660489020381221523812268702 28697167564520947170314014038670253281783219898668392349799158 35407169443312860837423115961300328664844607892218572759207572 4811

Ch’ti JUG A little over 10^3671  0000000000000000000000000000000000000000000000000 000000000000000000000000000  The search space is big! • Compare with WWW size • 22 020 000 000 pages  Each possible solution • 1096+ exams scheduled into • 80 periods • 28 rooms • Still need to calculate the score

Ch’ti JUG Throw hardware at it?  If 10^9 scores calculated per ms • Not possible today! • 31.579.200.000 ms in 1 year • < 10^11 ms in 1 year • 10^9 * 10^11 scores per year • = 10^20 scores per year  How many years? 10^3671 / 10^20 • = 10^3651 years  CPU 1000 times faster • It becomes 10^3648 years

Ch’ti JUG A dose of reality  Find the optimal solution? • Of a real world planning problem?  Not in our lifetimes!  Who cares? • Beat the human planner(s) (=easy) • Spend less resources • Save more money • Save the environment • Make more people happy • Never ending competition

Ch’ti JUG Smarter brute force?  Eliminate subtrees • Branch and bound • Still too many for loops • Still takes forever for (periodOfExam2 : periodList) { exam2.setPeriod(periodOfExam2); if (exam1.shareStudentWith(exam2) && periodOfExam1.equals(periodOfExam2)) { continue; // bug: best solution might break a hard constraint } ...

Ch’ti JUG Imperfect algorithms (mimic a human)  Deterministic • First in, first assigned, never changed • Easy to implement • Drools Planner score support • Fixed time (for example 18 seconds)  Metaheuristic • Move things around • Start from result of deterministic algorithm • Drools Planner implementations • More time = better score

Ch’ti JUG Deterministic: N queens  Demo  Not feasible • Not optimal  Good initialization • Jump 10 meter into the pool

Ch’ti JUG Deterministic: examination List<Exam> sortedExamList = sortExamsOnDifficulty(examList); for (exam : sortedExamList) { // Determine best remaining spot Score bestScoreOfExam = - INFINITY; for (period : periodList) { exam.setPeriod(period); for (room : roomList) { exam.setRoom(room); Score score = calculateScore(solution); if (score > bestScoreOfExam) { bestScoreOfExam = score; ... store bestPeriod, bestRoom } } } … assign exam to bestPeriod, bestRoom }

Ch’ti JUG Metaheuristic algorithms  Local search: 1st, 2nd, 3rd and 4th in ITC 2007 • Simple local search (Hill climbing) • Tabu search • Local search ++ • Simulated annealing • Great deluge • ...  Genetic algorithms: 5th in ITC 2007  Ant colony optimization  ...

Ch’ti JUG Move things around  Move = from solution A to solution B • Change the row of 1 queen • Give 2 queens each others rows • ...

Ch’ti JUG All moves from one solution  Number of moves < number of solutions • N queens • n*n < n^n • 4 queens • 16 < 256 • 8 queens • 64 < 16777216 • 64 queens • 4096 < 10^116

Ch’ti JUG Metaheuristic: local search

Ch’ti JUG

Ch’ti JUG Local optima  1) Deterministic StartingSolutionInitializer  2) Simple local search  3) Stuck in local optimum! Source: Wikipedia

Ch’ti JUG Tabu search = local search++  Solution tabu (high tabu size) • Been there, no need to go there again  Move tabu (low tabu size) • Done that recently, no need to do that again  Property tabu (low tabu size) • Changed that recently, no need to change that again

Ch’ti JUG Drool planner configuration <selector> <selector> <moveFactoryClass>...PeriodChangeMoveFactory</...> <relativeSelection>0.002</relativeSelection> </selector> ... <selector> <moveFactoryClass>...ExamSwitchMoveFactory</...> <relativeSelection>0.002</relativeSelection> </selector> </selector> <accepter> <completeSolutionTabuSize>1000</completeSolutionTabuSize> <completeMoveTabuSize>7</completeMoveTabuSize> </accepter> <forager> <foragerType>MAX_SCORE_OF_ALL</foragerType> </forager>

