6,994 research outputs found
Bidirectional branch and bound for controlled variable selection. Part III: local average loss minimization
The selection of controlled variables (CVs) from available measurements through
exhaustive search is computationally forbidding for large-scale processes. We
have recently proposed novel bidirectional branch and bound (B-3) approaches for
CV selection using the minimum singular value (MSV) rule and the local worst-
case loss criterion in the framework of self-optimizing control. However, the
MSV rule is approximate and worst-case scenario may not occur frequently in
practice. Thus, CV selection by minimizing local average loss can be deemed as
most reliable. In this work, the B-3 approach is extended to CV selection based
on local average loss metric. Lower bounds on local average loss and, fast
pruning and branching algorithms are derived for the efficient B-3 algorithm.
Random matrices and binary distillation column case study are used to
demonstrate the computational efficiency of the proposed method
Optimization in Telecommunication Networks
Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Mengerās disjoint paths theorem, and Ford-Fulkersonās max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;
Tame Decompositions and Collisions
A univariate polynomial f over a field is decomposable if f = g o h = g(h)
for nonlinear polynomials g and h. It is intuitively clear that the
decomposable polynomials form a small minority among all polynomials over a
finite field. The tame case, where the characteristic p of Fq does not divide n
= deg f, is fairly well-understood, and we have reasonable bounds on the number
of decomposables of degree n. Nevertheless, no exact formula is known if
has more than two prime factors. In order to count the decomposables, one wants
to know, under a suitable normalization, the number of collisions, where
essentially different (g, h) yield the same f. In the tame case, Ritt's Second
Theorem classifies all 2-collisions.
We introduce a normal form for multi-collisions of decompositions of
arbitrary length with exact description of the (non)uniqueness of the
parameters. We obtain an efficiently computable formula for the exact number of
such collisions at degree n over a finite field of characteristic coprime to p.
This leads to an algorithm for the exact number of decomposable polynomials at
degree n over a finite field Fq in the tame case
An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks
We present an exact and complete algorithm to isolate the real solutions of a
zero-dimensional bivariate polynomial system. The proposed algorithm
constitutes an elimination method which improves upon existing approaches in a
number of points. First, the amount of purely symbolic operations is
significantly reduced, that is, only resultant computation and square-free
factorization is still needed. Second, our algorithm neither assumes generic
position of the input system nor demands for any change of the coordinate
system. The latter is due to a novel inclusion predicate to certify that a
certain region is isolating for a solution. Our implementation exploits
graphics hardware to expedite the resultant computation. Furthermore, we
integrate a number of filtering techniques to improve the overall performance.
Efficiency of the proposed method is proven by a comparison of our
implementation with two state-of-the-art implementations, that is, LPG and
Maple's isolate. For a series of challenging benchmark instances, experiments
show that our implementation outperforms both contestants.Comment: 16 pages with appendix, 1 figure, submitted to ALENEX 201
Pseudo-scheduling: A New Approach to the Broadcast Scheduling Problem
The broadcast scheduling problem asks how a multihop network of broadcast
transceivers operating on a shared medium may share the medium in such a way
that communication over the entire network is possible. This can be naturally
modeled as a graph coloring problem via distance-2 coloring (L(1,1)-labeling,
strict scheduling). This coloring is difficult to compute and may require a
number of colors quadratic in the graph degree. This paper introduces
pseudo-scheduling, a relaxation of distance-2 coloring. Centralized and
decentralized algorithms that compute pseudo-schedules with colors linear in
the graph degree are given and proved.Comment: 8th International Symposium on Algorithms for Sensor Systems,
Wireless Ad Hoc Networks and Autonomous Mobile Entities (ALGOSENSORS 2012),
13-14 September 2012, Ljubljana, Slovenia. 12 page
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