Bahrom Sanugi

Enhanced Simulated Annealing Technique for the Single-Row Routing Problem

This paper presents ESSR (Enhanced Simulated annealing for Single-row Routing) model for solving the single-row routing problem. The main objective in this problem is to produce a realization that minimizes both the street congestion and the number of doglegs. Simulated annealing (SA) is a stochastic, hill-climbing and gradient-descent technique based on the statistical properties of particles undergoing thermal annealing. By performing slow cooling, the nets in the single-row routing problem align themselves according to a configuration with the lowest energy. The model has been known to produce reasonably good solutions for many NP-complete optimization problems, such as the single-row routing problem. In ESSR, our strategy is to minimize both the street congestion and the number of interstreet crossings (doglegs) by expressing a single energy function as their collective properties. This objective is achieved by representing the energy as the absolute sum of the heights of the net segments. To speed up convergence, we pivot the street congestion value while having the energy drops directly proportional to the number of doglegs. This action has the effect of minimizing the number of doglegs as the energy stabilizes. Our simulation work on ESSR produces optimal results in most cases for both the street congestion and the number of doglegs. Our experimental results compare well against results obtained from our earlier model (SRR-7) and two other methods reported in the literature.

Single-Row Transformation of Complete Graphs

A complete graph is a fully-connected graph where every node is adjacent to all other nodes in the graph. Very often, many applications in science and engineering are reducible to this type of graph. Hence, a simplified form of a complete graph contributes in providing the solutions to these problems. In this paper, we present a technique for transforming a complete graph into a single-row routing problem. Single-row routing is a classical technique in the VLSI design that is known to be NP-complete. We solved this problem earlier using a method called ESSR, and, the same technique is applied to the present work to transform a complete graph into its single-row routing representation. A parallel computing model is proposed which contributes in making the problem modular and scalable. We also discuss the application of this work on the channel assignment problem in the wireless cellular telephone networks.

A new fifth order five-stage runge-kutta method for initial value type problems in odes

In this paper, a new 5-stage explicit fifth order nonlinear Runge-Kutta method is developed based on geometric mean formulation in the functional values. Since it is impossible to attain a fifth order accuracy with a 5-stage explicit linear method, this strategy of nonlinear formulation proves advantageous over the usual linear formulation in terms of accuracy. The derivation of the method is given in detail along with the absolute stability consideration. A numerical example is provided which shows that this new method is well placed among the fifth order methods and it is superior when compared with fourth order Runge-Kutta method including a 5-stage ones.

Ad-hoc network design with multiple metrics using Taguchi's loss function

This paper presents an approach for tackling multiple metrics and various network parameters simultaneously to investigate the performance of wireless ad-hoc network routing protocols. The study uses Taguchis loss function to determine the best condition in yielding maximum throughput and minimum packet drop and routing overhead simultaneously for dynamic source routing (DSR) protocol. Studying the parameters one at a time or by trial and error until a first feasible design is found seems to be a common approach to design optimization. In this paper, the impact of ad-hoc network parameters such as terrain, network size, number of sources, packet transmitted rates, node speed and pause time on a multiple signal to noise ratio are investigated simultaneously. We present results based on simulation study according to Taguchi experimental design technique. Optimum levels of ad-hoc network parameters are suggested by using response table and response graph while contribution of significant parameter are estimated using analysis of variance (ANOVA). The results show that the terrain size, number of sources, transmission packet rates and nodes speed are the significant parameters affecting DSR performance in wireless ad-hoc networks.

A Neural Network Model For The Common Due Date Job Scheduling On Unrelated Parallel Machines

This paper presents an approach for scheduling under a common due date on parallel unrelated machine problems based on artificial neural network. The objective is to allocate and sequence the jobs on the machines so that the total cost is minimized. The total cost is the sum of the total earliness and the total tardiness cost. The multilayer Perceptron (MLP) neural network is a suitable model in our study due to the fact that the problem is NP-hard. In our study, neural network has been proven to be effective and robust in generating near optimal solutions to the problem.

On the probability of route existence in mobile wireless networks

This paper presents a route selection method in mobile wireless networks to a given destination based on the probability that the route is still available for a packet to be sent. The probability is based on the knowledge at each node of the geographic position of all the other nodes in the network and taking into account the mobility of the nodes and the dependencies between links in a computed route. We derive a simple closed form expression for the computation of the availability of a route, which can then be used to select the best route.

An integral equation approach for the numerical solution of the Riemann problem on a simply connected region with corners

In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integral equation on the boundary. By using results of Hille and Muskhelishvili, the theory is extended to include boundaries with corners which are rarely used for numerical computation. Following Swarztraubers derivation of an integral equation for the numerical solution of Dirichlet problem in a region of general shape, we use the Picard iteration method to obtain an iterative formula which removes singularities during numerical integration. The result is a direct method which does not involve conformal mapping. The numerical examples given demonstrate the effectiveness of this new strategy.

A Fifth -Order Five-Stage RK-Method Based on Harmonic Mean

In this paper a fifth-order five-stage Runge-Kutta formula based on Harmonic mean is developed for solving initial value problem of the type y′ = f(y), y(x 0) = y 0. The stability analysis reveals that the region of absolute stability for this method is larger than that of Taylor series’s method of order five. Numerical examples indicate that this method is superior when compared to some existing methods including the 5-stage GM-RK method, Taylor Series’s method of order 5, and RK5(6) method of Nystrom version.

A Mean-Field Annealing Model for the Single-Row Routing Problem

Abstract This paper presents a mean-field annealing model to solve the single-row routing problem. The concept is borrowed from the statistical mechanics properties of particles which combines features from the Hopfield neural network and the stochastic simulated annealing. The mean-field annealing approach approximates its solution deterministically rather than performing the slow hill-climbing search to its optimal solution, while at the same time, avoiding the local minima. The thermostatic annealing process aligns the particles (nets) into their optimal states which corresponds to a realization with the minimum street congestion at their equilibrium temperature. Our simulations are successful in generating several near-optimal realizations for various net sizes and configurations.

Penganggaran dan Pengawalan Ralat Dalam Kaedah HaM-4(4) Untuk Penyelesaian Masalah Nilai Awal

Dalam kertas ini satu kaedah baru yang berasaskan gabungan min harmoni dan min aritmatik berperingkat keempat dirumuskan. Kaedah ini, beserta kaedah Rungge-Kutta-Harmoni, RK-HaM dapat mambantu menganggarkan ralat dalam penyelesaian masalah nilai awal. Rantau kestabilan mutlak untuk kaedah ini juga dikaji. Contoh penyelesaian berangka yang dikemukakan menunjukkan keberkesanan kaedah ini. Katakunci: Kaedah RK-HaM; kaedah RK-AHM; Kaedah HaM-RK4(4); kestabilan anggaran ralat; pengawal ralat In this papaer a new fourth order formula based on harmonic and arithmatic means is formulated. The formula when used with the Harmonic-Rungge-Kutta formula is capable of estimating the local truncution error in solving initial value problems. The absolute stability region of the method is also studied. The numerical results presented showed the effectiveness of the method. Keywords: RK-HaM method; RK-AHM method; HaM-RK4(4) method; stability; error estimate; error control