Pusat Pengajian Sains Matematik - Geran Penyelidikan

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Now showing 1 - 5 of 7
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    Direction Set Based Methods For Adaptive Least Squares Problems: Improvements And Innovations
    (Universiti Sains Malaysia, 2008-06-01)
    Ahmad, Noor Atinah
    The main objective of this research is to provide a mathematically tractable solutions to the adaptive filtering problem by formulating the problem as an adaptive least squares problem. This approach follows the work of Chen (1998) in his study of direction-set based CDS) adaptive filtering algorithm. Through the said formulation, we relate the DS algorithm to a class of projection method. In particular, the simplified version of the algorithm, which is the Euclidean direction search (EDS) algorithm is shown to be related to a class of iterative methods called relaxation methods. This findings enable us to improve the EDS algorithm to the accelerated EDS where an acceleration parameter is introduced to optimize the step size during each line search. Our formulation also allows us to consider other types of search method, in particular the conjugate direction based methods. Global convergence of existing conjugate gradient (CG) based method are proved by viewing the methods as a form of conjugate gradient method without line search. Another globally convergent descent algorithm is developed based on pair-wise conjugation of gradient. In stochastic setting, this new algorithm proved to be comparable to existing CG based method. Furthermore, due to the absence of explicit computation of the stochastically recursive conjugate search directions, the algorithm provides a much lower computational complexity, which makes it more favorable for high speed computing. We also extend our formulation to the preconditioned adaptive least squares problem which is shown to be an appropriate formulation for transform-domain adaptive filtering. Although analyses of alternative pre conditioners are still at an early stage of research, we are able to provide a new preconditioner for the problem derived directly from the mathematical formulation of the problem.
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    Designing optimal routing solutions for logistic operations
    (Universiti Sains Malaysia, 2016-11-14)
    Joshua, Ignatius
    One way to generate a higher recycling rate is to handle materials recovery efficiently. Conventional recycling schemes require the recylates to be "clean", i.e. separated prior to coming into the material recovery facility (MRF). However, it is inconvenient to pre-sort their recyclates.To solve this problem, we propose multiple bins to be assigned to each personnel to maximize conveyor belt usage. We model the unload-and-switch cycle through a 2-nested routing problem. A numerical example validates the approach.
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    Comparison Between Genetic Algorithm And Prey-Predator Algorithm
    (Universiti Sains Malaysia, 2015-11-04)
    Ong, Hong Choon
    The use of metaheuristic algorithms to different problems becomes very common after the introduction of genetic algorithm in 1975. Most of these algorithms are inspired by real life biological phenomenon. We introduce a new metaheuristic algorithm inspired by prey-predator interaction of animals. In the algorithm, randomly generated solutions are assigned as a predator and preys depending on their performance on the objective function. We also compared the performance of this algorithm with the genetic algorithm on selected test problems and we showed that the new algorithm performed better in our publication. A more complete list of comparison with five algorithms were done in detail in the dissertation of a masters student under this grant. We also studied the properties of this new algorithm in the work of another two masters students with the work published in an indexed journal. The applications of these algorithms have gone far beyond the scientific field to different real problems as demonstrated in our publications. We are currently extending the newly introduced prey-predator algorithm to incorporate a more general scenario in the work of our current on-going PhD student.
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    Classification Of Moufang Loops Of Odd Order pq3
    (Universiti Sains Malaysia, 2014-01-31)
    BALASINGAM GNANARAJ, ANDREW RAJAH
    An open problem in the theory of Moufang loops is to classify those loops which are minimally non associative, that is, loops which are non associative but where all proper subloops are associative. A related question is to classify all integers n for which a minimally nonassociative Moufang loop exists. In [Possible orders of nonassociative Moufang loops, Comment. Math. Univ. Carolin. 41~2) (2000) 237-244], O. Chein and A. Rajah showed that a minimal non associative Moufang loop of order 2q can be constructed by using a non-abelian group of order q3. In [Moufang loops of odd order pq3, J. Algebra 235 (2001) 66-93], A. Rajah proved that for odd primes p < q, a nonassociative Moufang loops of order pq3 exists if and only if q:: 1 (mod p). We have completely classified all minimally nonassociative Moufang loops of order pq3 for primes p < q. This result has been published as a joint article with Wing Loon Chee and Stephen M. Gagola III titled "Classification of minimal non associative Moufang loops of order pq311 in International Journal of Algebra and Computation, Volume 23, NO.8 (2013) 1895-1908 on 22 January 2014.
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    Building and Developing Agent Based Modelling For Higher Order Logic in Neuro Symbolic Integration PHASE & YEAR
    (Universiti Sains Malaysia, 2016-03-21)
    Sathasivam, Saratha
    We will develop agent based modelling (ABM) for doing logic programming and Reverse Analysis method in doing higher order logic programming. Later, we will build another ABM for the upgraded method (integrating Boltzmann machine and Modify Activation Function). Agent-based Modelling (ABM) which also called individual-based modelling is a new computational modelling paradigm which is an analyzing systems that representing the 'agents' that involving and simulating of their interactions. We will test ABM for this upgraded method (higher order logic programming, Hopfield network, Boltzmann machine and activation function in some real life and simulated data sets. We are going to test this method on some constraint optimization problems.