1,106 research outputs found
Solving Linux Upgradeability Problems Using Boolean Optimization
Managing the software complexity of package-based systems can be regarded as
one of the main challenges in software architectures. Upgrades are required on
a short time basis and systems are expected to be reliable and consistent after
that. For each package in the system, a set of dependencies and a set of
conflicts have to be taken into account. Although this problem is
computationally hard to solve, efficient tools are required. In the best
scenario, the solutions provided should also be optimal in order to better
fulfill users requirements and expectations. This paper describes two different
tools, both based on Boolean satisfiability (SAT), for solving Linux
upgradeability problems. The problem instances used in the evaluation of these
tools were mainly obtained from real environments, and are subject to two
different lexicographic optimization criteria. The developed tools can provide
optimal solutions for many of the instances, but a few challenges remain.
Moreover, it is our understanding that this problem has many similarities with
other configuration problems, and therefore the same techniques can be used in
other domains.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083
Automatic Algorithm Selection for Pseudo-Boolean Optimization with Given Computational Time Limits
Machine learning (ML) techniques have been proposed to automatically select
the best solver from a portfolio of solvers, based on predicted performance.
These techniques have been applied to various problems, such as Boolean
Satisfiability, Traveling Salesperson, Graph Coloring, and others.
These methods, known as meta-solvers, take an instance of a problem and a
portfolio of solvers as input. They then predict the best-performing solver and
execute it to deliver a solution. Typically, the quality of the solution
improves with a longer computational time. This has led to the development of
anytime selectors, which consider both the instance and a user-prescribed
computational time limit. Anytime meta-solvers predict the best-performing
solver within the specified time limit.
Constructing an anytime meta-solver is considerably more challenging than
building a meta-solver without the "anytime" feature. In this study, we focus
on the task of designing anytime meta-solvers for the NP-hard optimization
problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability
and Maximum Satisfiability problems. The effectiveness of our approach is
demonstrated via extensive empirical study in which our anytime meta-solver
improves dramatically on the performance of Mixed Integer Programming solver
Gurobi, which is the best-performing single solver in the portfolio. For
example, out of all instances and time limits for which Gurobi failed to find
feasible solutions, our meta-solver identified feasible solutions for 47% of
these
Certifying Correctness for Combinatorial Algorithms : by Using Pseudo-Boolean Reasoning
Over the last decades, dramatic improvements in combinatorialoptimisation algorithms have significantly impacted artificialintelligence, operations research, and other areas. These advances,however, are achieved through highly sophisticated algorithms that aredifficult to verify and prone to implementation errors that can causeincorrect results. A promising approach to detect wrong results is touse certifying algorithms that produce not only the desired output butalso a certificate or proof of correctness of the output. An externaltool can then verify the proof to determine that the given answer isvalid. In the Boolean satisfiability (SAT) community, this concept iswell established in the form of proof logging, which has become thestandard solution for generating trustworthy outputs. The problem isthat there are still some SAT solving techniques for which prooflogging is challenging and not yet used in practice. Additionally,there are many formalisms more expressive than SAT, such as constraintprogramming, various graph problems and maximum satisfiability(MaxSAT), for which efficient proof logging is out of reach forstate-of-the-art techniques.This work develops a new proof system building on the cutting planesproof system and operating on pseudo-Boolean constraints (0-1 linearinequalities). We explain how such machine-verifiable proofs can becreated for various problems, including parity reasoning, symmetry anddominance breaking, constraint programming, subgraph isomorphism andmaximum common subgraph problems, and pseudo-Boolean problems. Weimplement and evaluate the resulting algorithms and a verifier for theproof format, demonstrating that the approach is practical for a widerange of problems. We are optimistic that the proposed proof system issuitable for designing certifying variants of algorithms inpseudo-Boolean optimisation, MaxSAT and beyond
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
MaxSAT Evaluation 2022 : Solver and Benchmark Descriptions
Non peer reviewe
Towards Next Generation Sequential and Parallel SAT Solvers
This thesis focuses on improving the SAT solving technology. The improvements focus on two major subjects: sequential SAT solving and parallel SAT solving.
To better understand sequential SAT algorithms, the abstract reduction system Generic CDCL is introduced. With Generic CDCL, the soundness of solving techniques can be modeled. Next, the conflict driven clause learning algorithm is extended with the three techniques local look-ahead, local probing and all UIP learning that allow more global reasoning during search. These techniques improve the performance of the sequential SAT solver Riss. Then, the formula simplification techniques bounded variable addition, covered literal elimination and an advanced cardinality constraint extraction are introduced. By using these techniques, the reasoning of the overall SAT solving tool chain becomes stronger than plain resolution. When using these three techniques in the formula simplification tool Coprocessor before using Riss to solve a formula, the performance can be improved further.
Due to the increasing number of cores in CPUs, the scalable parallel SAT solving approach iterative partitioning has been implemented in Pcasso for the multi-core architecture. Related work on parallel SAT solving has been studied to extract main ideas that can improve Pcasso. Besides parallel formula simplification with bounded variable elimination, the major extension is the extended clause sharing level based clause tagging, which builds the basis for conflict driven node killing. The latter allows to better identify unsatisfiable search space partitions. Another improvement is to combine scattering and look-ahead as a superior search space partitioning function. In combination with Coprocessor, the introduced extensions increase the performance of the parallel solver Pcasso. The implemented system turns out to be scalable for the multi-core architecture. Hence iterative partitioning is interesting for future parallel SAT solvers.
The implemented solvers participated in international SAT competitions. In 2013 and 2014 Pcasso showed a good performance. Riss in combination with Copro- cessor won several first, second and third prices, including two Kurt-Gödel-Medals. Hence, the introduced algorithms improved modern SAT solving technology
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
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