Over-constrained problems are ubiquitous in real-world decision and optimization problems. Plenty of modeling formalisms for various problem domains involving soft constraints have been proposed, such as weighted, fuzzy, or probabilistic constraints. All of them were shown to be instances of algebraic structures. In terms of modeling languages, however, the field of soft constraints lags behind the state of the art in classical constraint optimization. We introduce MiniBrass, a versatile soft constraint modeling language building on the unifying algebraic framework of partially ordered valuation structures (PVS) that is implemented as an extension of MiniZinc and MiniSearch. We first demonstrate the adequacy of PVS to naturally augment partial orders with a combination operation as used in soft constraints. Moreover, we provide the most general construction of a c-semiring from an arbitrary PVS. Both arguments draw upon elements from category theory. MiniBrass turns these theoretical considerations into practice: It offers a generic extensible PVS type system, reusable implementations of specific soft constraint formalisms as PVS types, operators for complex PVS products, and morphisms to transform PVS. MiniBrass models are compiled into MiniZinc to benefit from the wide range of solvers supporting FlatZinc. We evaluated MiniBrass on 28 “softened” MiniZinc benchmark problems with six different solvers. The results demonstrate the feasibility of our approach.

中文翻译：

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MiniBrass：MiniZinc的软约束

过度约束的问题在现实世界的决策和优化问题中无处不在。已经提出了针对涉及软约束的各种问题域的大量建模形式主义，例如加权约束，模糊约束或概率约束。它们全部都是代数结构的实例。但是，就建模语言而言，软约束领域在经典约束优化中落后于最新技术水平。我们介绍MiniBrass，这是一种通用的软约束建模语言，它建立在部分有序评估结构（PVS）的统一代数框架上，该框架被实现为MiniZinc和MiniSearch的扩展。我们首先展示了PVS是否足以通过软约束中使用的组合操作自然地增加部分订单。此外，我们提供了从任意PVS进行c-半球的最一般的构造。两种论点均基于范畴理论的要素。MiniBrass将这些理论考虑变为现实：它提供了通用的可扩展PVS类型系统，可重复使用的特定软约束形式（如PVS类型），可重复使用的PVS产品操作符以及用于转换PVS的态射。MiniBrass模型被编译到MiniZinc中，以受益于支持FlatZinc的各种求解器。我们用六个不同的求解器对28个“软化”的MiniZinc基准测试问题进行了评估。结果证明了我们方法的可行性。它提供了通用的可扩展PVS类型系统，可重复使用的特定软约束形式（如PVS类型），复杂PVS产品的运算符以及用于转换PVS的态射。MiniBrass模型被编译到MiniZinc中，以受益于支持FlatZinc的各种求解器。我们用六个不同的求解器对28个“软化”的MiniZinc基准测试问题进行了评估。结果证明了我们方法的可行性。它提供了通用的可扩展PVS类型系统，可重复使用的特定软约束形式（如PVS类型），复杂PVS产品的运算符以及用于转换PVS的态射。MiniBrass模型被编译到MiniZinc中，以受益于支持FlatZinc的各种求解器。我们用六个不同的求解器对28个“软化”的MiniZinc基准测试问题进行了评估。结果证明了我们方法的可行性。