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45
Generating satisfiable problem instances
 In AAAI/IAAI
, 2000
"... A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generat ..."
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Cited by 88 (9 self)
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A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generator and a complete search method to filter out the unsatisfiable instances. Unfortunately, this approach cannot be used to create problem instances that are beyond the reach of complete search methods. So far, it has proven to be surprisingly difficult to develop a direct generator for satisfiable instances only. In this paper, we propose a generator that only outputs satisfiable problem instances. We also show how one can finely control the hardness of the satisfiable instances by establishing a connection between problem hardness and a new kind of phase transition phenomenon in the space of problem instances. Finally, we use our problem distribution to show the easyhardeasy pattern in search complexity for local search procedures, analogous to the previously reported pattern for complete search methods.
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
When Gravity Fails: Local Search Topology
 Journal of Artificial Intelligence Research
, 1997
"... Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize platea ..."
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Cited by 71 (1 self)
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Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize plateaus for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e., global m...
Clustering at the Phase Transition
 In Proc. of the 14th Nat. Conf. on AI
, 1997
"... Many problem ensembles exhibit a phase transition that is associated with a large peak in the average cost of solving the problem instances. However, this peak is not necessarily due to a lack of solutions: indeed the average number of solutions is typically exponentially large. Here, we study this ..."
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Cited by 49 (4 self)
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Many problem ensembles exhibit a phase transition that is associated with a large peak in the average cost of solving the problem instances. However, this peak is not necessarily due to a lack of solutions: indeed the average number of solutions is typically exponentially large. Here, we study this situation within the context of the satisfiability transition in Random 3SAT. We find that a significant subclass of instances emerges as we cross the phase transition. These instances are characterized by having about 8595% of their variables occurring in unary prime implicates (UPIs), with their remaining variables being subject to few constraints. In such instances the models are not randomly distributed but all lie in a cluster that is exponentially large, but still admits a simple description. Studying the effect of UPIs on the local search algorithm Wsat shows that these "singlecluster" instances are harder to solve, and we relate their appearance at the phase transition to the peak...
Backbone Fragility and the Local Search Cost Peak
 Journal of Artificial Intelligence Research
, 2000
"... The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and lar ..."
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Cited by 45 (3 self)
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The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over di#erent instances. We make a number of significant contributions to the analysis of WSat on highcost random instances, using the recentlyintroduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for smallbackbone instances but is much less relevant for the largebackbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSat's search. This pattern leads us to introduce a measure of the ba...
A New Algorithm for RNA Secondary Structure Design
, 2003
"... The function of many RNAs crucially depends on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g.,in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA ..."
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Cited by 41 (2 self)
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The function of many RNAs crucially depends on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g.,in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA nanostructures. Here, we present a new algorithm for solving the following RNA secondary structure design problem: Given a secondary structure, find an RNA sequence (if any) that is predicted to fold to that structure. Unlike the (pseudoknotfree) secondary structure prediction problem, this problem appears to be computationally hard. Our new algorithm, "RNA Secondary Structure Designer (RNASSD)", is based on stochastic local search, a prominent general approach for solving hard combinatorial problems. A thorough empirical...
SATEncodings, Search Space Structure, and Local Search Performance
, 1999
"... Stochastic local search (SLS) algorithms for propositional satisfiability testing (SAT) have become popular and powerful tools for solving suitably encoded hard combinatorial from different domains like, e.g., planning. Consequently, there is a considerable interest in finding SATencodings whi ..."
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Cited by 40 (7 self)
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Stochastic local search (SLS) algorithms for propositional satisfiability testing (SAT) have become popular and powerful tools for solving suitably encoded hard combinatorial from different domains like, e.g., planning. Consequently, there is a considerable interest in finding SATencodings which facilitate the efficient application of SLS algorithms. In this work, we study how two encodings schemes for combinatorial problems, like the wellknown Constraint Satisfaction or Hamilton Circuit Problem, affect SLS performance on the SATencoded instances. To explain the observed performance differences, we identify features of the induces search spaces which affect SLS performance. We furthermore present initial results of a comparitive analysis of the performance of the SATencoding andsolving approach versus that of native SLS algorithms directly applied to the unencoded problem instances. 1
Tabu Search for Maximal Constraint Satisfaction Problems
 Proceedings of Third International Conference on Principles and Practice of Constraint Programming (CP97
, 1997
"... . This paper presents a Tabu Search (TS) algorithm for solving maximal constraint satisfaction problems. The algorithm was tested on a wide range of random instances (up to 500 variables and 30 values) . Comparisons were carried out with a minconflicts+randomwalk (MCRW) algorithm. Empirical eviden ..."
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Cited by 35 (4 self)
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. This paper presents a Tabu Search (TS) algorithm for solving maximal constraint satisfaction problems. The algorithm was tested on a wide range of random instances (up to 500 variables and 30 values) . Comparisons were carried out with a minconflicts+randomwalk (MCRW) algorithm. Empirical evidence shows that the TS algorithm finds results which are better than that of the MCRW algorithm.the TS algorithm is 3 to 5 times faster than the MCRW algorithm to find solutions of the same quality. Keywords: Tabu search, constraint solving, combinatorial optimization. 1 Introduction A finite Constraint Network (CN) is composed of a finite set X of variables, a set D of finite domains and a set C of constraints over subsets of X. A constraint is a subset of the Cartesian product of the domains of the variables involved that specifies which combinations of values are compatible. A CN is said to be binary if all the constraints have 2 variables. Given a CN, the Constraint Satisfaction Problem ...
Ants can solve Constraint Satisfaction Problems
 IEEE Transactions on Evolutionary Computation
, 2001
"... In this paper we describe a new incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone info ..."
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Cited by 28 (10 self)
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In this paper we describe a new incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone information is used to guide the search, as a heuristic for choosing values to be assigned to variables.
Problem Difficulty for Tabu Search in JobShop Scheduling
 Artificial Intelligence
, 2002
"... Tabu search algorithms are among the most effective approaches for solving the jobshop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from sim ..."
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Cited by 22 (8 self)
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Tabu search algorithms are among the most effective approaches for solving the jobshop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP  complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating suboptimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very highcost problem instances. Second, the model is significantly less accurate for structured, nonrandom JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than jobshop scheduling.