Abstract: This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the tractability problem.
Abstract: In this article, we propose a methodology for the
characterization of the suspended matter along Algiers-s bay. An
approach by multi layers perceptron (MLP) with training by back
propagation of the gradient optimized by the algorithm of Levenberg
Marquardt (LM) is used. The accent was put on the choice of the
components of the base of training where a comparative study made
for four methods: Random and three alternatives of classification by
K-Means. The samples are taken from suspended matter image,
obtained by analytical model based on polynomial regression by
taking account of in situ measurements. The mask which selects the
zone of interest (water in our case) was carried out by using a multi
spectral classification by ISODATA algorithm. To improve the
result of classification, a cleaning of this mask was carried out using
the tools of mathematical morphology. The results of this study
presented in the forms of curves, tables and of images show the
founded good of our methodology.
Abstract: In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.
Abstract: For a quick and accurate calculation of spatial neutron
distribution in nuclear power reactors 3D nodal codes are usually
used aiming at solving the neutron diffusion equation for a given
reactor core geometry and material composition. These codes use a
second order polynomial to represent the transverse leakage term. In
this work, a nodal method based on the well known nodal expansion
method (NEM), developed at COPPE, making use of this polynomial
expansion was modified to treat the transverse leakage term for the
external surfaces of peripheral reflector nodes.
The proposed method was implemented into a computational
system which, besides solving the diffusion equation, also solves the
burnup equations governing the gradual changes in material
compositions of the core due to fuel depletion. Results confirm the
effectiveness of this modified treatment of peripheral nodes for
practical purposes in PWR reactors.
Abstract: This paper presents unified theory for local (Savitzky-
Golay) and global polynomial smoothing. The algebraic framework
can represent any polynomial approximation and is seamless from
low degree local, to high degree global approximations. The representation
of the smoothing operator as a projection onto orthonormal
basis functions enables the computation of: the covariance matrix
for noise propagation through the filter; the noise gain and; the
frequency response of the polynomial filters. A virtually perfect Gram
polynomial basis is synthesized, whereby polynomials of degree
d = 1000 can be synthesized without significant errors. The perfect
basis ensures that the filters are strictly polynomial preserving. Given
n points and a support length ls = 2m + 1 then the smoothing
operator is strictly linear phase for the points xi, i = m+1. . . n-m.
The method is demonstrated on geometric surfaces data lying on an
invariant 2D lattice.
Abstract: The theory of Groebner Bases, which has recently been
honored with the ACM Paris Kanellakis Theory and Practice Award,
has become a crucial building block to computer algebra, and is
widely used in science, engineering, and computer science. It is wellknown
that Groebner bases computation is EXP-SPACE in a general
polynomial ring setting.
However, for many important applications in computer science
such as satisfiability and automated verification of hardware and
software, computations are performed in a Boolean ring. In this paper,
we give an algorithm to show that Groebner bases computation is PSPACE
in Boolean rings. We also show that with this discovery,
the Groebner bases method can theoretically be as efficient as
other methods for automated verification of hardware and software.
Additionally, many useful and interesting properties of Groebner
bases including the ability to efficiently convert the bases for different
orders of variables making Groebner bases a promising method in
automated verification.
Abstract: In this paper, we consider the control of time delay system
by Proportional-Integral (PI) controller. By Using the Hermite-
Biehler theorem, which is applicable to quasi-polynomials, we seek
a stability region of the controller for first order delay systems. The
essence of this work resides in the extension of this approach to
second order delay system, in the determination of its stability region
and the computation of the PI optimum parameters. We have used
the genetic algorithms to lead the complexity of the optimization
problem.
Abstract: The effect of a time delay on the transmission on
dengue fever is studied. The time delay is due to the presence of an
incubation period for the dengue virus to develop in the mosquito
before the mosquito becomes infectious. The conditions for the
existence of a Hopf bifurcation to limit cycle behavior are
established. The conditions are different from the usual one and they
are based on whether a particular third degree polynomial has
positive real roots. A theorem for determining whether for a given
set of parameter values, a critical delay time exist is given. It is
found that for a set of realistic values of the parameters in the model,
a Hopf bifurcation can not occur. For a set of unrealistic values of
some of the parameters, it is shown that a Hopf bifurcation can occur.
Numerical solutions using this last set show the trajectory of two of
the variables making a transition from a spiraling orbit to a limit
cycle orbit.
