Solving Finite Domain Constraint Hierarchies by Local Consistency and Tree Search

We provide a reformulation of the constraint hierarchies (CHs) framework based on the notion of error indicators. Adapting the generalized view of local consistency in semiring-based constraint satisfaction problems (SCSPs), we define constraint hierarchy k -consistency (CH-k-C) and give a CH-2-C enforcement algorithm. We demonstrate how the CH-2-C algorithm can be seamlessly integrated into the ordinary branch-and-bound algorithm to make it a finite domain CH solver. Experimentation confirms the efficiency and robustness of our proposed solver prototype. Unlike other finite domain CH solvers, our proposed method works for both local and global comparators. In addition, our solver can support arbitrary error functions

Solving finite domain constraint hierarchies by local consistency and tree search.

by Hui Kau Cheung Henry.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 107-112).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgments --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Organizations of the Thesis --- p.2Chapter 2 --- Background --- p.4Chapter 2.1 --- Constraint Satisfaction Problems --- p.4Chapter 2.1.1 --- Local Consistency Algorithm --- p.5Chapter 2.1.2 --- Backtracking Solver --- p.8Chapter 2.1.3 --- The Branch-and-Bound Algorithm --- p.10Chapter 2.2 --- Over-constrained Problems --- p.14Chapter 2.2.1 --- Weighted Constraint Satisfaction Problems --- p.15Chapter 2.2.2 --- Possibilistic Constraint Satisfaction Problems --- p.15Chapter 2.2.3 --- Fuzzy Constraint Satisfaction Problems --- p.16Chapter 2.2.4 --- Partial Constraint Satisfaction Problems --- p.17Chapter 2.2.5 --- Semiring-Based Constraint Satisfaction Problems --- p.18Chapter 2.2.6 --- Valued Constraint Satisfaction Problems --- p.22Chapter 2.3 --- The Theory of Constraint Hierarchies --- p.23Chapter 2.4 --- Related Work --- p.26Chapter 2.4.1 --- An Incremental Hierarchical Constraint Solver --- p.28Chapter 2.4.2 --- Transforming Constraint Hierarchies into Ordinary Con- straint System --- p.29Chapter 2.4.3 --- The SCSP Framework --- p.30Chapter 2.4.4 --- The DeltaStar Algorithm --- p.32Chapter 2.4.5 --- A Plug-In Architecture of Constraint Hierarchy Solvers --- p.34Chapter 3 --- Local Consistency in Constraint Hierarchies --- p.36Chapter 3.1 --- A Reformulation of Constraint Hierarchies --- p.37Chapter 3.1.1 --- Error Indicators --- p.37Chapter 3.1.2 --- A Reformulation of Comparators --- p.38Chapter 3.1.3 --- A Reformulation of Solution Set --- p.40Chapter 3.2 --- Local Consistency in Classical CSPs --- p.41Chapter 3.3 --- Local Consistency in SCSPs --- p.42Chapter 3.4 --- Local Consistency in CHs --- p.46Chapter 3.4.1 --- The Operations of Error Indicator --- p.47Chapter 3.4.2 --- Constraint Hierarchy k-Consistency --- p.49Chapter 3.4.3 --- A Comparsion between CHAC and PAC --- p.50Chapter 3.4.4 --- The CHAC Algorithm --- p.52Chapter 3.4.5 --- Time and Space Complexities of the CHAC Algorithm --- p.53Chapter 3.4.6 --- Correctness of the CHAC Algorithm --- p.56Chapter 4 --- A Consistency-Based Finite Domain Constraint Hierarchy Solver --- p.59Chapter 4.1 --- The Branch-and-Bound CHAC Solver --- p.59Chapter 4.2 --- Correctness of the Branch-and-Bound CHAC Solver --- p.61Chapter 4.3 --- An Example Execution Trace --- p.64Chapter 4.4 --- Experiments and Results --- p.66Chapter 4.4.1 --- Experimental Setup --- p.68Chapter 4.4.2 --- The First Experiment --- p.71Chapter 4.4.3 --- The Second Experiment --- p.94Chapter 5 --- Concluding Remarks --- p.103Chapter 5.1 --- Summary and Contributions --- p.103Chapter 5.2 --- Future Work --- p.104Bibliography --- p.10

Constraint-based graphical layout of multimodal presentations

When developing advanced multimodal interfaces, combining the characteristics of different modalities such as natural language, graphics, animation, virtual realities, etc., the question of automatically designing the graphical layout of such presentations in an appropriate format becomes increasingly important. So, to communicate information to the user in an expressive and effective way, a knowledge-based layout component has to be integrated into the architecture of an intelligent presentation system. In order to achieve a coherent output, it must be able to reflect certain semantic and pragmatic relations specified by a presentation planner to arrange the visual appearance of a mixture of textual and graphic fragments delivered by mode-specific generators. In this paper we will illustrate by the example of LayLab, the layout manager of the multimodal presentation system WIP, how the complex positioning problem for multimodal information can be treated as a constraint satisfaction problem. The design of an aesthetically pleasing layout is characterized as a combination of a general search problem in a finite discrete search space and an optimization problem. Therefore, we have integrated two dedicated constraint solvers, an incremental hierarchy solver and a finite domain solver, in a layered constraint solver model CLAY, which is triggered from a common metalevel by rules and defaults. The underlying constraint language is able to encode graphical design knowledge expressed by semantic/pragmatic, geometrical/topological, and temporal relations. Furthermore, this mechanism allows one to prioritize the constraints as well as to handle constraint solving over finite domains. As graphical constraints frequently have only local effects, they are incrementally generated by the system on the fly. Ultimately, we will illustrate the functionality of LayLab by some snapshots of an example run

Strategic directions in constraint programming

An abstract is not available

Nonminimal supersymmetric standard model with lepton number violation

We carry out a detailed analysis of the nonminimal supersymmetric standard model with lepton number violation. The model contains a unique trilinear lepton number violating term in the superpotential which can give rise to neutrino masses at the tree level. We search for the gauged discrete symmetries realized by cyclic groups which preserve the structure of the associated trilinear superpotential of this model, and which satisfy the constraints of the anomaly cancellation. The implications of this trilinear lepton number violating term in the superpotential and the associated soft supersymmetry breaking term on the phenomenology of the light neutrino masses and mixing is studied in detail. We evaluate the tree and loop level contributions to the neutrino mass matrix in this model. We search for possible suppression mechanism which could explain large hierarchies and maximal mixing angles.Comment: Latex file, 43 pages, 2 figure

Using hierarchical constraint satisfaction for lathe-tool selection in a CIM environment

In this paper we shall discuss how to treat the automatic selection of appropriate lathe tools in a computer-aided production planning (CAPP) application as a constraint satisfaction problem (CSP) over hierarchically structured finite domains. Conceptually it is straightforward to formulate lathe-tool selection in terms of a CSP, however the choice of constraint and domain representations and of the order in which the constraints are applied is nontrivial if a computationally tractable system design is to be achieved. Since the domains appearing in technical applications often can be modeled as a hierarchy, we investigate how constraint satisfaction algorithms can make use of this hierarchical structure. Moreover, many real-life problems are formulated in a way that no optimal solution can be found which satisfies all the given constraints. Therefore, in order to bring AI technology into real-world applications, it becomes very important to be able to cope with conflicting constraints and to relax the given CSP until a (suboptimal) solution can be found. For these reasons, the constraint system CONTAX has been developed, which incorporates an extended hierarchical arc-consistency algorithm together with discrete constraint relaxation and has been used to implement the lathe-tool selection module of the ARC-TEC planning system

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP