Curriculum-based course timetabling with SAT and MaxSAT

This paper describes our work on applying novel techniques based on propositional satisfiability (SAT) solvers and optimizers to the Curriculum-based Course Timetabling problem.Out of 32 standard benchmark instances derived from the Second International Timetabling Competition held in 2007, our techniques yield the best known solutions for 21 of them (19 of them being optimal), improving the previously best known solutions for 9.In addition, we obtain 18 new lower bounds for this benchmark set by applying a new full (Weighted) Partial MaxSAT approach of the Curriculum-based Course Timetabling problem.

[1]  Kaile Su,et al.  Within-problem Learning for Efficient Lower Bound Computation in Max-SAT Solving , 2008, AAAI.

[2]  Maria Luisa Bonet,et al.  Solving (Weighted) Partial MaxSAT through Satisfiability Testing , 2009, SAT.

[3]  Vasco M. Manquinho,et al.  Algorithms for Weighted Boolean Optimization , 2009, SAT.

[4]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[5]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[6]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[7]  K. Sakallah,et al.  Generic ILP versus specialized 0-1 ILP: an update , 2002, ICCAD 2002.

[8]  Albert Oliveras,et al.  A Framework for Certified Boolean Branch-and-Bound Optimization , 2010, Journal of Automated Reasoning.

[9]  Marco Cadoli,et al.  Compiling Problem Specifications into SAT , 2001, ESOP.

[10]  Sharad Malik,et al.  On Solving the Partial MAX-SAT Problem , 2006, SAT.

[11]  Olivier Bailleux,et al.  Efficient CNF Encoding of Boolean Cardinality Constraints , 2003, CP.

[12]  Jin-Kao Hao,et al.  Adaptive Tabu Search for course timetabling , 2010, Eur. J. Oper. Res..

[13]  Cesare Tinelli,et al.  Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.

[14]  Lawrence Ryan Efficient algorithms for clause-learning SAT solvers , 2004 .

[15]  Albert Oliveras,et al.  MiniMaxSAT: An Efficient Weighted Max-SAT solver , 2008, J. Artif. Intell. Res..

[16]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002 .

[17]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[18]  Tomáš Müller,et al.  Constraint-based Timetabling , 2002 .

[19]  Tom ITC2007 Solver Description: A Hybrid Approach , 2007 .

[20]  Adnan Darwiche,et al.  Solving Weighted Max-SAT Problems in a Reduced Search Space: A Performance Analysis , 2008, J. Satisf. Boolean Model. Comput..

[21]  Matthew W. Moskewicz,et al.  Cha : Engineering an e cient SAT solver , 2001, DAC 2001.

[22]  Joao Marques-Silva,et al.  Algorithms for Maximum Satisfiability using Unsatisfiable Cores , 2008, 2008 Design, Automation and Test in Europe.

[23]  Philipp Kostuch,et al.  The University Course Timetabling Problem with a Three-Phase Approach , 2004, PATAT.

[24]  Filip Mari,et al.  Timetabling Based on SAT Encoding: a Case Study , 2008 .

[25]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[26]  Albert Oliveras,et al.  Cardinality Networks and Their Applications , 2009, SAT.

[27]  DavisMartin,et al.  A Computing Procedure for Quantification Theory , 1960 .

[28]  Sharad Malik,et al.  Validating SAT solvers using an independent resolution-based checker: practical implementations and other applications , 2003, 2003 Design, Automation and Test in Europe Conference and Exhibition.

[29]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002, Discret. Appl. Math..

[30]  Armin Biere,et al.  PicoSAT Essentials , 2008, J. Satisf. Boolean Model. Comput..

[31]  Barry McCollum,et al.  The Second International Timetabling Competition (ITC-2007): Curriculum-based Course Timetabling (Track 3) — preliminary presentation — , 2007 .

[32]  Teresa Alsinet,et al.  An efficient solver for weighted Max-SAT , 2008, J. Glob. Optim..

[33]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[34]  Philipp Hertel,et al.  Formalizing Dangerous SAT Encodings , 2007, SAT.