Pareto optimization solves a constrained optimization task by reformulating the task as a bi-objective problem. Pareto optimization has been shown quite effective in applications; however, it has little theoretical support. This work theoretically compares Pareto optimization with a penalty approach, which is a common method transforming a constrained optimization into an unconstrained optimization. We prove that on two large classes of constrained Boolean optimization problems, minimum matroid optimization (P-solvable) and minimum cost coverage (NP-hard), Pareto optimization is more efficient than the penalty function method for obtaining the optimal and approximate solutions, respectively. Furthermore, on a minimum cost coverage instance, we also show the advantage of Pareto optimization over a greedy algorithm.

We increase the usefulness of Chu and Stuckey's work by automating it, that is, by developing a method to (a) automatically The exploitation of dominance relations in constraint identify symmetries for a given problem, and (b) optimization problems can lead to dramatic automatically construct the associated dominance breaking reductions in search space. We propose an automatic constraints. Note that these dominance breaking constraints method to detect some of the dominance relations are not symmetry breaking constraints, as the key element manually identified by Chu and Stuckey for is for f(σ(θ)) to be better. Further, the symmetries need to optimization problems, and to construct the associated be detected for the inherent satisfaction problem -- that is, dominance breaking constraints. Experimental the problem without the objective function -- or, otherwise, results show that the method is able to find several f(σ(θ)) will be equal to f(θ), not better.

Specifically, we present a top-down algorithm cn2mddg for compiling finite-domain CNs into multivalued decomposable We present and evaluate a top-down algorithm for decision graphs. The input of cn2mddg is a CN compiling finite-domain constraint networks (CNs) represented in the XCSP 2.1 format [Roussel and Lecoutre, into the language MDDG of multivalued decomposable 2009]. The output of our compilation algorithm is a representation decision graphs. Though it includes Decision-of the solutions of the CN in the language MDDG DNNF as a proper subset, MDDG offers the same key of multivalued decomposable decision graphs. MDDG is precisely tractable queries and transformations as Decision-the extension to non-Boolean domains of the language DNNF, which makes it useful for many applications. DDG [Fargier and Marquis, 2006] also known as Decision-Intensive experiments showed that our compiler DNNF [Oztok and Darwiche, 2014]: it is based on decomposable cn2mddg succeeds in compiling CNs which -nodes and (multivalued) decision nodes. Similarly are out of the reach of standard approaches based to Decision-DNNF, the MDDG language offers a number of on a translation of the input network to CNF, followed tractable queries, including (possibly weighted) solution finding by a compilation to Decision-DNNF. Furthermore, and counting, solution enumeration (solutions can be enumerated the sizes of the resulting compiled representations with polynomial delay), and optimization w.r.t. a linear turn out to be much smaller (sometimes by objective function. It also offers tractable transformations, several orders of magnitude).

Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown to relate with existing work on enumeration of implicit hitting sets, but also with recent work on QBF based on abstraction refinement. The paper then extends these ideas and develops a novel QBF algorithm, which generalizes the concept of enumeration of implicit hitting sets. Experimental results, obtained on representative problem instances, show that the novel algorithm is competitive with, and often outperforms, the state of the art in QBF solving.

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.