Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

Conjunto: Constraint Logic Programming with Finite Set Domains

Combinatorial problems involving sets and relations are currently tackled by integer programming and expressed with vectors or matrices of 0-1 variables. This is efficient but not flexible and unnatural in problem formulation. Toward a natural programming of combinatorial problems based on sets, graphs or relations, we define a new CLP language with set constraints. This language Conjunto 1 aims at combining the declarative aspect of Prolog with the efficiency of constraint solving techniques. We propose to constrain a set variable to range over finite set domains specified by lower and upper bounds for set inclusion. Conjunto is based on the inclusion and disjointness constraints applied to set expressions which comprise the union, intersection and difference symbols. The main contribution herein is the constraint handler which performs constraint propagation by applying consistency techniques over set constraints. 1 Introduction Various systems of set constraints have been define..

Constraints over structured domains

International audienceThe computer will be the most marvellous of all tools as soon as program writing and debugging will be no longer necessary-Jean-Louis Laurière (1976) A wide range of combinatorial search problems find a natural formulation in the language of sets, multisets, strings, functions, graphs or other structured objects. Bin-packing, set partitioning, set covering, combinatorial design problems, circuits and mapping problems are some of them. They are NP-complete problems originating from areas as diverse as combinatorial mathematics, operations research or artificial intelligence. These problems deal essentially with the search for discrete structured objects. While a high-level modeling approach seems more natural, many solutions have exploited the effectiveness of finite domains or mixed integer programming solvers. In this chapter we present higher level modeling facilities utilizing constraints over structured domains. What is a structured object? Let us consider the example of a bin-packing problem. The main constrained objects are the different bins, each describing a collection of un-ordered distinct elements, subject to disjointness constraints among them, weight constraints reflecting on each bin capacity and possible cardinality restrictions on the number of items allowed in each bin. Informally, such objects are structured in the sense that they involve more than one element in a specific setting. When Fikes introduced the notion of finite domain in 1970 [31], the idea was to approximate the range of an unknown integer (an integer variable) and to prune inconsistent values from such a domain that cannot belong to any solution. Already in the description of the language REF-ARF, Fikes proposed directions for future work such as: "considering the addition to the program of capabilities for handling unordered sets". Mid-eighties the seminal work of Van Hentenryck et al. integrated consistency techniques over finite integer domains into logic programming [90], and gave birth to the first finite domain constraint logic programming language CHIP (Constraint Handling In Prolog) [23], leading to a ne

Computational constraint models for decision support and holistic solution design

International audienceThe paradigm of constraint reasoning, aims at creating computerized solution models to tackle combinatorial search problems. The methodology and principles of such models are based on relationships among data and variables, specified as constraints that must hold for a solution to solve a decision or optimization problem. The relationships can be dependencies of any kind: geographical, engineering, environmental, or economic. Constraint models have been developed to this date to provide proactive analysis of some climate change issues, such as investment planning in renewable energies over a given horizon. The challenge of computerized constraint solution models is their reliability and effectiveness to become real world implementations. This is feasible if : 1) the modeling approach taken is holistic and specifies the complexity of real world scenarios, and 2) the users feel involved and become actual actors in the decision process. Constraint models facilitate a holistic approach by focusing on the solution model, and allowing heterogeneous data, variables and constraint types to be modeled independently of their solving. In this article we give an overview of such approaches to foster the implementation of climate change solutions

Large Scale Combinatorial Optimization: A Methodological Viewpoint

. The industrial and commercial worlds are increasingly competitive, requiring companies to be more productiveand more responsive to market changes (e.g. globalisation and privatisation). As a consequence, there is a strong need for solutions to large scale optimization problems, in domains such as production scheduling, transport, finance and network management. This means that more experts in constraint programming and optimization technology are required to develop adequate software. Given the computational complexity of Large Scale Combinatorial Optimization problems, a key question is how to help/guide in the tackling of LSCO problems in industry. Optimization technology is certainly reaching a level of maturity. Having emerged in the 50s within the Operational Research community, it has evolved and comprises new paradigms such as constraint programming and stochastic search techniques. There is a practical need, i.e. efficiency, scalability and tractability, to integrate techniques from the different paradigms. This adds complexity to the design of LSCO models and solutions. Various forms of guidance are available in the literature in terms of 1) case studies that map powerful algorithms to problem instances, and 2) visualization and programming tools that ease the modelling and solving of LSCOs. However, there is little guidance to address the process of building applications for new LSCO problems (independently of any language). This article gives an overview of the CHIC-2 methodology which aims at filling a gap in this direction. In particular, we describe some management issues specific to LSCOs such as risk management and team structures, and focus on the technical development guidance for scoping, designing and implementing LSCO appl..

New structures of symbolic constraint objects: sets and graphs (Extended Abstract)

A lot of work has been done up to now in designing Constraint Logic Programming Languages in order to solve combinatorial problems. Built-in computational domains in CLP support simple expression of problems and their efficient solution. Building a new computational domain comprising sets and graphs, this paper presents new symbolic constraints on set and graph structures in a CLP environment. Its main aim is to offer to the programmer the possibility to describe and solve in a natural, concise, declarative, expressive and efficient manner real Operations Research problems which are based on set and graph theory. 2 A constraint object is more suitable than a variable Usually the addition of new variables denoting sets to logic programs extends the unification algorithms to the involvment of these formulas [4]. As any added value to a language, it proves to be detrimental to the initial language performances. Moreover set unification is NP-complete [5]. Our constraint handler for sets ..

Constraints over structured domains

International audienceThe computer will be the most marvellous of all tools as soon as program writing and debugging will be no longer necessary-Jean-Louis Laurière (1976) A wide range of combinatorial search problems find a natural formulation in the language of sets, multisets, strings, functions, graphs or other structured objects. Bin-packing, set partitioning, set covering, combinatorial design problems, circuits and mapping problems are some of them. They are NP-complete problems originating from areas as diverse as combinatorial mathematics, operations research or artificial intelligence. These problems deal essentially with the search for discrete structured objects. While a high-level modeling approach seems more natural, many solutions have exploited the effectiveness of finite domains or mixed integer programming solvers. In this chapter we present higher level modeling facilities utilizing constraints over structured domains. What is a structured object? Let us consider the example of a bin-packing problem. The main constrained objects are the different bins, each describing a collection of un-ordered distinct elements, subject to disjointness constraints among them, weight constraints reflecting on each bin capacity and possible cardinality restrictions on the number of items allowed in each bin. Informally, such objects are structured in the sense that they involve more than one element in a specific setting. When Fikes introduced the notion of finite domain in 1970 [31], the idea was to approximate the range of an unknown integer (an integer variable) and to prune inconsistent values from such a domain that cannot belong to any solution. Already in the description of the language REF-ARF, Fikes proposed directions for future work such as: "considering the addition to the program of capabilities for handling unordered sets". Mid-eighties the seminal work of Van Hentenryck et al. integrated consistency techniques over finite integer domains into logic programming [90], and gave birth to the first finite domain constraint logic programming language CHIP (Constraint Handling In Prolog) [23], leading to a ne