Efficient local search for very large-scale satisfiability problems
ACM SIGART Bulletin
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Improvements to propositional satisfiability search algorithms
Improvements to propositional satisfiability search algorithms
A Parallel GRASP for MAX-SAT Problems
PARA '96 Proceedings of the Third International Workshop on Applied Parallel Computing, Industrial Computation and Optimization
Domain-independent extensions to GSAT: solving large structured satisfiability problems
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Local search algorithms for partial MAXSAT
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Variable-selection heuristics in local search for SAT
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
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For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most effective approaches. Most of the local search algorithms are based on the 1-flip neighborhood, which is the set of solutions obtainable by flipping the truth assignment of one variable. In this paper, we consider r-flip neighborhoods for r ≥ 2, and propose, for r = 2, 3, new implementations that reduce the number of candidates in the neighborhood without sacrificing the solution quality. For 2-flip (resp., 3-flip) neighborhood, we show that its expected size is O(n + m) (resp., O(m + t2n)), which is usually much smaller than the original size O(n2) (resp., O(n3)), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance. These neighborhoods are then used under the framework of tabu search etc., and compared with other existing algorithms based on 1-flip neighborhood. The results exhibit good prospects of the proposed algorithms.