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Improving probability selection based weights for satisfiability problems
Boolean Satisfiability problem (SAT) plays a prominent role in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications. Algorithms for solving SAT problems can be categorized into two main classes: complete algorithms and incomplete algorithms (typically stochastic local search (SLS) algorithms). SLS algorithms are among the most effective for solving uniform random SAT problems, while hybrid algorithms achieved great breakthroughs for solving hard random SAT (HRS) problem recently. However, there is a lack of algorithms that can effectively solve both uniform random SAT and HRS problems. In this paper, a new SLS algorithm named SelectNTS is proposed aiming at solving both uniform random SAT and HRS problem effectively. SelectNTS is essentially an improved probability selection based local search algorithm, the core of which includes new clause and variable selection heuristics: a new clause weighting scheme and a biased random walk strategy are utilized to select a clause, while a new probability selection strategy with the variation of configuration checking strategy is used to select a variable. Extensive experimental results show that SelectNTS outperforms the state-of-the-art random SAT algorithms and hybrid algorithms in solving both uniform random SAT and HRS problems effectively
Local Search For SMT On Linear and Multilinear Real Arithmetic
Satisfiability Modulo Theories (SMT) has significant application in various
domains. In this paper, we focus on quantifier-free Satisfiablity Modulo Real
Arithmetic, referred to as SMT(RA), including both linear and non-linear real
arithmetic theories. As for non-linear real arithmetic theory, we focus on one
of its important fragments where the atomic constraints are multi-linear. We
propose the first local search algorithm for SMT(RA), called LocalSMT(RA),
based on two novel ideas. First, an interval-based operator is proposed to
cooperate with the traditional local search operator by considering the
interval information. Moreover, we propose a tie-breaking mechanism to further
evaluate the operations when the operations are indistinguishable according to
the score function. Experiments are conducted to evaluate LocalSMT(RA) on
benchmarks from SMT-LIB. The results show that LocalSMT(RA) is competitive with
the state-of-the-art SMT solvers, and performs particularly well on
multi-linear instances
Improving Coarsening Schemes for Hypergraph Partitioning by Exploiting Community Structure
We present an improved coarsening process for multilevel hypergraph partitioning that incorporates global information about the community structure. Community detection is performed via modularity maximization on a bipartite graph representation. The approach is made suitable for different classes of hypergraphs by defining weights for the graph edges that express structural properties of the hypergraph. We integrate our approach into a leading multilevel hypergraph partitioner with strong local search algorithms and perform extensive experiments on a large benchmark set of hypergraphs stemming from application areas such as VLSI design, SAT solving, and scientific computing. Our results indicate that respecting community structure during coarsening not only significantly improves the solutions found by the initial partitioning algorithm, but also consistently improves overall solution quality
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
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
A Study of Local Minimum Avoidance Heuristics for SAT
Stochastic local search for satisfiability (SAT) has successfully been applied to solve a wide range of problems. However, it still suffers from a major shortcoming, i.e. being trapped in local minima. In this study, we explore different heuristics to avoid local minima. The main idea is to proactively avoid local minima rather than reactively escape from them. This is worthwhile because it is time consuming to successfully escape from a local minimum in a deep and wide valley. In addition, revisiting an encountered local minimum several times makes it worse. Our new trap avoidance heuristics that operate in two phases: (i) learning of pseudo-conflict information at each local minimum, and (ii) using this information to avoid revisiting the same local minimum. We present a detailed empirical study of different strategies to collect pseudo-conflict information (using either static or dynamic heuristics) as well as to forget the outdated information (using naive or time window smoothing). We select a benchmark suite that includes all random and structured instances used in the 2011 SAT competition and three sets of hardware and software verification problems. Our results show that the new heuristics significantly outperform existing stochastic local search solvers (including Sparrow2011 - the best local search solver for random instances in the 2011 SAT competition) on all tested benchmarks
When Gravity Fails: Local Search Topology
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
minima) of randomly generated problem instances form clusters, which behave
similarly to local minima. We revisit several enhancements of local search
algorithms and explain their performance in light of our results. Finally we
discuss strategies for creating the next generation of local search algorithms.Comment: See http://www.jair.org/ for any accompanying file
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