Rewriting Constraint Models with Metamodels

An important challenge in constraint programming is to rewrite constraint models into executable programs calculat- ing the solutions. This phase of constraint processing may require translations between constraint programming lan- guages, transformations of constraint representations, model optimizations, and tuning of solving strategies. In this paper, we introduce a pivot metamodel describing the common fea- tures of constraint models including different kinds of con- straints, statements like conditionals and loops, and other first-class elements like object classes and predicates. This metamodel is general enough to cope with the constructions of many languages, from object-oriented modeling languages to logic languages, but it is independent from them. The rewriting operations manipulate metamodel instances apart from languages. As a consequence, the rewriting operations apply whatever languages are selected and they are able to manage model semantic information. A bridge is created between the metamodel space and languages using parsing techniques. Tools from the software engineering world can be useful to implement this framework

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

An introduction to interval-based constraint processing.

Constraint programming is often associated with solving problems over finite domains. Many applications in engineering, CAD and design, however, require solving problems over continuous (real-valued) domains. While simple constraint solvers can solve linear constraints with the inaccuracy of floating-point arithmetic, methods based on interval arithmetic allow exact (interval) solutions over a much wider range of problems. Applications of interval-based programming extend the range of solvable problems from non-linear polynomials up to those involving ordinary differential equations. In this text, we give an introduction to current approaches, methods and implementations of interval-based constraint programming and solving. Special care is taken to provide a uniform and consistent notation, since the literature in this field employs many seemingly different, but yet conceptually related, notations and terminology

Multiagent cooperation for solving global optimization problems: an extendible framework with example cooperation strategies

This paper proposes the use of multiagent cooperation for solving global optimization problems through the introduction of a new multiagent environment, MANGO. The strength of the environment lays in itsflexible structure based on communicating software agents that attempt to solve a problem cooperatively. This structure allows the execution of a wide range of global optimization algorithms described as a set of interacting operations. At one extreme, MANGO welcomes an individual non-cooperating agent, which is basically the traditional way of solving a global optimization problem. At the other extreme, autonomous agents existing in the environment cooperate as they see fit during run time. We explain the development and communication tools provided in the environment as well as examples of agent realizations and cooperation scenarios. We also show how the multiagent structure is more effective than having a single nonlinear optimization algorithm with randomly selected initial points

Rewriting Constraint Models with Metamodels

International audienceAn important challenge in constraint programming is to rewrite constraint models into executable programs calculat- ing the solutions. This phase of constraint processing may require translations between constraint programming lan- guages, transformations of constraint representations, model optimizations, and tuning of solving strategies. In this paper, we introduce a pivot metamodel describing the common fea- tures of constraint models including different kinds of con- straints, statements like conditionals and loops, and other first-class elements like object classes and predicates. This metamodel is general enough to cope with the constructions of many languages, from object-oriented modeling languages to logic languages, but it is independent from them. The rewriting operations manipulate metamodel instances apart from languages. As a consequence, the rewriting operations apply whatever languages are selected and they are able to manage model semantic information. A bridge is created between the metamodel space and languages using parsing techniques. Tools from the software engineering world can be useful to implement this framework