Formal Concept Analysis (FCA) is a prominent field of applied mathematics using object-attribute relationships to define formal concepts — groups of objects with common attributes — which can be ordered into conceptual hierarchies, so-called concept lattices. We consider the problem of satisfiability of membership constraints, i.e., to determine if a formal concept exists whose object and attribute set include certain elements and exclude others. We analyze the computational complexity of this problem in general and for restricted forms of membership constraints. We perform the same analysis for generalizations of FCA to incidence structures of arity three (objects, attributes and conditions) and higher. We present a generic answer set programming (ASP) encoding of the membership constraint satisfaction problem, which allows for deploying available highly optimized ASP tools for its solution. Finally, we discuss the importance of membership constraints in the context of navigational approaches to data analysis.

We study the adjustment and use of the Max-sumalgorithm for solving Asymmetric Distributed ConstraintOptimization Problems (ADCOPs). First, we formalize asymmetric factor-graphs and apply the different versions of Max-sum to them. Apparently, in contrast to local search algorithms, most Max-sum versions perform similarly when solving symmetric and asymmetric problems and some even perform better on asymmetric problems. Second, we prove that the convergence properties of Max-sum ADVP (an algorithm that was previously found to outperform other Max-sum versions) and the quality of the solutions it produces are dependent on the order between nodes involved in each constraint, i.e., the inner constraint order (ICO). A standard ICO allows to reproduce the properties achieved for symmetric problems, and outperform previously proposed local search ADCOP algorithms. Third, we demonstrate that a non-standard ICO can be used to balance exploration and exploitation, resulting in the best performing Max-sum version on both symmetric and asymmetric standard benchmarks.

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.

Many natural phenomena exhibit power law spectra. In particular, so-called 1/f α noise series with α close to 1 (also called pink noise) occur in sound, music and countless human artifacts or natural events, from the fluctuations of the flood levels of the Nile to movements of the stock market. As a consequence, many generative models for 1/f noise have been designed to produce series that look or sound “natural” or “human”. In this paper, we formulate the generation of 1/f series as a hard constraint satisfaction problem, so that 1/f noise generation can be used as an add-on to arbitrary sequence generation problems. We take inspiration from a simple yet beautiful stochastic algorithm invented by Voss and introduce the Voss constraint. We show that Voss’ algorithm can be modeled as a tree of ternary sum constraints, leading to efficient filtering. We illustrate our constraint with a melody generation problem, and show that the addition of the Voss constraint tends indeed to produce sequences whose spectrum have a 1/f distribution, regardless of the other constraints of the problem. We discuss the advantages and limitations of this approach and possible extensions.

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.

The generation and GAC enforcement of a large number of weak nogoods in Symmetry Breaking During Search (SBDS) is costly and often not worthwhile in terms of prunings. In this paper, we propose weak-nogood consistency (WNC) for nogoods and a lazy propagator for SBDS (and its variants) using watched literal technology. We give formal results on the strength and relatively low space and time complexities of the lazy propagator. Nogoods collected for each symmetry are increasing. We further define generalized weak-incNGs consistency (GWIC) for a conjunction of increasing nogoods, and give a lazy propagator for the incNGs global constraint. We prove GWIC on a conjunction is equivalent to WNC on individual nogoods, and give the space and time complexities. Various lazy versions of SBDS and its variants are implemented. We give experimentation to demonstrate the efficiency of the lazy versions as compared to state of the art symmetry breaking methods.

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.

The tastes of a user can be represented in a natural way by using qualitative preferences. In this paper, we explore how ontological knowledge expressed via existential rules can be combined with CP-theories to (i) represent qualitative preferences along with domain knowledge, and (ii) perform preference-based answering of conjunctive queries (CQs). We call these combinations ontological CP-theories (OCP-theories). We define skyline and k-rank answers to CQs based on the user’s preferences encoded in an OCP-theory, and provide an algorithm for computing them. We also provide precise complexity (including data tractability) results for deciding consistency, dominance, and CQ skyline membership for OCP-theories.

This work compares two actions' concurrency and co-occurrence employed in temporal modeling languages, one with a PDDL-style action modeling languages used by the AI planning community, exclusion mechanism, and another with an explicit and argue that they explain why MILP or SMT have notion of resources, and investigates their seemed unattractive. Specifically, we observe that PDDL 2.1 implications on constraint-based search. The first [Fox and Long, 2003] induces temporal gaps between consecutive mechanism forces temporal gaps in action schedules interdependent actions, and these gaps often induce and have a high performance penalty. The second twice the number of steps in the plans than what is necessary, mechanism avoids the gaps, with dramatically with strong negative performance implications. The gaps are improved performance.

It allows a constraint to play each one. Each machine, after being used, returns a reward solver to exploit various levels of propagation during from a distribution specific to that machine. The goal is search, and in many cases it shows better performance to maximize the sum of rewards obtained through a sequence than static/predefined. The crucial point of plays [Gittins, 1989]. is to make adaptive constraint propagation automatic, We use a MAB model to select the right level of propagation so that no expert knowledge or parameter (also called level of consistency) to enforce at each node specification is required. In this work, we propose during the exploration of the search tree. We specify a simple a simple learning technique, based on multiarmed reward function and the upper confidence bound (UCB) to estimate bandits, that allows to automatically select the best arm, namely the best consistency to apply.