Reformulation Algorithm Research Articles

Solvability Analysis of high-order Linear Differential-Algebraic Equations with time-varying coefficients

In this paper, we study the solvability analysis of arbitrarily high-order linear differential-algebraic equations (DAEs) with time-varying coefficients, using the algebraic-behavior approach. We propose a concept of strangeness-index and construct condensed forms for high-order linear DAEs. We also discuss other structural properties like the existence and uniqueness of a solution, consistency and smoothness requirements for an initial vector and for an inhomogeneity. Our work extends the algebraic approach for DAEs and combines this approach with the behavior approach to establish a reformulation algorithm that reveals an underlying ordinary differential equation (ODE) and all hidden constraints in the DAE. This direct treatment of the system addresses the limitations of the classical approach to transforming the system into a first-order DAE. We illustrate our theoretical results with applications in mechanical systems and electrical circuits. This comprehensive study into general high-order systems is a natural progression from the extensive study of first and second-order DAEs.

Multistage Mixed-Integer Robust Optimization for Power Grid Scheduling: An Efficient Reformulation Algorithm

The penetration of renewables into power systems is gradually increasing, but its inherent uncertainty poses tremendous challenges to the coordinated operation of power grids. To overcome the demerits of canonical two-stage mixed-integer robust optimization (RO) method that neglects the nonanticipativity requirement and the computational burden in engineering applications, this paper offers a reformulated multistage mixed-integer RO method for regional power grid scheduling. Firstly, a multistage mixed-integer RO scheduling model is established considering the scheduling requests in real-world projects. The scheduling plans under the nominal scenario are determined ahead of uncertainty in the first-stage optimization, and the multistage max-min optimization with binary recourse variables is then executed for feasibility-checking with respect to the nonanticipative realization of uncertainty. Secondly, a dedicated reformulation algorithm is proposed for this intractable multistage mixed-integer RO model. Based on the implicit affine strategy, the multistage max-min optimization is equivalently encapsulated to a single-stage max-min problem, and the dual Fourier-Motzkin elimination is put forward to eliminate both continuous and binary recourse variables in the resulting feasibility-checking optimization. Therefore, the original multistage mixed-integer RO is finally recast as a mixed-integer linear programming that can be solved directly. Numerical tests on an actual 16-bus grid, the IEEE 118-bus system and the 319-bus provincial grid verify the superiority and applicability of the proposed reformulated mixed-integer RO scheduling method, which is of great significance in guiding system operations.

Traffic Forecasting Based on Integration of Adaptive Subgraph Reformulation and Spatio-Temporal Deep Learning Model

Traffic forecasting provides the foundational guidance for many typical applications in the smart city management, such as urban traffic control, congestion avoidance, and navigation guidance. Many researchers have focused on the spatio-temporal correlations under fixed topology structure in traffic network to improve the traffic forecasting accuracy. Despite their advantages, the existing approaches are not completely discussed that the association relationship among traffic network nodes are not invariable under different traffic conditions. In this paper, a novel traffic forecasting framework is proposed by integrating the dynamic association of traffic nodes with the spatio-temporal deep learning model. To be specific, an adaptive subgraph reformulation algorithm is designed first based on the specific forecasting interval to reduce the interference of irrelevant spatio-temporal information. After that, by enhancing the attention mechanism with the generative decoder, a spatio-temporal deep learning model with only one forward operation is proposed to avoid the degradation of accuracy in the long-term prediction, in which the spatio-temporal information and the external factors (such as weather and holiday) are fused together to be as an input vector. Based on the reformulated subgraph constructed of traffic nodes with closer spatio-temporal correlation, experiments show that the proposed framework consistently outperforms other GNN (Graph Neural Network)-based state-of-the-art baselines for various forecasting intervals on a real-world dataset.

A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems

ABSTRACT We propose a new two-level vertex-searching algorithm framework that finds a global optimal solution to the continuous bilevel linear fractional programming problem over a compact polyhedron, in which both the upper and the lower objectives are linear fractional. Our solution method adopts the vertex-searching approach on the polyhedron, and the search space is determined by the set of candidates of optimal base to the lower level problem. In order to search base, a modified enumerative scheme, that is a new upper bound filter scheme inserted into the classical enumerative scheme, is proposed. The main solution procedure is designed on solving a sequence of upper and lower level mathematical programs; instead of a single-level problem reformulation approach, which is popularly and widely used in literature. An extension on general upper level objective functions such as quasiconvex/quasiconcave for the proposed vertex-searching approach is discussed. Numerical experiments show that our algorithm leads us to a global optimum. We conclude that our proposed algorithm framework has the simplest solution procedure and has potential efficiency advantages, which may reduce the complexity of enumerative schemes for medium or large-scale problems, while comparing with existing global algorithms such as the Kth-best algorithm (a two-level vertex-searching algorithm) and the single-level duality-based reformulation algorithm (a single-level vertex-searching algorithm).

