Pseudo-Boolean Optimization by Implicit Hitting Sets

Recent developments in applying and extending Boolean satisfiability (SAT) based techniques have resulted in new types of approaches to pseudo-Boolean optimization (PBO), complementary to the more classical integer programming techniques. In this paper, we develop the first approach to pseudo-Boolean optimization based on instantiating the so-called implicit hitting set (IHS) approach, motivated by the success of IHS implementations for maximum satisfiability (MaxSAT). In particular, we harness recent advances in native reasoning techniques for pseudo-Boolean constraints, which enable efficiently identifying inconsistent assignments over subsets of objective function variables (i.e. unsatisfiable cores in the context of PBO), as a basis for developing a native IHS approach to PBO, and study the impact of various search techniques applicable in the context of IHS for PBO. Through an extensive empirical evaluation, we show that the IHS approach to PBO can outperform other currently available PBO solvers, and also provides a complementary approach to PBO when compared to classical integer programming techniques

Pseudo-Boolean Optimization by Implicit Hitting Sets

Peer reviewe

Embarrassingly Parallel Search

International audienceWe propose the Embarrassingly Parallel Search, a simple and efficient method for solving constraint programming problems in parallel. We split the initial problem into a huge number of independent subproblems and solve them with available workers (i.e., cores of machines). The decomposition into subproblems is computed by selecting a subset of variables and by enumerating the combinations of values of these variables that are not detected inconsistent by the propagation mechanism of a CP Solver. The experiments on satisfaction problems and on optimization problems suggest that generating between thirty and one hundred subproblems per worker leads to a good scalability. We show that our method is quite competitive with the work stealing approach and able to solve some classical problems at the maximum capacity of the multi-core machines. Thanks to it, a user can parallelize the resolution of its problem without modifying the solver or writing any parallel source code and can easily replay the resolution of a problem

MaxSAT-Based Bi-Objective Boolean Optimization

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A Maximum Satisfiability Based Approach to Bi-Objective Boolean Optimization

Many real-world problem settings give rise to NP-hard combinatorial optimization problems. This results in a need for non-trivial algorithmic approaches for finding optimal solutions to such problems. Many such approaches—ranging from probabilistic and meta-heuristic algorithms to declarative programming—have been presented for optimization problems with a single objective. Less work has been done on approaches for optimization problems with multiple objectives. We present BiOptSat, an exact declarative approach for finding so-called Pareto-optimal solutions to bi-objective optimization problems. A bi-objective optimization problem arises for example when learning interpretable classifiers and the size, as well as the classification error of the classifier should be taken into account as objectives. Using propositional logic as a declarative programming language, we seek to extend the progress and success in maximum satisfiability (MaxSAT) solving to two objectives. BiOptSat can be viewed as an instantiation of the lexicographic method and makes use of a single SAT solver that is preserved throughout the entire search procedure. It allows for solving three tasks for bi-objective optimization: finding a single Pareto-optimal solution, finding one representative solution for each Pareto point, and enumerating all Pareto-optimal solutions. We provide an open-source implementation of five variants of BiOptSat, building on different algorithms proposed for MaxSAT. Additionally, we empirically evaluate these five variants, comparing their runtime performance to that of three key competing algorithmic approaches. The empirical comparison in the contexts of learning interpretable decision rules and bi-objective set covering shows practical benefits of our approach. Furthermore, for the best-performing variant of BiOptSat, we study the effects of proposed refinements to determine their effectiveness

Improvements to the Implicit Hitting Set Approach to Pseudo-Boolean Optimization

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Global Inverse Consistency for Interactive Constraint Satisfaction

International audienceSome applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples

Enabling Incrementality in the Implicit Hitting Set Approach to MaxSAT Under Changing Weights

Recent advances in solvers for the Boolean satisfiability (SAT) based optimization paradigm of maximum satisfiability (MaxSAT) have turned MaxSAT into a viable approach to finding provably optimal solutions for various types of hard optimization problems. In various types of real-world problem settings, a sequence of related optimization problems need to solved. This calls for studying ways of enabling incremental computations in MaxSAT, with the hope of speeding up the overall computation times. However, current state-of-the-art MaxSAT solvers offer no or limited forms of incrementality. In this work, we study ways of enabling incremental computations in the context of the implicit hitting set (IHS) approach to MaxSAT solving, as both one of the key MaxSAT solving approaches today and a relatively well-suited candidate for extending to incremental computations. In particular, motivated by several recent applications of MaxSAT in the context of interpretability in machine learning calling for this type of incrementality, we focus on enabling incrementality in IHS under changes to the objective function coefficients (i.e., to the weights of soft clauses). To this end, we explain to what extent different search techniques applied in IHS-based MaxSAT solving can and cannot be adapted to this incremental setting. As practical result, we develop an incremental version of an IHS MaxSAT solver, and show it provides significant runtime improvements in recent application settings which can benefit from incrementality but in which MaxSAT solvers have so-far been applied only non-incrementally, i.e., by calling a MaxSAT solver from scratch after each change to the problem instance at hand