Kristiansen, Simon

Stidsen, Thomas Riis

Sørensen, Matias

An algorithm based on Adaptive Large Neighborhood Search (ALNS) for solving the generalized High School Timetabling problem in XHSTT-format (Post et al (2012a)) is presented. This algorithm was among the nalists of round 2 of the International Timetabling Competition 2011 (ITC2011). For problem description and results we refer to Post et al (2012b)

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Downloaded from orbit.dtu.dk on: Dec 20, 2017International Timetabling Competition 2011: An Adaptive Large Neighborhood SearchalgorithmSørensen, Matias; Kristiansen, Simon; Stidsen, Thomas Jacob RiisPublished in:Proceedings of the Ninth International Conference on the Practice and Theory of Automated Timetabling(PATAT 2012)Publication date:2012Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Sørensen, M., Kristiansen, S., & Stidsen, T. R. (2012). International Timetabling Competition 2011: An AdaptiveLarge Neighborhood Search algorithm. In Proceedings of the Ninth International Conference on the Practice andTheory of Automated Timetabling (PATAT 2012) (pp. 489-492)International Timetabling Competition 2011:An Adaptive Large Neighborhood Search algorithmMatias Sørensen · Simon Kristiansen ·Thomas R. StidsenKeywords Adaptive Large Neighborhood Search · High School Timetabling ·International Timetabling Competition 2011 · XHSTT1 IntroductionAn algorithm based on Adaptive Large Neighborhood Search (ALNS) for solv-ing the generalized High School Timetabling problem in XHSTT-format (Postet al (2012a)) is presented. This algorithm was among the ﬁnalists of round2 of the International Timetabling Competition 2011 (ITC2011). For problemdescription and results we refer to Post et al (2012b).2 Adaptive Large Neighborhood SearchAdaptive Large Neighborhood Search was ﬁrst developed as a metaheuristicfor the class of Vehicle Routing Problems (Pisinger and Ropke (2005); Ropkeand Pisinger (2006)). It has been applied for few other problem classes as well,including Project Scheduling (Muller (2009, 2010)), Lot-sizing (Muller andSpoorendonk (2011)), Optimal Statistic Median Problem (Katterbauer et al(2012)).Recently we have developed a framework based on ALNS for solving com-binatorial optimization problems (written in C# 4.0). This framework is partof the commercial product Lectio1, where it is used to solve various practi-cal timetabling problems, see Kristiansen et al (2011); Sørensen and Stidsen(2012) and Kristiansen and Stidsen (2012).The pseudo code for a general ALNS algorithm is given in Algorithm 1.Matias Sørensen [msso@dtu.dk], Simon Kristiansen, Thomas R. StidsenOperations Research, DTU Management EngineeringTechnical University of Denmark1 http://www.lectio.dkCloud-based administration system for high schools. Developed by MaCom A/S, Vesterbro-gade 48 1., 1620 Copenhagen V, Denmark2 Matias Sørensen et al.Algorithm 1 Adaptive Large Neighborhood Search1: candidate solution x, remove-methods Ω−, insert-methods Ω+2: xbest = x3: while stop-criterion not met do4: x′ = x5: RemoveStrategy: select q as some quantity to be removed6: AdaptiveStrategy: select remove-method r ∈ Ω− and insert-method i ∈ Ω+7: remove requests from x′ using r(q)8: insert requests into x′ using i9: AdaptiveStrategy: update performance indicators10: if c(x′) ≤ c(xbest) then11: xbest = x′12: end if13: AcceptStrategy: set candidate solution x to either x′, xbest or x itself14: end while15: return xbestThe main points of the algorithm are described below in general terms. In each iteration, a remove and insertion method is chosen and appliedto the candidate solution. The combination of these methods deﬁnes theneighborhood of the algorithm, hence there exists |Ω−| · |Ω+| diﬀerentneighborhoods. RemoveStrategy: Governs the selection of q. This has major inﬂuence onhow much computational time each iteration requires. AdaptiveStrategy: Responsible for selecting remove and insertion meth-ods in each iteration, and updating their respective performance indicatorsof these method by some metric. AcceptStrategy: Determines which solution to use as candidate solutionfor next iteration. This could in principle be any known solution, but isusually selected as either the current candidate solution x itself, the newlyproduced solution x′, or the current best solution xbest.3 Algorithm setup for ITC2011Here we describe our implementation of a ALNS algorithm for the XHSTTformat. The choice of ALNS strategies are brieﬂy mentioned below. Moredetails will be available in the full paper. RemoveStrategy: The remove and insertion methods deal with sub-events.q is deﬁned as the sum of the duration of the sub-events which are re-moved from the solution. We select q as a random number, bounded by apercentage of the total duration of all instance events. AdaptiveStrategy: We have chosen a metric essentially based on two pa-rameters for each method; The number of times the method was part ofan iteration which yielded a better solution than the current one, and theITC2011: An ALNS algorithm 3relative gap between the current solution and the resulting solution fromapplying the method. AcceptStrategy: An acceptance criteria borrowed from Simulated An-nealing (SA) is used, with the following additional property: If no newbest solution has been found in a number of iterations, the temperature isincreased by a factor, and the candidate solution is set to the best knownsolution. The intention is to allow more diverse exploring of the area aroundthe best known solution, in case the algorithm gets 'stuck'.Let a move be a small perturbation on a solution. The following moves areused in this