A novel bilevel model and solution algorithms for multi-period interdiction problem with fortification

Service systems are in significant danger of terrorist attacks aimed at disrupting their critical components. These attacks seek to exterminate vital assets such as transportation networks, services, and supplies. In the present paper, we propose a multi-period planning based on capacity recovery to allocate fortification/interdiction resources in a service system. The problem involves a dynamic Stackelberg game between a defender (leader) and an attacker (follower). The decisions of the defender are the services provided to customers and the fortification resources allocated to facilities in each period as the total demand-weighted distances are minimized. Following this, the attacker allocates interdiction resources to facilities that resulted in the service capacity reduction in each period. In this model, excess fortification/interdiction budgets and capacity in one period can be used in the next period. Moreover, facilities have a predefined capacity to serve the customers with varying demands during the time horizon. To solve this problem, two different types of approaches are implemented and compared. The first method is an exact reformulation algorithm based on the decomposition of the problem into a restricted master problem (RMP) and a slave problem (SP). The second one is a high performance metaheuristic algorithm, i.e., genetic algorithm (GA) developed to overcome the decomposition method’s impracticability on large-scale problem instances. We also compare the results with some novel metaheuristic algorithms such as teaching learning based optimization (TLBO) and dragonfly algorithm (DA). Computational results show the superiority of GA against TLBO and DA.

Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel

Although many investigations on elastic turbulence have been conducted in recent years, two major research topics still call for in-depth mechanistic investigations. Specifically, one is heat transfer performance affected by elastic turbulence; the other is so-called high Weissenberg number problem (HWNP) in numerical simulation of viscoelastic fluid flow. Taking these two topics into account simultaneously, the coupled problem becomes heat transfer characteristic of viscoelastic fluid in elastic turbulence at high Weissenberg number (Wi) and very low Reynolds number (Re). In this work, we implement numerical simulations by embedding log-conformation reformulation algorithm into the open-source software OpenFOAM. The heat transfer process of viscoelastic fluid flow in a three-dimensional (3D) curvy channel is simulated over a wide range of Wi. For the first time, significant heat transfer enhancement induced by elastic turbulence in a curvy channel at high Wi was identified numerically. When Wi is above the critical value of O(1), the heat transfer performance is found to be dramatically improved by elastic turbulence and then approaches a saturation. From the transient analysis of flow motions in the axial and cross sections, it can be seen that the flow twists and wiggles in the curvy channel and the field synergy effect of viscoelastic fluid flow becomes more intensive than that of Newtonian fluid flow. These effects give rise to the extremely irregular flow motions in the cross section and consequently lead to heat transfer enhancement.

Reformulating XQuery queries using GLAV mapping and complex unification

This paper describes an algorithm for reformulation of XQuery queries. The mediation is based on an essential component called mediator. Its main role is to reformulate a user query, written in terms of global schema, into queries written in terms of source schemas. Our algorithm is based on the principle of logical equivalence, simple and complex unification, to obtain a better reformulation. It takes XQuery query, global schema (written in XMLSchema), and mappings GLAV as input parameters and provides resultant query written in terms of source schemas. The results of implementation show the proper functioning of the algorithm.

(Non-)Succinctness of uniform interpolants of general terminologies in the description logic [formula omitted

EL is a popular description logic, used as a core formalism in large existing knowledge bases. Uniform interpolants of knowledge bases are of high interest, e.g. in scenarios where a knowledge base is supposed to be partially reused. However, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bound on the size of uniform EL interpolants has remained unknown. In this article, we propose an approach to computing a finite uniform interpolant for a general EL terminology if it exists. To this end, we develop a quadratic representation of EL TBoxes as regular tree grammars. Further, we show that, if a finite uniform EL interpolant exists, then there exists one that is at most triple exponential in the size of the original TBox, and that, in the worst case, no smaller interpolants exist, thereby establishing tight worst-case bounds on their size. Beyond showing these bounds, the notions and results established in this paper also provide useful insights for designing efficient ontology reformulation algorithms, for instance, within the context of module extraction.

View selection in Semantic Web databases

We consider the setting of a Semantic Web database, containing both explicit data encoded in RDF triples, and implicit data, implied by the RDF semantics. Based on a query workload, we address the problem of selecting a set of views to be materialized in the database, minimizing a combination of query processing, view storage, and view maintenance costs. Starting from an existing relational view selection method, we devise new algorithms for recommending view sets, and show that they scale significantly beyond the existing relational ones when adapted to the RDF context. To account for implicit triples in query answers, we propose a novel RDF query reformulation algorithm and an innovative way of incorporating it into view selection in order to avoid a combinatorial explosion in the complexity of the selection process. The interest of our techniques is demonstrated through a set of experiments.

OLAP query reformulation in peer-to-peer data warehousing

Inter-business collaborative contexts prefigure a distributed scenario where companies organize and coordinate themselves to develop common and shared opportunities, but traditional business intelligence systems do not provide support to this end. To fill this gap, in this paper we envision a peer-to-peer data warehousing architecture based on a network of heterogeneous peers, each exposing query answering functionalities aimed at sharing business information. To enhance the decision making process, an OLAP query expressed on a peer needs to be properly reformulated on the local multidimensional schemata of the other peers. To this end, we present a language for the definition of mappings between the multidimensional schemata of peers and we introduce a query reformulation framework that relies on the translation of mappings, queries, and multidimensional schemata onto the relational level. Then, we formalize a query reformulation algorithm and prove two properties: correctness and closure, that are essential in a peer-to-peer setting. Finally, we discuss the main implementation issues related to the reformulation setting proposed, with specific reference to the case in which the local multidimensional engines hosted by peers use the standard MDX language.

Query Processing in a Mediator Based Framework for Linked Data Integration

In this paper, the authors present a three-level mediator based framework for linked data integration. In the approach, the mediated schema is represented by a domain ontology, which provides a conceptual representation of the application. Each relevant data source is described by a source ontology, published on the Web according to the Linked Data principles. Each source ontology is rewritten as an application ontology, whose vocabulary is restricted to be a subset of the vocabulary of the domain ontology. The main contribution of the paper is an algorithm for reformulating a user query into sub-queries over the data sources. The reformulation algorithm exploits inter-ontology links to return more complete query results. The approach is illustrated by an example of a virtual store mediating access to online booksellers.

P2P schema‐mapping over network‐bound XML data

AbstractThe rise in availability of web‐based data sources has led to new challenges in data integration systems for obtaining decentralized, wide‐scale sharing of data preserving semantics. In this paper, we present a framework for integrating heterogeneous XML data sources distributed over a large‐scale, highly dynamic network of autonomous nodes. We highlight a query reformulation algorithm to combine and query‐distributed XML databases through a decentralized point‐to‐point mediation process among the different data sources by using P2P schema‐mappings. More precisely, our integration model is based on path‐to‐path mappings, using the XPath language. We demonstrate the usefulness and scalability of our ideas and algorithms with a detailed set of experiments. Finally, we discuss our experience implementing the above‐cited query reformulation algorithm as a Web service within the GDIS system, a service‐based Grid architecture. We have evaluated GDIS on several real‐world schemas with promising results. Copyright © 2010 John Wiley & Sons, Ltd.

Extended algorithm for XML query reformulation

Query reformulation is a key issue of the data integration,and it automatically rewrites the user's query request to the data source request directly.Recently the University of Michigan and the IBM AImaden Research Center presented a novel algorithm for constraint-based XML query reformulation,but it did not consider the problem of complex schema matching and limited the algorithm application.Based on the original query reformulation algorithm,an extended algorithm for XML query reformulation was presented,expanding the application scope of the original algorithm.The correctness and time complexity of the extended algorithm were also given.

A service-oriented system for distributed data querying and integration on Grids

Data Grids rely on the coordinated sharing of and interaction across multiple autonomous database management systems. They provide transparent access to heterogeneous and autonomous data resources stored on Grid nodes. Data sharing tools for Grids must include both distributed query processing and data integration functionality. This paper presents the implementation of a data sharing system that (i) is tailored to data Grids, (ii) supports well established and widely spread relational DBMSs, and (iii) adopts a hybrid architecture by relying on a peer model for query reformulation to retrieve semantically equivalent expressions, and on a wrapper-mediator integration model for accessing and querying distributed data sources. The system builds upon the infrastructure provided by the OGSA-DQP distributed query processor and the XMAP query reformulation algorithm. The paper discusses the implementation methodology, and presents empirical evaluation results.

Graph-based query rewriting for knowledge sharing between peer ontologies

Peer knowledge management systems (PKMS) offer a flexible architecture for decentralized knowledge sharing. In PKMSs, the knowledge sharing and evolution processes are based on peer ontologies. Finding an effective and efficient query rewriting algorithm for regular expression queries is vital for knowledge sharing between peers in PKMSs; and for this our solution is characterized by graph-based query rewriting. Based on the graphs for both axioms and mappings, we design a novel algorithm, regular expression rewriting algorithm, to rewrite regular expression queries along semantic paths. The simulation results show that the performance of our algorithm is better than Mork’s reformulation algorithms [P. Mork, Peer architectures for knowledge sharing, PhD thesis, University of Washington, 2005. <http://www.mitre.org/staffpages/pmork/>], and our algorithm is more effective than the naive rewriting algorithm.

