Interactive Cost Configuration Over Decision Diagrams

Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrack-free user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over real-world configuration models and product-catalogue datasets. Response times are generally within a fraction of a second even for very large instances

Compiling CSPs into Tree-Driven Automata for Interactive Solving (2003)

Held in conjunction with 9th International Conference on Principles and Practice of Constraint Programming (CP 2003)International audienceConstraint programming techniques are widely used to model and solve decision problems and many algorithms have been developed to solve automatically and efficiently families of CSPs; nevertheless, they do not help solve interactive decision support problems, like product configuration. In such problems, the user chooses the values of the variables, and the role of the system is not to solve the CSP, but to help the user in this task. Dynamic global consistency maintaining is one of the most useful functionalities that should be offered by such a CSP platform. Unfortunately, this task is intractable in the worst case. Since interactivity requires short response times, intractability must be circumvented some way. To this end, compilation methods have been proposed that transform the original problem into a data structure allowing a short response time. In this paper, we extend the work of Amilhastre et al. [1] and Vempaty [15] by the use of a new structure, tree-driven automata, that takes advantage of the structural characteristics of configuration problems (decomposition of the components into independent subcomponents). Tree-driven automata can be far more compact than classical automata while keeping their good properties, especially a tractable complexity for the maintenance of global consistency

On Formal Methods for Large-Scale Product Configuration

<p>In product development companies mass customization is widely used to achieve better customer satisfaction while keeping costs down. To efficiently implement mass customization, product platforms are often used. A product platform allows building a wide range of products from a set of predefined components. The process of matching these components to customers' needs is called product configuration. Not all components can be combined with each other due to restrictions of various kinds, for example, geometrical, marketing and legal reasons. Product design engineers develop configuration constraints to describe such restrictions. The number of constraints and the complexity of the relations between them are immense for complex product like a vehicle. Thus, it is both error-prone and time consuming to analyze, author and verify the constraints manually. Software tools based on formal methods can help engineers to avoid making errors when working with configuration constraints, thus design a correct product faster.</p> <p>This thesis introduces a number of formal methods to help engineers maintain, verify and analyze product configuration constraints. These methods provide automatic verification of constraints and computational support for analyzing and refactoring constraints. The methods also allow verifying the correctness of one specific type of constraints, item usage rules, for sets of mutually-exclusive required items, and automatic verification of equivalence of different formulations of the constraints. The thesis also introduces three methods for efficient enumeration of valid partial configurations, with benchmarking of the methods on an industrial dataset.</p> <p>Handling large-scale industrial product configuration problems demands high efficiency from the software methods. This thesis investigates a number of search-based and knowledge-compilation-based methods for working with large product configuration instances, including Boolean satisfiability solvers, binary decision diagrams and decomposable negation normal form. This thesis also proposes a novel method based on supervisory control theory for efficient reasoning about product configuration data. The methods were implemented in a tool, to investigate the applicability of the methods for handling large product configuration problems. It was found that search-based Boolean satisfiability solvers with incremental capabilities are well suited for industrial configuration problems.</p> <p>The methods proposed in this thesis exhibit good performance on practical configuration problems, and have a potential to be implemented in industry to support product design engineers in creating and maintaining configuration constraints, and speed up the development of product platforms and new products.</p

Computing explanations for interactive constraint-based systems

Constraint programming has emerged as a successful paradigm for modelling combinatorial problems arising from practical situations. In many of those situations, we are not provided with an immutable set of constraints. Instead, a user will modify his requirements, in an interactive fashion, until he is satisfied with a solution. Examples of such applications include, amongst others, model-based diagnosis, expert systems, product configurators. The system he interacts with must be able to assist him by showing the consequences of his requirements. Explanations are the ideal tool for providing this assistance. However, existing notions of explanations fail to provide sufficient information. We define new forms of explanations that aim to be more informative. Even if explanation generation is a very hard task, in the applications we consider, we must manage to provide a satisfactory level of interactivity and, therefore, we cannot afford long computational times. We introduce the concept of representative sets of relaxations, a compact set of relaxations that shows the user at least one way to satisfy each of his requirements and at least one way to relax them, and present an algorithm that efficiently computes such sets. We introduce the concept of most soluble relaxations, maximising the number of products they allow. We present algorithms to compute such relaxations in times compatible with interactivity, achieving this by indifferently making use of different types of compiled representations. We propose to generalise the concept of prime implicates to constraint problems with the concept of domain consequences, and suggest to generate them as a compilation strategy. This sets a new approach in compilation, and allows to address explanation-related queries in an efficient way. We define ordered automata to compactly represent large sets of domain consequences, in an orthogonal way from existing compilation techniques that represent large sets of solutions

Knowledge compilation for online decision-making : application to the control of autonomous systems = Compilation de connaissances pour la décision en ligne : application à la conduite de systèmes autonomes

La conduite de systèmes autonomes nécessite de prendre des décisions en fonction des observations et des objectifs courants : cela implique des tâches à effectuer en ligne, avec les moyens de calcul embarqués. Cependant, il s'agit généralement de tâches combinatoires, gourmandes en temps de calcul et en espace mémoire. Réaliser ces tâches intégralement en ligne dégrade la réactivité du système ; les réaliser intégralement hors ligne, en anticipant toutes les situations possibles, nuit à son embarquabilité. Les techniques de compilation de connaissances sont susceptibles d'apporter un compromis, en déportant au maximum l'effort de calcul avant la mise en situation du système. Ces techniques consistent à traduire un problème dans un certain langage, fournissant une forme compilée de ce problème, dont la résolution est facile et la taille aussi compacte que possible. La traduction peut être très longue, mais n'est effectuée qu'une seule fois, hors ligne. Il existe de nombreux langages-cible de compilation, notamment le langage des diagrammes de décision binaires (BDDs), qui ont été utilisés avec succès dans divers domaines (model-checking, configuration, planification). L'objectif de la thèse était d'étudier l'application de la compilation de connaissances à la conduite de systèmes autonomes. Nous nous sommes intéressés à des problèmes réels de planification, qui impliquent souvent des variables continues ou à grand domaine énuméré (temps ou mémoire par exemple). Nous avons orienté notre travail vers la recherche et l'étude de langages-cible de compilation assez expressifs pour permettre de représenter de tels problèmes.Controlling autonomous systems requires to make decisions depending on current observations and objectives. This involves some tasks that must be executed online-with the embedded computational power only. However, these tasks are generally combinatory; their computation is long and requires a lot of memory space. Entirely executing them online thus compromises the system's reactivity. But entirely executing them offline, by anticipating every possible situation, can lead to a result too large to be embedded. A tradeoff can be provided by knowledge compilation techniques, which shift as much as possible of the computational effort before the system's launching. These techniques consists in a translation of a problem into some language, obtaining a compiled form of the problem, which is both easy to solve and as compact as possible. The translation step can be very long, but it is only executed once, and offline. There are numerous target compilation languages, among which the language of binary decision diagrams (BDDs), which have been successfully used in various domains of artificial intelligence, such as model-checking, configuration, or planning. The objective of the thesis was to study how knowledge compilation could be applied to the control of autonomous systems. We focused on realistic planning problems, which often involve variables with continuous domains or large enumerated domains (such as time or memory space). We oriented our work towards the search for target compilation languages expressive enough to represent such problems