SUNNY-CP and the MiniZinc Challenge

In Constraint Programming (CP) a portfolio solver combines a variety of different constraint solvers for solving a given problem. This fairly recent approach enables to significantly boost the performance of single solvers, especially when multicore architectures are exploited. In this work we give a brief overview of the portfolio solver sunny-cp, and we discuss its performance in the MiniZinc Challenge---the annual international competition for CP solvers---where it won two gold medals in 2015 and 2016. Under consideration in Theory and Practice of Logic Programming (TPLP)Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Between Subgraph Isomorphism and Maximum Common Subgraph

When a small pattern graph does not occur inside a larger target graph, we can ask how to find "as much of the pattern as possible" inside the target graph. In general, this is known as the maximum common subgraph problem, which is much more computationally challenging in practice than subgraph isomorphism. We introduce a restricted alternative, where we ask if all but k vertices from the pattern can be found in the target graph. This allows for the development of slightly weakened forms of certain invariants from subgraph isomorphism which are based upon degree and number of paths. We show that when k is small, weakening the invariants still retains much of their effectiveness. We are then able to solve this problem on the standard problem instances used to benchmark subgraph isomorphism algorithms, despite these instances being too large for current maximum common subgraph algorithms to handle. Finally, by iteratively increasing k, we obtain an algorithm which is also competitive for the maximum common subgraph

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

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

Monotone Temporal Planning : tractability, extensions and applications (Extended abstract)

International audienceWe describe a polynomially-solvable class of temporal planning problems. Polynomiality follows from two assumptions. Firstly, by supposing that each fluent (fact) can be established by at most one action, we can quickly determine which actions are necessary in any plan. Secondly, the monotonicity of fluents allows us to express planning as an instance of STP ≠  (Simple Temporal Problem with difference constraints). This class includes temporally-expressive problems requiring the concurrent execution of actions, with potential applications in the chemical, pharmaceutical and construction industries. Any (temporal) planning problem has a monotone relaxation, which can lead to the polynomial-time detection of its unsolvability in certain cases. Indeed our relaxation is orthogonal to the relaxation based on ignoring deletes used in classical planning since it preserves deletes and can also exploit temporal information

Enriching Solutions to Combinatorial Problems via Solution Engineering

International audienceExisting approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions, as well as problem-specific desires that may only be discovered or articulated by the user after further analysis of solver output. We propose a general framework for problems of a combinatorial nature that can generate a set of of multiple (near-)optimal, diverse solutions, that are further infused with desirable features. We call our approach solution engineering. A key novelty is that desirable solution properties need not be explicitly modeled in advance. We customize the framework to both the mathematical programming and constraint programming technologies, and subsequently demonstrate its prac-ticality by implementing and then conducting computational experiments on existing test instances from the literature. Our computational results confirm the very real possibility of generating sets of solutions infused with features that might otherwise remain undiscovered

Refined Core Relaxation for Core-Guided MaxSAT Solving

Maximum satisfiability (MaxSAT) is a viable approach to solving NP-hard optimization problems. In the realm of core-guided MaxSAT solving - one of the most effective MaxSAT solving paradigms today - algorithmic variants employing so-called soft cardinality constraints have proven very effective. In this work, we propose to combine weight-aware core extraction (WCE) - a recently proposed approach that enables relaxing multiple cores instead of a single one during iterations of core-guided search - with a novel form of structure sharing in the cardinality-based core relaxation steps performed in core-guided MaxSAT solvers. In particular, the proposed form of structure sharing is enabled by WCE, which has so-far not been widely integrated to MaxSAT solvers, and allows for introducing fewer variables and clauses during the MaxSAT solving process. Our results show that the proposed techniques allow for avoiding potential overheads in the context of soft cardinality constraint based core-guided MaxSAT solving both in theory and in practice. In particular, the combination of WCE and structure sharing improves the runtime performance of a state-of-the-art core-guided MaxSAT solver implementing the central OLL algorithm

Refined Core Relaxation for Core-Guided MaxSAT Solving

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