Ch’ti JUG Termination  Synchronous (configured) • Max timeMillis/seconds/minutes/hours spend • Score attained • Max step count • Max unimproved step count  Asynchronous (from another thread) • planner.terminateEarly();

Ch’ti JUG Double time !=> double score Examination test data 7 Soft score Time (hours:minutes)

Ch’ti JUG Benchmarker utility  Battle of different planner configurations • Different algorithms (tabu search, ...) • Different moves • Different settings  On multiple datasets  Results are ranked: • Best one wins  Coming soon: • Graph: best score over time

Ch’ti JUG JAVA vs SQL vs DRL for (q1 : queenList) { for (q2 : queenList) { if (q1.getId() < q2.getId() && q1.getY() == q2.getY()) { ... } } } select * from Queen q1, Queen q2 where q1.id < q2.id and q1.y = q2.y; rule "multipleQueensHorizontal" when $q1 : Queen($id : id, $y : y); $q2 : Queen(id > $id, y == $y);

Ch’ti JUG N queens: score rule rule "multipleQueensHorizontal" when $q1 : Queen($id : id, $y : y); $q2 : Queen(id > $id, y == $y); then insertLogical(new IntConstraintOccurrence( "multipleQueensHorizontal", ConstraintType.NEGATIVE_HARD, 1, $q1, $q2)); end

Ch’ti JUG Score rule isolation rule "multipleQueensHorizontal" when $q1 : Queen($id : id, $y : y); $q2 : Queen(id > $id, y == $y); then ... end rule "multipleQueensAscendingDiagonal" when $q1 : Queen($id : id, $ascendingD : ascendingD); $q2 : Queen(id > $id, ascendingD == $ascendingD); then ... end rule "multipleQueensDescendingDiagonal" when $q1 : Queen($id : id, $descendingD : descendingD); $q2 : Queen(id > $id, descendingD == $descendingD); then ... end

Ch’ti JUG

Ch’ti JUG Examination: period spread  2 exams that share students should be a number of periods apart rule "periodSpread" when $iw : InstitutionalWeighting(periodSpreadPenality != 0); // For any 2 conflicting exams in the same period ... $topicConflict : TopicConflict($leftT : leftTopic, $rightT : rightTopic); $leftExam : Exam(topic == $leftT, $leftPeriod : period); $rightExam : Exam(topic == $rightT, $rightPeriod : period); // … which are in within the periodSpread eval(Math.abs($leftPeriod.getPeriodIndex() - $rightPeriod.getPeriodIndex()) < ($iw.getPeriodSpreadLength() + 1)); then insertLogical(new IntConstraintOccurrence(... NEGATIVE_SOFT, $topicConflict.getStudentSize() * $iw.getPeriodSpreadPenality(), $leftExam, $rightExam)); end

Ch’ti JUG Summary  Drools Planner solves planning problems  Adding constraints is easy and scalable  Switching/combining algorithms is easy

Ch’ti JUG Q&A  Home page • http://www.jboss.org/drools/drools-planner.html  Reference manual • http://www.jboss.org/drools/documentation.html  Blog • http://blog.athico.com/search/label/planner  Twitter • #droolsplanner 64

Ch’ti JUG Thanks for your attention!  Home page • http://www.jboss.org/drools/drools-planner.html  Reference manual • http://www.jboss.org/drools/documentation.html  Blog • http://blog.athico.com/search/label/planner  Twitter • #droolsplanner 65

Ch’ti JUG Licence  Les photos et logos appartiennent à leurs auteurs respectifs  Le contenu de la présentation est sous licence Creative Commons 2.0 France • Contrat Paternité • Pas d'Utilisation Commerciale • Partage des Conditions Initiales à l'Identique  http://creativecommons.org/licenses/by-nc-sa/2.0/fr/

Ch’ti JUG Cocktail  Merci pour votre attention  Merci à Cylande pour son sponsoring

Drools Planner Chtijug 2010

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