243,451 research outputs found
Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations
© 2013 IEEE. Complementing missing information and priority vector are of significance important aspects in group decision making (GDM) with incomplete hesitant fuzzy linguistic preference relations (HFLPRs). In this paper, an integer programming model is developed based on additive consistency to estimate missing values of incomplete HFLPRs by using additive consistency. Once the missing values are complemented, a mixed 0-1 programming model is established to derive the priority vectors from complete HFLPRs, in which the underlying idea of the mixed 0-1 programming model is the probability sampling in statistics and minimum deviation between the priority vector and HFLPR. In addition, we also propose a new GDM approach for incomplete HFLPRs by integrating the integer programming model and the mixed 0-1 programming model. Finally, two case studies and comparative analysis detail the application of the proposed models
A CENTER OF A POLYTOPE: AN EXPOSITORY REVIEW AND A PARALLEL IMPLEMENTATION
ABSTRACT. The solution space of the rectangular linear system Az b, subject to x> 0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem. KEY WORDS AND PHRASES. Center of a polytope, consistency check, Euclidean distance, initial feasible solution, linear programming, Moore-Penrose inverse, nonnegative solution
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
Proposed Consistent Exception Handling for the BLAS and LAPACK
Numerical exceptions, which may be caused by overflow, operations like
division by 0 or sqrt(-1), or convergence failures, are unavoidable in many
cases, in particular when software is used on unforeseen and difficult inputs.
As more aspects of society become automated, e.g., self-driving cars, health
monitors, and cyber-physical systems more generally, it is becoming
increasingly important to design software that is resilient to exceptions, and
that responds to them in a consistent way. Consistency is needed to allow users
to build higher-level software that is also resilient and consistent (and so on
recursively). In this paper we explore the design space of consistent exception
handling for the widely used BLAS and LAPACK linear algebra libraries, pointing
out a variety of instances of inconsistent exception handling in the current
versions, and propose a new design that balances consistency, complexity, ease
of use, and performance. Some compromises are needed, because there are
preexisting inconsistencies that are outside our control, including in or
between existing vendor BLAS implementations, different programming languages,
and even compilers for the same programming language. And user requests from
our surveys are quite diverse. We also propose our design as a possible model
for other numerical software, and welcome comments on our design choices
Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models
Constraint Programming viewed as Rule-based Programming
We study here a natural situation when constraint programming can be entirely
reduced to rule-based programming. To this end we explain first how one can
compute on constraint satisfaction problems using rules represented by simple
first-order formulas. Then we consider constraint satisfaction problems that
are based on predefined, explicitly given constraints. To solve them we first
derive rules from these explicitly given constraints and limit the computation
process to a repeated application of these rules, combined with labeling.We
consider here two types of rules. The first type, that we call equality rules,
leads to a new notion of local consistency, called {\em rule consistency} that
turns out to be weaker than arc consistency for constraints of arbitrary arity
(called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule
consistency coincides with the closure under the well-known propagation rules
for Boolean constraints. The second type of rules, that we call membership
rules, yields a rule-based characterization of arc consistency. To show
feasibility of this rule-based approach to constraint programming we show how
both types of rules can be automatically generated, as {\tt CHR} rules of
\cite{fruhwirth-constraint-95}. This yields an implementation of this approach
to programming by means of constraint logic programming. We illustrate the
usefulness of this approach to constraint programming by discussing various
examples, including Boolean constraints, two typical examples of many valued
logics, constraints dealing with Waltz's language for describing polyhedral
scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming
Journa
Internal Design of the DSS
This technical report describes the implementation of the DSS middleware with focus on the design of the abstract entity interface and the coordination layer. Key concepts are highlighted and described, on the level of C++ classes
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