3,855 research outputs found
The Configurable SAT Solver Challenge (CSSC)
It is well known that different solution strategies work well for different
types of instances of hard combinatorial problems. As a consequence, most
solvers for the propositional satisfiability problem (SAT) expose parameters
that allow them to be customized to a particular family of instances. In the
international SAT competition series, these parameters are ignored: solvers are
run using a single default parameter setting (supplied by the authors) for all
benchmark instances in a given track. While this competition format rewards
solvers with robust default settings, it does not reflect the situation faced
by a practitioner who only cares about performance on one particular
application and can invest some time into tuning solver parameters for this
application. The new Configurable SAT Solver Competition (CSSC) compares
solvers in this latter setting, scoring each solver by the performance it
achieved after a fully automated configuration step. This article describes the
CSSC in more detail, and reports the results obtained in its two instantiations
so far, CSSC 2013 and 2014
Why solutions can be hard to find: a featural theory of cost for a local search algorithm on random satisfiability instances
The local search algorithm WSat is one of the most successful algorithms for solving
the archetypal NP-complete problem of satisfiability (SAT). It is notably effective at
solving Random-3-SAT instances near the so-called 'satisfiability threshold', which
are thought to be universally hard. However, WSat still shows a peak in search
cost near the threshold and large variations in cost over different instances. Why
are solutions to the threshold instances so hard to find using WSat? What features
characterise threshold instances which make them difficult for WSat to solve?
We make a number of significant contributions to the analysis of WSat on these
high-cost random instances, using the recently-introduced concept of the backbone
of a SAT instance. The backbone is the set of literals which are implicates of an
instance. We find that the number of solutions predicts the cost well for small-backbone
instances but is much less relevant for the large-backbone instances which appear near
the threshold and dominate in the overconstrained region. We undertake a detailed
study of the behaviour of the algorithm during search and uncover some interesting
patterns. These patterns lead us to introduce a measure of the backbone fragility of
an instance, which indicates how persistent the backbone is as clauses are removed.
We propose that high-cost random instances for WSat are those with large backbones
which are also backbone-fragile. We suggest that the decay in cost for WSat beyond
the satisfiability threshold, which has perplexed a number of researchers, is due to the
decreasing backbone fragility. Our hypothesis makes three correct predictions. First,
that a measure of the backbone robustness of an instance (the opposite to backbone
fragility) is negatively correlated with the WSat cost when other factors are controlled
for. Second, that backbone-minimal instances (which are 3-SAT instances altered so
as to be more backbone-fragile) are unusually hard for WSat. Third, that the clauses
most often unsatisfied during search are those whose deletion has the most effect on
the backbone.
Our analysis of WSat on random-3-SAT threshold instances can be seen as a featural
theory of WSat cost, predicting features of cost behaviour from structural features of
SAT instances. In this thesis, we also present some initial studies which investigate
whether the scope of this featural theory can be broadened to other kinds of random
SAT instance. random-2+p-SAT interpolates between the polynomial-time problem
Random-2-SAT when p = 0 and Random-3-SAT when p = 1. At some value
p ~ pq ~ 0.41, a dramatic change in the structural nature of instances is predicted by
statistical mechanics methods, which may imply the appearance of backbone fragile
instances. We tested NovELTY+, a recent variant of WSat, on rand o m- 2 +p-SAT
and find some evidence that growth of its median cost changes from polynomial to
superpolynomial between p = 0.3 and p = 0.5. We also find evidence that it is the
onset of backbone fragility which is the cause of this change in cost scaling: typical
instances at p — 0.5 are more backbone-fragile than their counterparts at p — 0.3.
Not-All-Equal (NAE) 3-SAT is a variant of the SAT problem which is similar
to it in most respects. However, for NAE 3-SAT instances no implicate literals are
possible. Hence the backbone for NAE 3-SAT must be redefined. We show that under
a redefinition of the backbone, the pattern of factors influencing WSat cost at the
NAE Random-3-SAT threshold is much the same as in Random-3-SAT, including
the role of backbone fragility
An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem
Although Path-Relinking is an effective local search method for many
combinatorial optimization problems, its application is not straightforward in
solving the MAX-SAT, an optimization variant of the satisfiability problem
(SAT) that has many real-world applications and has gained more and more
attention in academy and industry. Indeed, it was not used in any recent
competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a
new local search algorithm called IPBMR for the MAX-SAT, that remedies the
drawbacks of the Path-Relinking method by using a careful combination of three
components: a new strategy named Path-Breaking to avoid unpromising regions of
the search space when generating trajectories between two elite solutions; a
weak and a strong mutation strategies, together with restarts, to diversify the
search; and stochastic path generating steps to avoid premature local optimum
solutions. We then present experimental results to show that IPBMR outperforms
two of the best state-of-the-art MAX-SAT solvers, and an empirical
investigation to identify and explain the effect of the three components in
IPBMR
Backbone Fragility and the Local Search Cost Peak
The local search algorithm WSat is one of the most successful algorithms for
solving the satisfiability (SAT) problem. It is notably effective at solving
hard Random 3-SAT instances near the so-called `satisfiability threshold', but
still shows a peak in search cost near the threshold and large variations in
cost over different instances. We make a number of significant contributions to
the analysis of WSat on high-cost random instances, using the
recently-introduced 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 small-backbone instances but is much
less relevant for the large-backbone 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 backbone
fragility of an instance, which indicates how persistent the backbone is as
clauses are removed. We propose that high-cost random instances for local
search are those with very large backbones which are also backbone-fragile. We
suggest that the decay in cost beyond the satisfiability threshold is due to
increasing backbone robustness (the opposite of backbone fragility). Our
hypothesis makes three correct predictions. First, that the backbone robustness
of an instance is negatively correlated with the local search cost when other
factors are controlled for. Second, that backbone-minimal instances (which are
3-SAT instances altered so as to be more backbone-fragile) are unusually hard
for WSat. Third, that the clauses most often unsatisfied during search are
those whose deletion has the most effect on the backbone. In understanding the
pathologies of local search methods, we hope to contribute to the development
of new and better techniques
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