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Evidence for Invariants in Local Search
 IN PROCEEDINGS OF AAAI97
, 1997
"... It is well known that the performance of a stochastic local search procedure depends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general priniciples for tuning the procedures. We present two statisti ..."
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Cited by 183 (11 self)
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It is well known that the performance of a stochastic local search procedure depends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general priniciples for tuning the procedures. We present two statistical measures of the local search process that allow one to quickly find the optimal noise settings. These properties are independent of the fine details of the local search strategies, and appear to be relatively independent of the structure of the problem domains. We applied these principles to the problem of evaluating new search heuristics, and discovered two promising new strategies.
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 169 (14 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
Iterated local search
 Handbook of Metaheuristics, volume 57 of International Series in Operations Research and Management Science
, 2002
"... Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions th ..."
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Cited by 121 (15 self)
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Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for a given optimization engine. The success of Iterated Local Search lies in the biased sampling of this set of local optima. How effective this approach turns out to be depends mainly on the choice of the local search, the perturbations, and the acceptance criterion. So far, in spite of its conceptual simplicity, it has lead to a number of stateoftheart results without the use of too much problemspecific knowledge. But with further work so that the different modules are well adapted to the problem at hand, Iterated Local Search can often become a competitive or even state of the art algorithm. The purpose of this review is both to give a detailed description of this metaheuristic and to show where it stands in terms of performance. O.M. acknowledges support from the Institut Universitaire de France. This work was partially supported by the “Metaheuristics Network”, a Research Training Network funded by the Improving Human Potential programme of the CEC, grant HPRNCT199900106. The information provided is the sole responsibility of the authors and does not reflect the Community’s opinion. The Community is not responsible for any use that might be made of data appearing in this publication. 1 1
Local search algorithms for SAT: An empirical evaluation
 JOURNAL OF AUTOMATED REASONING
, 2000
"... Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large num ..."
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Cited by 62 (18 self)
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Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly wellknown families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SATencoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithmdependent and problemdependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the bestperforming algorithms and shows how this can be overcome.
Tabu Search for SAT
 In Proceedings of AAAI’97
"... In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional ..."
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Cited by 43 (2 self)
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In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional
New Upper Bounds for Maximum Satisfiability
 Journal of Algorithms
, 1999
"... The (unweighted) Maximum Satisfiability problem (MaxSat) is: given a boolean formula in conjunctive normal form, find a truth assignment that satisfies the most number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved i ..."
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Cited by 36 (2 self)
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The (unweighted) Maximum Satisfiability problem (MaxSat) is: given a boolean formula in conjunctive normal form, find a truth assignment that satisfies the most number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved in time O(F  1.3803 K ), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F . We also prove the time bounds O(F 1.3995 k ), where k is the maximum number of satisfiable clauses, and O(1.1279 F  ) for the same problem. For Max2Sat this implies a bound of O(1.2722 K ). # An extended abstract of this paper was presented at the 26th International Colloquium on Automata, Languages, and Programming (ICALP'99), LNCS 1644, SpringerVerlag, pages 575584, held in Prague, Czech Republic, July 1115, 1999. + Supported by a Feodor Lynen fellowship (1998) of the Alexander von HumboldtStiftung, Bonn, and the Center for Discrete Ma...
Iterated Robust Tabu Search for MAXSAT
 In Proc. of the 16th Conf. of the Canadian Society for Computational Studies of Intelligence
, 2003
"... MAXSAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for M ..."
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Cited by 23 (7 self)
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MAXSAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two wellknown SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current stateoftheart MAXSAT algorithms on various widely studied classes of unweighted and weighted MAXSAT instances, particularly for Random3SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAXSAT instances.
Exploiting Variable Dependency in Local Search
 In Abstracts of the Poster Sessions of IJCAI97
, 1997
"... Stochastic search has recently been shown to be successful for solving large boolean satisfiability problems. However, systematic methods tend to be more effective in problem domains with a large number of dependent variables: that is, variables whose truth values are directly determined by a smalle ..."
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Cited by 19 (1 self)
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Stochastic search has recently been shown to be successful for solving large boolean satisfiability problems. However, systematic methods tend to be more effective in problem domains with a large number of dependent variables: that is, variables whose truth values are directly determined by a smaller set of independent variables. In systematic search, truth values can be efficiently propagated from the independent to the dependent variables by unit propagation. Such propagation is more expensive in traditional stochastic procedures. In this paper we propose a mechanism for effectively dealing with dependent variables in stochastic search. We also provide empirical data showing the procedure outperforms the best previous stochastic and systematic search procedures on large formulas with a high ratio of dependent to independent variables. 1 Introduction Recent years have seen significant progress in our ability to solve large propositional satisfiability problems. Randomly generated pro...
New upper bounds for MaxSat
 Charles University, Praha, Faculty of Mathematics and Physics
, 1998
"... We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(F  · 1.3972 K), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time b ..."
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Cited by 15 (5 self)
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We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(F  · 1.3972 K), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time bounds O(F  · 1.3995 k), where k is the maximum number of satisfiable clauses, and O((1.1279) F  ) for the same problem. For Max2Sat this implies a bound of O(1.2722 K). An exponential time approximation algorithm by Dantsin et al. uses an exact algorithm for MaxSat as a building block and is therefore also improved.
MAGMA: A Multiagent Architecture for Metaheuristics
 IEEE TRANS. ON SYSTEMS, MAN AND CYBERNETICS  PART B
, 2002
"... In this work we introduce a multiagent architecture conceived as a conceptual and practical framework for metaheuristic algorithms (MAGMA, MultiAGent Metaheuristics Architecture). Metaheuristics can be seen as the result of the interaction among di erent kinds of agents: level 0 agents constructing ..."
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Cited by 11 (1 self)
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In this work we introduce a multiagent architecture conceived as a conceptual and practical framework for metaheuristic algorithms (MAGMA, MultiAGent Metaheuristics Architecture). Metaheuristics can be seen as the result of the interaction among di erent kinds of agents: level 0 agents constructing initial solutions, level1 agents improving solutions and level2 agents providing the high level strategy. In this framework, classical metaheuristic algorithms can be smoothly accommodated and extended, and new algorithms can be easily designed by defining which agents are involved and their interactions. Furthermore, with the introduction of a fourth level of agents, coordinating lower level agents, MAGMA can also describe, in a uniform way, cooperative search and, in general, any combination of metaheuristics. We propose