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Complexity of continuous, 3SATlike constraint satisfaction problems
 In IJCAI01 Workshop on Stochastic Search Algorithms
, 2001
"... Continuous constrained optimization is at the core of many realworld applications such as planning, scheduling, control, and diagnosis of physical systems (car, planes, factories). Effective constraintbased techniques must handle the complexity of realworld continuous constraint problems by dynami ..."
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Continuous constrained optimization is at the core of many realworld applications such as planning, scheduling, control, and diagnosis of physical systems (car, planes, factories). Effective constraintbased techniques must handle the complexity of realworld continuous constraint problems by dynamically adapting solvers to the structure of the problem. Toward this end, we analyze continuous constraint satisfaction problem formulations based on (discrete) 3SAT problems, which have a strong relation between structure and search cost. We compare the search complexities of three different problem formulations and three randomized search algorithms. This allows us not only to compare different problems and solution approaches, but also to connect back to results from similar studies on SAT problems. In particular, we find that median search cost is characterized by simple parameters such as the constrainttovariable ratio, and that discrete search algorithms such as GSAT have continuous counterparts with similar behavior. 1
SAT, local search dynamics and density of states
"... This paper presents an analysis of the search space of the well known NPcomplete SAT problem. The analysis is based on a measure called "density of states" (d.o.s). We show experimentally that the distribution of assignments can be approximated by a normal law. This distribution allows us ..."
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This paper presents an analysis of the search space of the well known NPcomplete SAT problem. The analysis is based on a measure called "density of states" (d.o.s). We show experimentally that the distribution of assignments can be approximated by a normal law. This distribution allows us to get some insights about the behavior of local search algorithms.
Abstract Towards a Characterisation of the Behaviour of Stochastic Local Search Algorithms for SAT
"... Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the runtime behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the runtime distribution provi ..."
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Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the runtime behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the runtime distribution provides important information about the behaviour of SLS algorithms. In this paper we investigate the empirical runtime distributions for Walksat, one of the most powerful SLS algorithms for the Propositional Satisfiability Problem (SAT). Using statistical analysis techniques, we show that on hard Random3SAT problems, Walksat’s runtime behaviour can be characterised by exponential distributions. This characterisation can be generalised to various SLS algorithms for SAT and to encoded problems from other domains. This result also has a number of consequences which are of theoretical as well as practical interest. One of these is the fact that these algorithms can be easily parallelised such that optimal speedup is achieved for hard problem instances. 1
Boosting Local Search with Artificial Ants (long paper
 Research Report, LISI
"... Local Search: Incomplete approaches for solving CSPs are usually based on local search —or neighborhood search — techniques [4]: the idea is to start from an inconsistent complete assignment of values to the variables,and then gradually and iteratively repair it by changing some variablevalue assig ..."
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Local Search: Incomplete approaches for solving CSPs are usually based on local search —or neighborhood search — techniques [4]: the idea is to start from an inconsistent complete assignment of values to the variables,and then gradually and iteratively repair it by changing some variablevalue assignments,preferably towards better ones. One of the main problems with local search is that it may get stuck in local optima,i.e.,complete assignments that cannot be locally improved by changing one conflicting variable/value assignment,and that are not globally optimal. Therefore,local search has been combined with different metaheuristics in order to help it escape from local optima,e.g.,simulated annealing or tabu search [2]. Local search has proved to be effective and efficient to solve very large CSPs. However,like complete search,it often has more difficulties in solving problems that are within the phase transition region —where the solvable probability is around 50%. Indeed,before the phase transition region, problems are weakly constrained and have many solutions so that local search can usually easily find one. On the other side,beyond the phase transition region,problems
SLS Algorithms for SAT: Irregular Instances, Search Stagnation, and Mixture Models (Extended Abstract)
, 2002
"... Holger H. Hoos University of British Columbia Computer Science Department hoos@cs.ubc.ca 1 ..."
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Holger H. Hoos University of British Columbia Computer Science Department hoos@cs.ubc.ca 1
unknown title
"... Stochastic local search (SLS) algorithms for prepositional 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 fa ..."
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Stochastic local search (SLS) algorithms for prepositional 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
THE REQUIREMENTS FOR THE DEGREE OF
, 2004
"... c ○ Kevin R. G. Smyth, 2004In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this ..."
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c ○ Kevin R. G. Smyth, 2004In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature)