The last decade has seen a growing interest in solver portfolios, automated solver configuration, and runtime prediction methods. At their core, these methods rely on a deterministic, consistent behaviour from the underlying algorithms and solvers. However, modern state-of-the-art solvers have elementsof stochasticity built in such as randomised variable and value selection, tie-breaking, and randomised restarting. Such features can elicit dramatic variations in the overall performance between repeated runs of the solver,often by several orders of magnitude. Despite the success of the aforementioned fields, such performance variations in the underlying solvers have largely been ignored. Supported by a large-scale empirical study employing many years of industrial SAT Competition instances including repeated runs, we present statistical and empirical evidence that such a performance variation phenomenon necessitates a change in the evaluation of portfolio, runtime prediction, and automated configuration methods. In addition, we demonstrate that this phenomenon can have a significant impact on empirical solver competitions. Specifically, we show that the top three solvers from the 2014 SAT Competition could have been ranked in any permutation. These findings demonstrate the need for more statistically well-founded regimes in empirical evaluations.

A popular technique for the analysis of web query languages relies on the translation of queries into logical formulas. These formulas are then solved for satisfiability using an off-the-shelf satisfiability solver. A critical aspect in this approach is the size of the obtained logical formula, since it constitutes a factor that affects the combined complexity of the global approach. We present logical combinators whose benefit is to provide an exponential gain in succinctness in terms of the size of the logical representation. This opens the way for solving a wide range of problems such as satisfiability and containment for expressive query languages in exponential-time, even though their direct formulation into the underlying logic results in an exponential blowup of the formula size, yielding an incorrectly presumed two-exponential time complexity. We illustrate this from a practical point of view on a few examples such as numerical occurrence constraints and tree frontier properties which are concrete problems found with semi-structured data.

It is now readily accepted that automated algorithm configuration is a necessity for ensuring optimized performance of solvers on a particular problem domain. Even the best developers who have carefully designed their solver are not always able to manually find the best parameter settings for it. Yet, the opportunity for improving performance has been repeatedly demonstrated by configuration tools like ParamILS, SMAC, and GGA. However, all these techniques currently assume a static environment, where demonstrative instances are procured beforehand, potentially unlimited time is provided to adequately search the parameter space, and the solver would never need to be retrained. This is not always the case in practice. The ReACT system, proposed in 2014, demonstrated that a solver could be configured during runtime as new instances arrive in a steady stream. This paper further develops that approach and shows how a ranking scheme, like TrueSkill, can further improve the configurator's performance, making it able to quickly find good parameterizations without adding any overhead on the time needed to solve any new instance, and then continuously improve as new instances are evaluated. The enhancements to ReACT that we present enable us to even outperform existing static configurators like SMAC in a non-dynamic setting.

The aim of this paper is to propose a new approach interweaving preference elicitation and search to solve multiobjective optimization problems. We present an interactive search procedure directed by an aggregation function, possibly non-linear (e.g. an additive disutility function, a Choquet integral), defining the overall cost of solutions. This function is parameterized by weights that are initially unknown. Hence, we insert comparison queries in the search process to obtain useful preference information that will progressively reduce the uncertainty attached to weights. The process terminates by recommending a near-optimal solution ensuring that the gap to optimality is below the desired threshold. Our approach is tested on multiobjective state space search problems and appears to be quite efficient both in terms of number of queries and solution times.

Adaptive constraint propagation has recently received a great attention. It allows a constraint solver to exploit various levels of propagation during search, and in many cases it shows better performance than static/predefined. The crucial point is to make adaptive constraint propagation automatic, so that no expert knowledge or parameter specification is required. In this work, we propose a simple learning technique, based on multi-armed bandits, that allows to automatically select among several levels of propagation during search. Our technique enables the combination of any number of levels of propagation whereas existing techniques are only defined for pairs. An experimental evaluation demonstrates that the proposed technique results in a more efficient and stable solver.

We propose a new approach that exploits the good properties of core-guided and model-guided MaxSAT solvers. In particular, we show how to effectively exploit the structure of unsatisfiable cores in MaxSAT instances. Experimental results on industrial instances show that the proposed approach outperforms both complete and incomplete state-of-the-art MaxSAT solvers at the last international MaxSAT Evaluation in terms of robustness and total number of solved instances.

Dynamic Programming (DP) over tree decompositions is a well-established method to solve problems — that are in general NP-hard — efficiently for instances of small treewidth. Experience shows that (i) heuristically computing a tree decomposition has negligible runtime compared to the DP step; (ii) DP algorithms exhibit a high variance in runtime when using different tree decompositions; in fact, given an instance of the problem at hand, even decompositions of the same width might yield extremely diverging runtimes. We thus propose here a novel and general method that is based on a selection of the best decomposition from an available pool of heuristically generated ones. For this purpose, we require machine learning techniques based on features of the decomposition rather than on the actual problem instance. We report on extensive experiments in different problem domains which show a significant speedup when choosing the tree decomposition according to this concept over simply using an arbitrary one of the same width.

At each node of the search tree, Branch and Bound solvers for Max-SAT compute the lower bound (LB) by estimating the number of disjoint inconsistent subsets (IS) of the formula. IS are detected thanks to unit propagation (UP) then transformed by max-resolution to ensure that they are counted only once. However, it has been observed experimentally that the max-resolution transformations impact the capability of UP to detect further IS. Consequently, few transformations are learned and the LB computation is redundant. In this paper, we study the effect of the transformations on the UP mechanism. We introduce the notion of UP-resiliency of a transformation, which quantifies its impact on UP. It provides, from a theoretical point of view, an explanation to the empirical efficiency of the learning scheme developed in the last ten years. The experimental results we present give evidences of UP-resiliency relevance and insights on the behavior of the learning mechanism.

A number of effective techniques for constraint-based optimization can be used to generate either diverse or high-quality solutions independently, but no framework is devoted to accomplish both simultaneously. In this paper, we tackle this issue with a generic paradigm that can be implemented in most existing solvers. We show that our technique can be specialized to produce diverse solutions of high quality in the context of over-constrained problems. Furthermore, our paradigm allows us to consider diversity from a different point of view, based on generic concepts expressed by global constraints.

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex techniques to find only local optima, even with extensions like random restarts and simulated annealing. We observe that, in many cases, the local modes of the objective function have combinatorial structure, and thus ideas from combinatorial optimization can be brought to bear. Based on this, we propose a problem-decomposition approach to nonconvex optimization. Similarly to DPLL-style SAT solvers and recursive conditioning in probabilistic inference, our algorithm, RDIS, recursively sets variables so as to simplify and decompose the objective function into approximately independent sub-functions, until the remaining functions are simple enough to be optimized by standard techniques like gradient descent. The variables to set are chosen by graph partitioning, ensuring decomposition whenever possible. We show analytically that RDIS can solve a broad class of nonconvex optimization problems exponentially faster than gradient descent with random restarts. Experimentally, RDIS outperforms standard techniques on problems like structure from motion and protein folding.