An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms

Many nonconvex nonlinear programming (NLP) problems of practical interest involve bilinear terms and linear constraints, as well as, potentially, other convex and nonconvex terms and constraints. In such cases, it may be possible to augment the formulation with additional linear constraints (a subset of Reformulation-Linearization Technique constraints) which do not affect the feasible region of the original NLP but tighten that of its convex relaxation to the extent that some bilinear terms may be dropped from the problem formulation. We present an efficient graph-theoretical algorithm for effecting such exact reformulations of large, sparse NLPs. The global solution of the reformulated problem using spatial Branch-and Bound algorithms is usually significantly faster than that of the original NLP. We illustrate this point by applying our algorithm to a set of pooling and blending global optimization problems.

Schema mediation for large-scale semantic data sharing

Intuitively, data management and data integration tools should be well suited for exchanging information in a semantically meaningful way. Unfortunately, they suffer from two significant problems: they typically require a common and comprehensive schema design before they can be used to store or share information, and they are difficult to extend because schema evolution is heavyweight and may break backward compatibility. As a result, many large-scale data sharing tasks are more easily facilitated by non-database-oriented tools that have little support for semantics.The goal of the peer data management system (PDMS) is to address this need: we propose the use of a decentralized, easily extensible data management architecture in which any user can contribute new data, schema information, or even mappings between other peers’ schemas. PDMSs represent a natural step beyond data integration systems, replacing their single logical schema with an interlinked collection of semantic mappings between peers’ individual schemas.This paper considers the problem of schema mediation in a PDMS. Our first contribution is a flexible language for mediating between peer schemas that extends known data integration formalisms to our more complex architecture. We precisely characterize the complexity of query answering for our language. Next, we describe a reformulation algorithm for our language that generalizes both global-as-view and local-as-view query answering algorithms. Then we describe several methods for optimizing the reformulation algorithm and an initial set of experiments studying its performance. Finally, we define and consider several global problems in managing semantic mappings in a PDMS.

The Piazza peer data management project

A major problem in today's information-driven world is that sharing heterogeneous, semantically rich data is incredibly difficult. Piazza is a peer data management system that enables sharing heterogeneous data in a distributed and scalable way. Piazza assumes the participants to be interested in sharing data, and willing to define pairwise mappings between their schemas. Then, users formulate queries over their preferred schema, and a query answering system expands recursively any mappings relevant to the query, retrieving data from other peers. In this paper, we provide a brief overview of the Piazza project including our work on developing mapping languages and query reformulation algorithms, assisting the users in defining mappings, indexing, and enforcing access control over shared data.

A classification approach to Boolean query reformulation

One of the difficulties in using current Boolean-based information retrieval systems is that it is hard for a user, especially a novice, to formulate an effective Boolean query. Query reformulation can be even more difficult and complex than formulation since users often have difficulty incorporating the new information gained from the previous search into the next query. In this article, query reformulation is viewed as a classification problem, that is, classifying documents as either relevant or nonrelevant. A new reformulation algorithm is proposed which builds a tree-structured classifier, called a query tree, at each reformulation from a set of feedback documents retrieved from the previous search. The query tree can easily be transformed into a Boolean query. The query tree is compared to two query reformulation algorithms on benchmark test sets (CACM, CISI, and Medlars). In most experiments, the query tree showed significant improvements in precision over the two algorithms compared in this study. We attribute this improved performance to the ability of the query tree algorithm to select good search terms and to represent the relationships among search terms into a tree structure.

A METHODOLOGY FOR QUERY REFORMULATION IN CIS USING SEMANTIC KNOWLEDGE

We consider Cooperative Information Systems (CIS) that are multidatabase systems (MDBMS), with a common object-oriented model, based on the ODMG standard, together with local databases that may be relational, object-oriented, or dedicated data servers. The MDBMS interface (or mediator interface) that describes this CIS could be different from the union of the local interfaces that describe each local database. In particular, the mediator interface may be defined by semantic knowledge that includes views over particular local databases, integrity constraints, and knowledge about data replication in local databases. We present a methodology for query reformulation which is based on the uniform representation of all semantic knowledge in the form of integrity assertions and mapping rules. A reformulation algorithm exploits this semantic knowledge, and performs semantic rewriting based on pattern-matching, to obtain a query on the union of the local interfaces. A decomposition algorithm then produces a composite query, and local sub-queries, one for each local interface. The reformulation is general enough to re-use the results of previously computed queries in the CIS. We have implemented this reformulation technique in our Flora compiler prototype which we used for validation and experimentation with O2 databases.