Efficient Operations On MDDs For Building Constraint Programming Models

International audienceWe propose improved algorithms for defining the most common operations on Multi-Valued Decision Diagrams (MDDs): creation, reduction, complement , intersection, union, difference, symmetric difference, complement of union and complement of intersection. Then, we show that with these algorithms and thanks to the recent development of an efficient algorithm establishing arc consistency for MDD based constraints (MDD4R), we can simply solve some problems by modeling them as a set of operations between MDDs. We apply our approach to the regular constraint and obtain competitive results with dedicated algorithms. We also experiment our technique on a large scale problem: the phrase generation problem and we show that our approach gives equivalent results to those of a specific algorithm computing a complex automaton

Constraints First: A New MDD-based Model to Generate Sentences Under Constraints

This paper introduces a new approach to generating strongly constrained texts. We consider standardized sentence generation for the typical application of vision screening. To solve this problem, we formalize it as a discrete combinatorial optimization problem and utilize multivalued decision diagrams (MDD), a well-known data structure to deal with constraints. In our context, one key strength of MDD is to compute an exhaustive set of solutions without performing any search. Once the sentences are obtained, we apply a language model (GPT-2) to keep the best ones. We detail this for English and also for French where the agreement and conjugation rules are known to be more complex. Finally, with the help of GPT-2, we get hundreds of bona-fide candidate sentences. When compared with the few dozen sentences usually available in the well-known vision screening test (MNREAD), this brings a major breakthrough in the field of standardized sentence generation. Also, as it can be easily adapted for other languages, it has the potential to make the MNREAD test even more valuable and usable. More generally, this paper highlights MDD as a convincing alternative for constrained text generation, especially when the constraints are hard to satisfy, but also for many other prospects.Comment: To be published in Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI 202

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Existing exact solution methods for KEP either are designed for the case where only cyclic exchanges are considered, or can handle long chains but are scalable as long as cycles are short. We develop the first decomposition method that is able to deal with long cycles and long chains for large realistic instances. More specifically, we propose a branch-and-price framework, in which the pricing problems are solved (for the first time in packing problems in a digraph) through multi-valued decision diagrams. Also, we present a new upper bound on the optimal value of KEP, stronger than the one proposed in the literature, which is obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths

A Decision Diagram Operation for Reachability

Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple decision diagram operation called REACH that also computes fixpoints. In contrast to saturation, it does not require a partitioning of the transition relation. We give sequential algorithms implementing the new operation for both binary and multi-valued decision diagrams, and moreover provide parallel counterparts. We implement these algorithms and experimentally compare their performance against saturation on 692 model checking benchmarks in different languages. The results show that the REACH operation often outperforms saturation, especially on transition relations with low locality. In a comparison between parallelized versions of REACH and saturation we find that REACH obtains comparable speedups up to 16 cores, although falls behind saturation at 64 cores. Finally, in a comparison with the state-of-the-art model checking tool ITS-tools we find that REACH outperforms ITS-tools on 29% of models, suggesting that REACH can be useful as a complementary method in an ensemble tool

Emergence through conflict : the Multi-Disciplinary Design System (MDDS)

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009.Includes bibliographical references (p. 413-430).This dissertation proposes a framework and a group of systematic methodologies to construct a computational Multi-Disciplinary Design System (MDDS) that can support the design of complex systems within a variety of domains. The way in which the resulting design system is constructed, and the capabilities it brings to bare, are totally different from the methods used in traditional sequential design. The MDDS embraces diverse areas of research that include design science, systems theory, artificial intelligence, design synthesis and generative algorithms, mathematical modeling and disciplinary analyses, optimization theory, data management and model integration, and experimental design among many others. There are five phases to generate the MDDS. These phases involve decomposition, formulation, modeling, integration, and exploration. These phases are not carried out in a sequential manner, but rather in a continuous move back and forth between the different phases. The process of building the MDDS begins with a top-down decomposition of a design concept. The design, seen as an object, is decomposed into its components and aspects, while the design, seen as a process, is decomposed into developmental levels and design activities. Then based on the process decomposition, the architecture of the MDDS is formulated into hierarchical levels each of which comprises a group of design cycles that include design modules at different degrees of abstraction. Based on the design object decomposition, the design activities which include synthesis, analysis, evaluation and optimization are modeled within the design modules.(cont.) Subsequently through a bottom-up approach, the design modules are integrated into a data flow network. This network forms MDDS as an integrated system that acts as a holistic structured functional unit that explores the design space in search of satisfactory solutions. The MDDS emergent properties are not detectable through the properties and behaviors of its parts, and can only be enucleated through a holistic approach. The MDDS is an adaptable system that is continuously dependent on, and responsive to, the uncertainties of the design process. The evolving MDDS is thus characterized a multi-level, multi-module, multi-variable and multi-resolution system. Although the MDDS framework is intended to be domain-independent, several MDDS prototypes were developed within this dissertation to generate exploratory building designs.by Anas Alfaris.Ph.D

Implementation and Applications of Ad Hoc Constraints

Ph.DDOCTOR OF PHILOSOPH