Bee swarm optimization for solving the MAXSAT problem using prior knowledge

This paper explores rule decomposition for solving the MAXSAT problem. Four approaches are proposed to steer a bee swarm optimization metaheuristic. Two decomposition methods are proposed: direct and indirect. The first one applies the Kmeans algorithm, while the second one transforms a MAXSAT instance into a transactional database before performing decomposition using the Apriori algorithm. Several experiments conducted on DIMACS benchmark instances, and some other hard and large SAT instances have been carried out. Results show clear improvement compared to the state-of-the-art MAXSAT algorithms in terms of the quality of the obtained solutions. They show that the proposed approaches are stable when dealing with hard instances such as Parity8 from DIMACS. Results also demonstrate the superiority of the proposed approaches for medium and large instances. The proposed approaches could be applied to other optimization problems such as the weighted MAXSAT problem, the MAXCSP and coloring problems. They may also be adapted for other metaheuristics and decomposition methods.

[1]  Wei Wu,et al.  CCLS: An Efficient Local Search Algorithm for Weighted Maximum Satisfiability , 2015, IEEE Transactions on Computers.

[2]  Shaowei Cai,et al.  An effective variable selection heuristic in SLS for weighted Max-2-SAT , 2015, J. Heuristics.

[3]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[4]  Lakhdar Sais,et al.  Decomposition Based SAT Encodings for Itemset Mining Problems , 2015, PAKDD.

[5]  Carlos Ansótegui,et al.  The Community Structure of SAT Formulas , 2012, SAT.

[6]  Djamal Habet,et al.  On the Extension of Learning for Max-SAT , 2014, STAIRS.

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

[8]  Philip S. Yu,et al.  Top 10 algorithms in data mining , 2007, Knowledge and Information Systems.

[9]  Tsutomu Maruyama,et al.  FPGA acceleration of SAT/Max-SAT solving using variable-way cache , 2014, 2014 24th International Conference on Field Programmable Logic and Applications (FPL).

[10]  Vangelis Th. Paschos,et al.  Approximating MAX SAT by moderately exponential and parameterized algorithms , 2012, Theor. Comput. Sci..

[11]  Kazuhisa Seto,et al.  Solving Sparse Instances of Max SAT via Width Reduction and Greedy Restriction , 2014, Theory of Computing Systems.

[12]  Dirk Thierens,et al.  On the usefulness of linkage processing for solving MAX-SAT , 2013, GECCO '13.

[13]  Tomasz Imielinski,et al.  Mining association rules between sets of items in large databases , 1993, SIGMOD Conference.

[14]  Holger H. Hoos,et al.  UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT & MAX-SAT , 2004, SAT.

[15]  Alexander A. Kolokolov,et al.  Analysis and Solving SAT and MAX-SAT Problems Using an L-partition Approach , 2013, J. Math. Model. Algorithms Oper. Res..

[16]  Enrique Alba,et al.  Fitness Probability Distribution of Bit-Flip Mutation , 2013, Evolutionary Computation.

[17]  Lakhdar Sais,et al.  Boolean satisfiability for sequence mining , 2013, CIKM.

[18]  Allen Van Gelder,et al.  Partitioning Methods for Satisfiability Testing on Large Formulas , 2000, Inf. Comput..

[19]  Rahul Santhanam,et al.  Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP , 2015, SAT.

[20]  Jiangchuan Liu,et al.  Broadband wireless network planning using evolutionary algorithms , 2013, 2013 IEEE Congress on Evolutionary Computation.

[21]  Habiba Drias,et al.  Cooperative Bees Swarm for Solving the Maximum Weighted Satisfiability Problem , 2005, IWANN.

[22]  Youcef Djenouri,et al.  Bees Swarm Optimization Metaheuristic Guided by Decomposition for Solving MAX-SAT , 2016, ICAART.

[23]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[24]  Giandomenico Spezzano,et al.  Parallel hybrid method for SAT that couples genetic algorithms and local search , 2001, IEEE Trans. Evol. Comput..

[25]  Noureddine Bouhmala,et al.  A Variable Neighborhood Walksat-Based Algorithm for MAX-SAT Problems , 2014, TheScientificWorldJournal.

[26]  Habiba Drias,et al.  Multilevel Bee Swarm Optimization for Large Satisfiability Problem Instances , 2013, IDEAL.

[27]  Alex S. Fukunaga,et al.  Evolving Local Search Heuristics for SAT Using Genetic Programming , 2004, GECCO.

[28]  Daniel C. Lee,et al.  MAX-SAT problem using evolutionary algorithms , 2014, 2014 IEEE Symposium on Swarm Intelligence.

[29]  Matthias Poloczek,et al.  On Some Recent Approximation Algorithms for MAX SAT , 2014, LATIN.

[30]  Noureddine Bouhmala.  A multilevel learning automata for MAX-SAT , 2015, Int. J. Mach. Learn. Cybern..

[31]  Djamal Habet,et al.  Local Max-Resolution in Branch and Bound Solvers for Max-SAT , 2014, 2014 IEEE 26th International Conference on Tools with Artificial Intelligence.

[32]  Ali Husseinzadeh Kashan,et al.  DisABC: A new artificial bee colony algorithm for binary optimization , 2012, Appl. Soft Comput..

[33]  Habiba Drias,et al.  Pruning irrelevant association rules using knowledge mining , 2014, Int. J. Bus. Intell. Data Min..

[34]  Bart Selman,et al.  Domain-Independent Extensions to GSAT : Solving Large StructuredSatis ability , 1993 .

[35]  Djamel Djenouri,et al.  Data Mining-Based Decomposition for Solving the MAXSAT Problem: Toward a New Approach , 2017, IEEE Intelligent Systems.

[36]  Jin-Kao Hao,et al.  GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem , 2006, Evolutionary Computation.

[37]  Graham Kendall,et al.  Population based Monte Carlo tree search hyper-heuristic for combinatorial optimization problems , 2015, Inf. Sci..

[38]  Habiba Drias,et al.  Datamining techniques and swarm intelligence for problem solving: Application to SAT , 2013, 2013 World Congress on Nature and Biologically Inspired Computing.

[39]  Maria Ercsey-Ravasz,et al.  Analog dynamics for solving max-SAT problems , 2014, 2014 14th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA).

[40]  Reza Akbari,et al.  A novel bee swarm optimization algorithm for numerical function optimization , 2010 .

[41]  Patrice Boizumault,et al.  Guiding VNS with Tree Decomposition , 2011, 2011 IEEE 23rd International Conference on Tools with Artificial Intelligence.

[42]  Habiba Drias,et al.  Bees swarm optimisation using multiple strategies for association rule mining , 2014, Int. J. Bio Inspired Comput..

[43]  Riccardo Poli,et al.  Extending Particle Swarm Optimisation via Genetic Programming , 2005, EuroGP.