9th International Conference on the Practice and Theory of Automated Timetabling, Son, Norway, 28-31 August 201

Kheiri, Ahmed

Parkes, Andrew J.

Özcan, Ender

English

Open Research Exeter

Noname manuscript No.(will be inserted by the editor)HySST: Hyper-heuristic Search Strategies andTimetablingAhmed Kheiri  Ender Ozcan Andrew J. ParkesReceived: date / Accepted: date1 IntroductionHigh school timetabling (HST) is a well-known real-world combinatorial opti-misation problem. It requires the scheduling of events and resources, such ascourses, classes of students, teachers, rooms and more within a xed number oftime slots subject to a set of constraints. In a standard fashion, constraints areseparated into `hard'1 and soft. The hard constraints must be satised in orderto achieve feasibility, whereas the soft constraints represent preferences and asolution for a given problem; solutions are expected to satisfy all hard con-straints and as many soft constraints as possible. The HST problem is knownto be NP-complete [2] even in simplied forms. For a recent survey of HSTsee [4]. Also, see [5] for a description of the specic HST version studied here,and also of the third international timetabling competition, ITC2011. Briey,the ITC2011 problem instances contain 15 types of constraints and a candidatesolution is evaluated in terms of two components: feasibility and preferences.The evaluation function computes the weighted hard and soft constraint vi-olations for a given solution as infeasibility and objective values, respectively.For the comparison of algorithms, a solution is considered to be better thananother if it has a smaller infeasibility value, or an equal infeasibility valueand a smaller objective value.Our approach to solving the HST is based on development of a hyper-heuristic (see [1] for a recent survey) in order to intelligently control theapplication of a range of neighbourhood move operators. Hyper-heuristicsexplore the space of (meta-)heuristics, as opposed to directly searching thespace of solutions, and generally, split into one of two types: selection hyper-heuristics that select between existing low-level heuristics, and generationUniversity of Nottingham, School of Computer ScienceJubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UKf axk, exo, ajp g@cs.nott.ac.uk1 In the competition, such constraints are not strictly hard but are simply much moreheavily penalised than the 'soft' constraints.Algorithm HySST Solver ITC2011S = create initial solution(); // takes tinit timetremaining = toverall   tinitSbest = S;while (tremaining notExceeded)Sstage best = S;Sstage start = S;while (tstage notExceeded) // stage entryLLH = SelectRandomlyFrom(MutationalHeuristics);S0 = ApplyHeuristic(LLH;S);if (S0 isBetterThan Sbest) then Sbest = S0;if (S0 isBetterThan Sstage best) then Sstage best = S0;S =MoveAcceptance(S; S0; ); // can accept with factor (1 + ) worseif (Sstage best isNotBetterThan Sstage start ) thenS = ApplyHillClimbing(S); // uses the hill climbing heuristicsreturn Sbest;Fig. 1 Pseudocode of the implemented hyper-heuristic. Here  is a small (tunable) param-eter that controls the level of worsening moves that are acceptable.hyper-heuristics that build the decision procedures used with the heuristics. Aselection hyper-heuristic generally includes both heuristic selection and moveacceptance within a single point search framework (that is, without the use ofpopulations of solutions): At each iteration, a candidate new solution is pro-duced by selecting and applying a heuristic (neighbourhood operator) froma set of low level heuristics; A `move acceptance' component then decideswhether or not the candidate should replace the incumbent solution.In this work, we develop and exploit a generalised selective hyper-heuristic(though envisage that future work could well exploit generative methods). Webuild on a previous study [3] that demonstrated the eectiveness of a gen-eralised version of the iterated local search approach. Specically, our hyper-heuristic uses a structured and staged application of multiple perturbative andhill climbing operators as opposed to simple selection from a single pool of alloperators.2 Hyper-heuristic Search for High School TimetablingThe search algorithm is implemented as a time contract algorithm and com-pletes its execution in toverall time. It consists of an initial construction phasefollowed by an extended improvement; see Figure 1 for the pseudocode. Theinitial construction of a complete solution is performed using the general solverimplemented by Je Kingston in the KHE library2. The improvement phaseuses the remaining time left (tremaining) after the construction of the initial so-lution which takes tinit time. Subsequently, a hyper-heuristic is used to controland mix a set of 11 low-level domain-specic heuristics and that are (mostly)2 http://sydney.edu.au/engineering/it/~jeff/khe/fairly simple moves such as moving a task to a dierent resource, or swaps ofevents. They are divided into two sets; 9 mutational operators that do a ran-domised move, and 2 hill climbing operators that search their neighbourhoodsfor better solutions. Note that the construction phase often gives a solution inwhich hard constraints are violated, and so the improvement phase also needsto improve the hard constraints. The hyper-heuristic divides the search intostages where each stage takes a prexed amount of time (tstage). In each stage,rstly and repeatedly, one of the 9 mutational heuristics is applied and themove is accepted if it is improving or is not worsening by more than a smallamount. If no improvement is achieved during a stage, a hill climbing phase isapplied using the 2 hill climbing heuristics. Unlike most of the mutational oper-ators, these 2 hill-climbing heuristics are capable of making quite large changesto a solution. The hill climbing phase is itself also slightly non-standard. Oneof the operators is designed using neighbourhood structures based on ejectionchains while the other operator is a type of rst improvement hill climbingoperator. Both hill climbing operators attempt to make moves which respecta particular constraint type while hoping to improve upon the other types ofconstraint violations but might have a net worsening of the objective, how-ever, then such worsening moves are rejected. A hill climbing step is alwaysnon-worsening and so can be repeatedly applied in standard fashion until alocal minimum is reached. A notable dierence from standard methods (suchas in memetic algorithms) is that we found that performance is better if thehill climbing is not applied if the mutational operators managed to improvethe best solution. We suspect that excessive use of the hill climbing somehowgives over-optimised local solutions that afterwards lead to restricted move-ment within the search space.In summary, we have developed and applied a hyper-heuristic to intelli-gently and eectively exploit a suite of neighbourhood move operators. Sincethe aim of hyper-heuristics is to separate adaptive search control from thedetails of the specic domain, we naturally also envisage our hyper-heuristiccould be applied to other PATAT-related problems, such as to the timetablingof university examinations and courses.References1. Burke, E.K., Gendreau, M., Hyde, M., Kendall, G., Ochoa, G., Ozcan, E., Qu, R.: Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society(to appear)2. Even, S., Itai, A., Shamir, A.: On the Complexity of Timetable and MulticommodityFlow Problems. SIAM Journal on Computing 5(4), 691{703 (1976)3. Ozcan, E., Bilgin, B., Korkmaz, E.E.: A comprehensive analysis of hyper-heuristics. In-telligent Data Analysis 12(1), 3{23 (2008)4. Pillay, N.: An overview of school timetabling research. In: Proceedings of the 8th In-ternational Conference on the Practice and Theory of Automated Timetabling (PATAT2010), pp. 321{335 (2010)5. Post, G., Gaspero, L.D., Kingston, J.H., McCollum, B., Schaerf, A.: The third interna-tional timetabling competition. In: Proceedings of the Ninth International Conferenceon the Practice and Theory of Automated Timetabling (PATAT 2012) (2012)

HySST: hyper-heuristic search strategies and timetabling

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HySST: hyper-heuristic search strategies and timetabling

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