Finding global minimum using filled function method

Filled function method is an optimization method for finding global minimizers. Filled function method is a combination of a local search in findings local solutions as well as global solution. It is basically a construction and eventually the inclusion of an auxiliary function called the filled function into the algorithm. Optimizing the objective function at an initial point will only yield a local minimizer. By using the auxiliary function, the local minimizer is shifted to a new lower basin of the objective function. The shifted point is the new initial solution for the local search to find the next local minimizer, where the function value is lower. The process continued until the global minimizer is achieved. This research used several test functions to examine the effectiveness of the method in finding global solution. The results show that this method works successfully and further research directions are discussed

Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model

In this paper, we present the numerical solution for the optimal control problem of monodomain model with Rogersmodified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan method for computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used

Implicit second and third orders runge-kutta for handling discontinuities in delay differential equations

Implicit Runge-Kutta (RK) methods have been developed and implemented in solving Delay Differential Equations (DDEs) systems which often encounter discontinuities. These discontinuities might occur after and even before the initial solution. The methods are chosen because they can be modified to handle discontinuities by means of mapping of past values and they are in fact the most well-organized way to handle the so-called stiff differential equations, which are differential equations usually characterized by a rapidly decaying solution. The advantage of implicit Runge-Kutta methods is in their superior stability compared to the explicit methods, more so when applied to stiff equations. Our objective is to develop a scheme for solving DDEs using implicit RK2 and RK3. Our numerical scheme is able to successfully handle discontinuities in the system and produces results with acceptable error. We compare the result from [1] which used explicit RK2 and RK4 with our findings. Our result is markedly better than [1] even in the lower order RK

Constrained artificial bee colony algorithm for optimization problems

Artificial Bee Colony (ABC) algorithm is a well known swarm intelligence algorithms which have shown a competitive performance with respect to other population-based algorithms. However, this algorithm has poor exploitation ability. To address this issue, an Improved Constrained Artificial Bee Colony (icABC) algorithm is proposed where three new solution search equations are introduced respectively to employed bee, onlooker bee and scout bee phases. This algorithm is tested on several constrained benchmark Problems. The numerical results demonstrate that the icABC is competitive with other state-of-the-art constrained ABC algorithm under consideration

Optimal control of vector-borne disease with direct transmission

This paper introduces the usage of three controls as a way to reduce the occurrence of vector-borne disease. The governing equation of the dynamical system used in this paper describes both direct and indirect transmission mode of vector-borne disease. This means that the disease can be transmitted in two different ways. First, it can be transmitted through mosquito bites and the other is through human blood transfusion. The three controls that are incorporated in the dynamical system include a measurement of basic practice for blood donation procedure, self-prevention effort and vector control strategy by health authority. The optimality system of the three controls is characterized using optimal control theory and the existence and uniqueness of the optimal control are established. Then, the effect of the incorporation of the three controls is investigated by performing numerical simulation

FUZZY DELAY DIFFERENTIAL EQUATIONS WITH HYBRID SECOND AND THIRD ORDERS RUNGE-KUTTA METHOD

This paper considers fuzzy delay differential equations with known statedelays. A dynamic problem is formulated by time-delay differential equations and an efficient scheme using a hybrid second and third orders Runge-Kutta method is developed and applied. Runge-Kutta is well-established methods and can be easily modified to overcome the discontinuities, which occur in delay differential equations. Our objective is to develop a scheme for solving fuzzy delay differential equations. A numerical example was run, and the solutions were validated with the exact solution. The numerical results from C program will show that the hybrid Runge-Kutta scheme able to calculate the fuzzy solutions successfully

The effect of the influx of foreign labour in Malaysia by augmented MRW model

There are pros and cons in hiring foreign labour on the economy. The influx of foreign labour is a common phenomenon, but when their involvement is unlimited it will be one serious issue. Malaysia is one of the developing countries where industrial and construction sectors are in need of labour and this has opened up opportunities for foreign labour. Their inflow into Malaysia is increasing every year and this has caused problems such as time-consuming construction due to low-skilled labour and crime problems caused by problematic labour. We augmented Mankiw-Romer-Weil model by isolating the foreign labour element in human capital to find the effect of the influx of foreign labour in Malaysian economic growth. The results from our model show that the employment of foreign labour increases the rate of human capital but decreases the rate of physical capital. Therefore, the level of the production function also decreases

The Newton-like properties of the updating mechanism of a model-reality differences algorithm

The Dynamic Integrated Systems Optimization and Parameter Estimation (DISOPE) algorithm is an algorithm for solving nonlinear optimal control problems and is of the gradient descent type. The updating step of DISOPE plays an important role in terminating the iterations of the algorithm and hence in determining its rate of convergence. In this paper, the mechanism was shown to have Newton-like properties and the order convergence establishe