Solving weighted CSPs with meta-constraints by reformulation into satisfiability modulo theories

Abstract

We introduce WSimply, a new framework for modelling and solving Weighted Constraint Satisfaction Problems (WCSP) using Satisfiability Modulo Theories (SMT) technology. In contrast to other well-known approaches designed for extensional representation of goods or no-goods, and with few declarative facilities, our approach aims to follow an intensional and declarative syntax style. In addition, our language has built-in support for some meta-constraints, such as priority and homogeneity, which allows the user to easily specify rich requirements on the desired solutions, such as preferences and fairness.We propose two alternative strategies for solving these WCSP instances using SMT. The first is the reformulation into Weighted SMT (WSMT) and the application of satisfiability test based algorithms from recent contributions in the Weighted Maximum Satisfiability field. The second one is the reformulation into an operation research-like style which involves an optimisation variable or objective function and the application of optimisation SMT solvers.We present experimental results of two well-known problems: the Nurse Rostering Problem (NRP) and a variant of the Balanced Academic Curriculum Problem (BACP), and provide some insights into the impact of the addition of metaconstraints on the quality of the solutions and the solving time.

Won't Take No for an Answer: Resource-Driven Requirements Adaptation

“…Quantifying adaptation may allow the use of constraint solving in requirements adaptation and, therefore, combining adaptation with substitution. Existing work on Weighted Constraint Satisfaction Problems [38] may provide other efficient solutions. Furthermore, the approach in this paper relies on explicit numerical values associated with each substitution.…”

MiniBrass: Soft constraints for MiniZinc

“…As mentioned before, Toulbar2 is a dedicated WCSP solver using search strategies (e.g., [2,63]) and soft constraint propagation and filtering [18]. Also, [6] offers WSimply, a specification language for weighted CSP with a transformation to SMT.…”

“…Probably closest to our approach, [5] proposed the higher-level language "w-MiniZinc" which would extend MiniZinc to weighted CSP. However, their approach ended up not be-ing implemented (although they provide a similar concept with WSimply [6]) and did not involve other (abstract) types of soft constraints such as those subsumed by c-semirings. MiniBrass, by contrast, is designed to be easily extended with new types and puts a layer of abstraction on top of MiniZinc, being its target language of compilation.…”

“…While c-semirings additionally allowed for partiality to better represent incomparable decisions, valued constraints put a total ordering first instead of an operator for the supremum. 6 Totality is beneficial for solving as it reduces search to more well-known scalar optimization tasks with a unique optimal solution degree and allow for more efficient pruning. Soft local consistency techniques with nonidempotent combination operators further require so-called "fair" valuation structures that admit a difference operator a b -which is not mandatory for a PVS.…”

“…For one thing, they are the native formalism Toulbar2 supports, for another thing the task boils down to minimizing a numeric value in conventional models which is directly supported by MiniZinc. On the one hand, Toulbar2 can be seen as the only true state-of-the-art alternative to MiniBrass (given that WSimply [6] has no MiniZinc or Numberjack interface and only runs on a 32 bit Linux distribution) -on the other hand it serves as a well-supported backend. Therefore, this evaluation cannot be truly seen in a competitive light as MiniBrass is a modeling language.…”