Abstract: Our aim in this piece of work is to demonstrate the
power of the Laplace Adomian decomposition method (LADM) in
approximating the solutions of nonlinear differential equations
governing the two-dimensional viscous flow induced by a shrinking
sheet.
Abstract: The human friendly interaction is the key function of a human-centered system. Over the years, it has received much attention to develop the convenient interaction through intention recognition. Intention recognition processes multimodal inputs including speech, face images, and body gestures. In this paper, we suggest a novel approach of intention recognition using a graph representation called Intention Graph. A concept of valid intention is proposed, as a target of intention recognition. Our approach has two phases: goal recognition phase and intention recognition phase. In the goal recognition phase, we generate an action graph based on the observed actions, and then the candidate goals and their plans are recognized. In the intention recognition phase, the intention is recognized with relevant goals and user profile. We show that the algorithm has polynomial time complexity. The intention graph is applied to a simple briefcase domain to test our model.
Abstract: Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.
Abstract: In the process of polyethylene extrusion polymer
material similar to powder or granule is under compression, melting
and transmission operation and on base of special form, extrudate has
been produced. Twin-screw extruders are applicable in industries
because of their high capacity. The powder mixing with chemical
additives and melting with thermal and mechanical energy in three
zones (feed, compression and metering zone) and because of gear
pump and screw's pressure, converting to final product in latest plate.
Extruders with twin-screw and short distance between screws are
better than other types because of their high capacity and good
thermal and mechanical stress.
In this paper, process of polyethylene extrusion and various tapes
of extruders are studied. It is necessary to have an exact control on
process to producing high quality products with safe operation and
optimum energy consumption.
The granule size is depending on granulator motor speed. Results
show at constant feed rate a decrease in granule size was found whit
Increase in motor speed. Relationships between HDPE feed rate and
speed of granulator motor, main motor and gear pump are calculated
following as:
x = HDPE feed flow rate, yM = Main motor speed
yM = (-3.6076e-3) x^4+ (0.24597) x^3+ (-5.49003) x^2+ (64.22092)
x+61.66786 (1)
x = HDPE feed flow rate, yG = Gear pump speed
yG = (-2.4996e-3) x^4+ (0.18018) x^3+ (-4.22794) x^2+ (48.45536)
x+18.78880 (2)
x = HDPE feed flow rate, y = Granulator motor speed
10th Degree Polynomial Fit: y = a+bx+cx^2+dx^3... (3)
a = 1.2751, b = 282.4655, c = -165.2098,
d = 48.3106, e = -8.18715, f = 0.84997
g = -0.056094, h = 0.002358, i = -6.11816e-5
j = 8.919726e-7, k = -5.59050e-9
Abstract: We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Abstract: In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.
Abstract: The optimization and control problem for 4D trajectories
is a subject rarely addressed in literature. In the 4D navigation
problem we define waypoints, for each mission, where the arrival
time is specified in each of them. One way to design trajectories for
achieving this kind of mission is to use the trajectory optimization
concepts. To solve a trajectory optimization problem we can use
the indirect or direct methods. The indirect methods are based on
maximum principle of Pontryagin, on the other hand, in the direct
methods it is necessary to transform into a nonlinear programming
problem. We propose an approach based on direct methods with a
pseudospectral integration scheme built on Chebyshev polynomials.
Abstract: As we know, most differential equations concerning
physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be
so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e.,
We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this
reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be
necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.
Abstract: In this paper back-propagation artificial neural network
(BPANN )with Levenberg–Marquardt algorithm is employed to
predict the deformation of the upsetting process. To prepare a
training set for BPANN, some finite element simulations were
carried out. The input data for the artificial neural network are a set
of parameters generated randomly (aspect ratio d/h, material
properties, temperature and coefficient of friction). The output data
are the coefficient of polynomial that fitted on barreling curves.
Neural network was trained using barreling curves generated by
finite element simulations of the upsetting and the corresponding
material parameters. This technique was tested for three different
specimens and can be successfully employed to predict the
deformation of the upsetting process
Abstract: The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.
Abstract: In this paper, a novel deinterlacing algorithm is
proposed. The proposed algorithm approximates the distribution of the
luminance into a polynomial function. Instead of using one
polynomial function for all pixels, different polynomial functions are
used for the uniform, texture, and directional edge regions. The
function coefficients for each region are computed by matrix
multiplications. Experimental results demonstrate that the proposed
method performs better than the conventional algorithms.
Abstract: New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.