implementation: Move Mse,t denotes the assigning of sub-eventse to time t. Mr,er,se denotes the assigning of resource r to event resource eron sub-event se. Furthermore we also implement the corresponding unassign-moves, denoted M¬se,t and M¬r,er,se, respectively.Using these moves a total of 9 insertion methods (all more or less basedon the greedy principle, e.g. regret heuristics (Potvin and Rousseau (1993);Sørensen and Stidsen (2012)), and 14 remove methods (all based on someelement of relatedness and an element of randomness) are implemented. Thesemethods are divided into three categories, based on what they (un-)assign:Only times, only resources, or both times and resources.An example of a remove method is the following, which removes sub-eventsfrom non-preferred times: Given an XHSTT instance, and a solution S to thisinstance. Find all tuples 〈se, t〉 of S, where sub-event se is assigned time t,and t is not a preferred time for sub-event se (see Prefer times constraints,Kingston (2010)). Let the set of these tuples be denoted U . Select randomlya subset of these tuples U ⊆ U such that the sum of the duration of all sub-events of the tuples in U equals q. Perform an unassign time move M¬se,t foreach of the tuples in U .An example of an insertion method is the following: Let ∆ (M) ∈ R bethe proﬁt of performing move M on the solution at hand S. Select Mbest =argminse,t (∆ (Mse,t)), and if ∆ (Mbest) ≤ 0, apply Mbest to S and repeat,otherwise stop. This is a greedy method which assigns times to sub-events,until no proﬁtable move can be found.In the full paper all insert/remove methods will be described in detail.The ﬁnal algorithm contains 9 free parameters, which were tuned for bestperformance using the irace package (see López-Ibáñez et al (2011); Birattari(2005)).4 Final remarksThis paper documents how Adaptive Large Neighborhood Search can be ap-plied to problems in XHSTT format.The proposed algorithm was applied to all instances in archive XHSTT-ITC2011, and showed competitive results in most cases (comparing to the bestknown solutions at that point in time).4 Matias Sørensen et al.ALNS has not been used much in the ﬁeld of timetabling, but we seeno reason to believe that ALNS should not perform well on other (related)problems in this ﬁeld.Acknowledgements Thank you goes to Michael Herold for fruitful discussions concerningALNS strategies. Thank you to Manuel López-Ibáñez for help using the irace package. Andﬁnally thank you to David Pisinger for advice on ALNS implementation.ReferencesBirattari M (2005) The Problem of Tuning Metaheuristics as seen from a Machine LearningPerspective, vol 292 Dissertations in Artiﬁcial Intelligence - Inﬁx, 1st edn. SpringerKatterbauer K, Oguz C, Salman S (2012) Hybrid adaptive large neighborhood search forthe optimal statistic median problem. Computers & Operations Research 39(11):2679 2687Kingston JH (2010) The hseval high school timetable evaluator. URL http://it.usyd.edu.au/~jeff/hseval.cgiKristiansen S, Stidsen TR (2012) Adaptive large neighborhood search for student sectioningat danish high schools. In: Proceedings of the Ninth International Conference on thePractice and Theory of Automated Timetabling (PATAT 2012)Kristiansen S, Sørensen M, Stidsen T, Herold M (2011) Adaptive large neighborhood searchfor the consultation timetabling problem, to appearLópez-Ibáñez M, Dubois-Lacoste J, Stützle T, Birattari M (2011) The irace package: It-erated racing for automatic algorithm conﬁguration. Tech. Rep. TR/IRIDIA/2011-004,Université Libre de Bruxelles, IRIDIA, Av F. D. Roosevelt 50, CP 194/6 1050 Bruxelles,Belgium, http://iridia.ulb.ac.be/iraceMuller L (2009) An adaptive large neighborhood search algorithm for the resource-constrained project scheduling problem. In: MIC 2009: The VIII Metaheuristics In-ternational ConferenceMuller L (2010) An adaptive large neighborhood search algorithm for the multi-moderesource-constrained project scheduling problem. l, Department of Management En-gineering, Technical University of Denmark Produktionstorvet, Building 426, DK-2800Kgs. Lyngby, DenmarkMuller L, Spoorendonk S (2011) A hybrid adaptive large neighborhood search algorithm ap-plied to a lot-sizing problem. European Journal of Operational Research Volume 218(Is-sue 3):614623Pisinger D, Ropke S (2005) A general heuristic for vehicle routing problems. Computers &Operations Research 34:24032435Post G, Ahmadi S, Daskalaki S, Kingston J, Kyngas J, Nurmi C, Ranson D (2012a) Anxml format for benchmarks in high school timetabling. Annals of Operations Research194:385397Post G, Gaspero LD, Kingston JH, McCollum B, Schaerf A (2012b) The third internationaltimetabling competition. In: Proceedings of the Ninth International Conference on thePractice and Theory of Automated Timetabling (PATAT 2012), Son, NorwayPotvin JY, Rousseau JM (1993) A parallel route building algorithm for the vehicle routingand scheduling problem with time windows. European Journal of Operational Research66(3):331  340Ropke S, Pisinger D (2006) An adaptive large neighborhood search heuristic for the pickupand delivery problem with time windows. Transportation Science 40:455472Sørensen M, Stidsen TR (2012) High school timetabling: Modeling and solving a largenumber of cases in denmark. In: Proceedings of the Ninth International Conference onthe Practice and Theory of Automated Timetabling (PATAT 2012)

International Timetabling Competition 2011: An Adaptive Large Neighborhood Search algorithm

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International Timetabling Competition 2011: An Adaptive Large Neighborhood Search algorithm

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