Tarmo: A Framework for Parallelized Bounded Model Checking

This paper investigates approaches to parallelizing Bounded Model Checking (BMC) for shared memory environments as well as for clusters of workstations. We present a generic framework for parallelized BMC named Tarmo. Our framework can be used with any incremental SAT encoding for BMC but for the results in this paper we use only the current state-of-the-art encoding for full PLTL. Using this encoding allows us to check both safety and liveness properties, contrary to an earlier work on distributing BMC that is limited to safety properties only. Despite our focus on BMC after it has been translated to SAT, existing distributed SAT solvers are not well suited for our application. This is because solving a BMC problem is not solving a set of independent SAT instances but rather involves solving multiple related SAT instances, encoded incrementally, where the satisfiability of each instance corresponds to the existence of a counterexample of a specific length. Our framework includes a generic architecture for a shared clause database that allows easy clause sharing between SAT solver threads solving various such instances. We present extensive experimental results obtained with multiple variants of our Tarmo implementation. Our shared memory variants have a significantly better performance than conventional single threaded approaches, which is a result that many users can benefit from as multi-core and multi-processor technology is widely available. Furthermore we demonstrate that our framework can be deployed in a typical cluster of workstations, where several multi-core machines are connected by a network

Parallel local search for solving Constraint Problems on the Cell Broadband Engine (Preliminary Results)

We explore the use of the Cell Broadband Engine (Cell/BE for short) for combinatorial optimization applications: we present a parallel version of a constraint-based local search algorithm that has been implemented on a multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16 SPUs per blade). This algorithm was chosen because it fits very well the Cell/BE architecture and requires neither shared memory nor communication between processors, while retaining a compact memory footprint. We study the performance on several large optimization benchmarks and show that this achieves mostly linear time speedups, even sometimes super-linear. This is possible because the parallel implementation might explore simultaneously different parts of the search space and therefore converge faster towards the best sub-space and thus towards a solution. Besides getting speedups, the resulting times exhibit a much smaller variance, which benefits applications where a timely reply is critical

An adaptive prefix-assignment technique for symmetry reduction

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay's canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelizability---prefix-assignments can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability---the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the practical applicability of our technique, we have prepared an experimental open-source implementation of the technique and carry out a set of experiments that demonstrate ability to reduce symmetry on hard instances. Furthermore, we demonstrate that the implementation effectively parallelizes to compute clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie

Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates

The optimization of algorithm (hyper-)parameters is crucial for achieving peak performance across a wide range of domains, ranging from deep neural networks to solvers for hard combinatorial problems. The resulting algorithm configuration (AC) problem has attracted much attention from the machine learning community. However, the proper evaluation of new AC procedures is hindered by two key hurdles. First, AC benchmarks are hard to set up. Second and even more significantly, they are computationally expensive: a single run of an AC procedure involves many costly runs of the target algorithm whose performance is to be optimized in a given AC benchmark scenario. One common workaround is to optimize cheap-to-evaluate artificial benchmark functions (e.g., Branin) instead of actual algorithms; however, these have different properties than realistic AC problems. Here, we propose an alternative benchmarking approach that is similarly cheap to evaluate but much closer to the original AC problem: replacing expensive benchmarks by surrogate benchmarks constructed from AC benchmarks. These surrogate benchmarks approximate the response surface corresponding to true target algorithm performance using a regression model, and the original and surrogate benchmark share the same (hyper-)parameter space. In our experiments, we construct and evaluate surrogate benchmarks for hyperparameter optimization as well as for AC problems that involve performance optimization of solvers for hard combinatorial problems, drawing training data from the runs of existing AC procedures. We show that our surrogate benchmarks capture overall important characteristics of the AC scenarios, such as high- and low-performing regions, from which they were derived, while being much easier to use and orders of magnitude cheaper to evaluate

Estimating parallel runtimes for randomized algorithms in constraint solving

International audienceThis paper presents a detailed analysis of the scalability and par-allelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a Constraint-Based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21% w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique