Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure

Tools for reformulating logical forms into zero-one mixed integer programs (MIPS)

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Programming (ILP) formulation or a Mixed Integer Programming (MIP) formulation is presented. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. A prototype user interface by which logical forms can be reformulated and the corresponding MIP constructed and analysed within an existing Mathematical Programming modelling system is illustrated. Finally, the steps to formulate a discrete optimisation model in this way are demonstrated by means of an example

A constraint-based framework to model harmony for algorithmic composition

Music constraint systems provide a rule-based approach to composition. Existing systems allow users to constrain the harmony, but the constrainable harmonic information is restricted to pitches and intervals between pitches. More abstract analytical information such as chord or scale types, their root, scale degrees, enharmonic note representations, whether a note is the third or fifth of a chord and so forth are not supported. However, such information is important for modelling various music theories. This research proposes a framework for modelling harmony at a high level of abstraction. It explicitly represents various analytical information to allow for complex theories of harmony. It is designed for efficient propagation-based constraint solvers. The framework supports the common 12-tone equal temperament, and arbitrary other equal temperaments. Users develop harmony models by applying user-defined constraints to its music representation. Three examples demonstrate the expressive power of the framework: (1) an automatic melody harmonisation with a simple harmony model; (2) a more complex model implementing large parts of Schoenberg’s tonal theory of harmony; and (3) a composition in extended tonality. Schoenberg’s comprehensive theory of harmony has not been computationally modelled before, neither with constraints programming nor in any other way.

Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined

From types to type requirements: Genericity for model-driven engineering

The final publication is available at Springer via http://dx.doi.org/10.1007/s10270-011-0221-0Model-driven engineering (MDE) is a software engineering paradigm that proposes an active use of models during the development process. This paradigm is inherently type-centric, in the sense that models and their manipulation are defined over the types of specific meta-models. This fact hinders the reuse of existing MDE artefacts with other meta-models in new contexts, even if all these meta-models share common characteristics. To increase the reuse opportunities of MDE artefacts, we propose a paradigm shift from type-centric to requirement-centric specifications by bringing genericity into models, meta-models and model management operations. For this purpose, we introduce so-called concepts gathering structural and behavioural requirements for models and meta-models. In this way, model management operations are defined over concepts, enabling the application of the operations to any meta-model satisfying the requirements imposed by the concept. Model templates rely on concepts to define suitable interfaces, hence enabling the definition of reusable model components. Finally, similar to mixin layers, templates can be defined at the meta-model level as well, to define languages in a modular way, as well as layers of functionality to be plugged-in into other meta-models. These ideas have been implemented in MetaDepth, a multi-level meta-modelling tool that integrates action languages from the Epsilon family for model management and code generation.This work has been sponsored by the Spanish Ministry of Science and Innovation with projects METEORIC (TIN2008-02081) and Go Lite (TIN2011-24139), and by the R&D program of the Community of Madrid with project “e-Madrid” (S2009/TIC-1650)

A tree search approach for the solution of set problems using alternative relaxations

A number of alternative relaxations for the family of set problems (FSP) in general and set covering problems (SCP) in particular are introduced and discussed. These are (i) Network flow relaxation, (ii) Assignment relaxation, (iii) Shortest route relaxation, (iv) Minimum spanning tree relaxation. A unified tree search method is developed which makes use of these relaxations. Computational experience of processing a collection of test problems is reported

Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)

SP models combine the paradigm of dynamic linear programming with modelling of random parameters, providing optimal decisions which hedge against future uncertainties. Advances in hardware as well as software techniques and solution methods have made SP a viable optimisation tool. We identify a growing need for modelling systems which support the creation and investigation of SP problems. Our SPInE system integrates a number of components which include a flexible modelling tool (based on stochastic extensions of the algebraic modelling languages AMPL and MPL), stochastic solvers, as well as special purpose scenario generators and database tools. We introduce an asset/liability management model and illustrate how SPInE can be used to create and process this model as a multistage SP application

Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking

Model-based mutation testing uses altered test models to derive test cases that are able to reveal whether a modelled fault has been implemented. This requires conformance checking between the original and the mutated model. This paper presents an approach for symbolic conformance checking of action systems, which are well-suited to specify reactive systems. We also consider nondeterminism in our models. Hence, we do not check for equivalence, but for refinement. We encode the transition relation as well as the conformance relation as a constraint satisfaction problem and use a constraint solver in our reachability and refinement checking algorithms. Explicit conformance checking techniques often face state space explosion. First experimental evaluations show that our approach has potential to outperform explicit conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582