A review of the literature on local search algorithms for MAX-SAT

The satisfiability problem in propositional logic (SAT) is the task to decide for a given propositional formula whether it has a model. This problem plays a prominent role in various areas of computer science, mathematical logic and artificial intelligence, but also in applications such as asynchronous circuit synthesis [29], inductive inference [41], integrity of databases [3], hardware verification and many others. SAT was also the first problem to be proven complete [11] and as such is amongst the central problems in theoretical computer science.

[1]  S Kirkpatrick,et al.  Critical Behavior in the Satisfiability of Random Boolean Expressions , 1994, Science.

[2]  Jens Gottlieb,et al.  Improving the Performance of Evolutionary Algorithms for the Satisfiability Problem by Refining Functions , 1998, PPSN.

[3]  Roberto Battiti,et al.  Solving MAX-SAT with non-oblivious functions and history-based heuristics , 1996, Satisfiability Problem: Theory and Applications.

[4]  Darrell Whitley,et al.  Examining the role of local optima and schema processing in genetic search , 1999 .

[5]  Andrea Roll.  Criticality and Parallelism in GSAT , 2001, Electron. Notes Discret. Math..

[6]  Maurizio Martelli,et al.  Integrity Constraints for Logic Databases , 1985, J. Log. Program..

[7]  Toshihide Ibaraki,et al.  Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT , 1998, COCOON.

[8]  Mauricio G. C. Resende,et al.  A GRASP for satisfiability , 1993, Cliques, Coloring, and Satisfiability.

[9]  Paola Campadelli,et al.  A Genetic Model: Analysis and Application to MAXSAT , 2000, Evolutionary Computation.

[10]  Byungki Cha,et al.  Performance Test of Local Search Algorithms Using New Types of Random CNF Formulas , 1995, IJCAI.

[11]  Mauricio G. C. Resende,et al.  A continuous approach to inductive inference , 1992, Math. Program..

[12]  Brian Borchers,et al.  A Two-Phase Exact Algorithm for MAX-SAT and Weighted MAX-SAT Problems , 1998, J. Comb. Optim..

[13]  Thomas Stützle,et al.  Tabu Search vs. Random Walk , 1997, KI.

[14]  Toshihide Ibaraki,et al.  Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT , 1999, J. Comb. Optim..

[15]  David P. Williamson,et al.  New 3/4-Approximation Algorithms for the Maximum Satisfiability Problem , 1994, SIAM J. Discret. Math..

[16]  Lakhdar Sais,et al.  Tabu Search for SAT , 1997, AAAI/IAAI.

[17]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[18]  Holger H. Hoos,et al.  Stochastic Local Search-Methods , 1998 .

[19]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[20]  Johan Håstad,et al.  Some optimal inapproximability results , 2001, JACM.

[21]  J. Hooker.  Resolution vs. cutting plane solution of inference problems: Some computational experience , 1988 .

[22]  Jeremy Frank,et al.  When Gravity Fails: Local Search Topology , 1997, J. Artif. Intell. Res..

[23]  Toby Walsh,et al.  An Empirical Analysis of Search in GSAT , 1993, J. Artif. Intell. Res..

[24]  Soraya B. Rana.  Examining the Role of Local Optima and Schema Processing in Genetic Search , 1998 .

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

[26]  Panos M. Pardalos,et al.  Approximate solution of weighted MAX-SAT problems using GRASP , 1996, Satisfiability Problem: Theory and Applications.

[27]  Mihalis Yannakakis,et al.  On the approximation of maximum satisfiability , 1992, SODA '92.

[28]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[29]  L. Darrell Whitley,et al.  Genetic Algorithm Behavior in the MAXSAT Domain , 1998, PPSN.

[30]  Bart Selman,et al.  Evidence for Invariants in Local Search , 1997, AAAI/IAAI.

[31]  Dale Schuurmans,et al.  Local search characteristics of incomplete SAT procedures , 2000, Artif. Intell..

[32]  Benjamin W. Wah,et al.  Discrete Lagrangian-Based Search for Solving MAX-SAT Problems , 1997, IJCAI.

[33]  Paola Alimonti.  New Local Search Approximation Techniques for Maximum Generalized Satisfiability Problems , 1996, Inf. Process. Lett..

[34]  Paul Morris,et al.  The Breakout Method for Escaping from Local Minima , 1993, AAAI.

[35]  Rajeev Motwani,et al.  On syntactic versus computational views of approximability , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[36]  Toby Walsh,et al.  Towards an Understanding of Hill-Climbing Procedures for SAT , 1993, AAAI.

[37]  Henry A. Kautz,et al.  Solving Problems with Hard and Soft Constraints Using a Stochastic Algorithm for MAX-SAT , 1995 .

[38]  Bart Selman,et al.  Noise Strategies for Improving Local Search , 1994, AAAI.

[39]  Holger H. Hoos,et al.  GSAT versus Simulated Annealing , 1994, ECAI.

[40]  Roberto Battiti,et al.  Reactive Search, a history-based heuristic for MAX-SAT , 1996 .

[41]  J. K. Lowe,et al.  Some results and experiments in programming techniques for propositional logic , 1986, Comput. Oper. Res..

[42]  Yuichi Asahiro,et al.  Random generation of test instances with controlled attributes , 1993, Cliques, Coloring, and Satisfiability.

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

[44]  John E. Mitchell,et al.  A branch and cut algorithm for MAX-SAT and weighted MAX-SAT , 1996, Satisfiability Problem: Theory and Applications.

[45]  Zhe Wu,et al.  Trap Escaping Strategies in Discrete Lagrangian Methods for Solving Hard Satisfiability and Maximum Satisfiability Problems , 1999, AAAI/IAAI.

[46]  A. D. Parreira,et al.  Variable Neighbourhood Search for Maximum Weight Satisfiability Problem , 2000 .

[47]  Jeremy Frank,et al.  Weighting for Godot: Learning Heuristics for GSAT , 1996, AAAI/IAAI, Vol. 1.

[48]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[49]  Jun Gu,et al.  Asynchronous circuit synthesis with Boolean satisfiability , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[50]  Panos M. Pardalos,et al.  Satisfiability Problem: Theory and Applications , 1997 .

[51]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[52]  William M. Spears,et al.  Simulated annealing for hard satisfiability problems , 1993, Cliques, Coloring, and Satisfiability.

[53]  Luca Trevisan,et al.  Gadgets, Approximation, and Linear Programming , 2000, SIAM J. Comput..

[54]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[55]  Christian Blum,et al.  Critical Parallelization of Local Search for MAX-SAT , 2001, AI*IA.

[56]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[57]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[58]  Ian P. Gent,et al.  Unsatisfied Variables in Local Search , 1995 .

[59]  Holger H. Hoos,et al.  Stochastic local search - methods, models, applications , 1998, DISKI.

[60]  Eugene C. Freuder,et al.  Comparative studies of constraint satisfaction and Davis-Putnam algorithms for maximum satisfiability problems , 1993, Cliques, Coloring, and Satisfiability.

[61]  Roberto Battiti,et al.  Reactive search, a history-sensitive heuristic for MAX-SAT , 1997, JEAL.

[62]  Panos M. Pardalos,et al.  A Parallel GRASP for MAX-SAT Problems , 1996, PARA.

[63]  Uriel Feige,et al.  Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.