scholarly journals PENERAPAN COCKROACH SWARM OPTIMIZATION ALGORITHM (CSOA) PADA PENYELESAIAN PERSAMAAN POLINOMIAL YANG MEMILIKI AKAR KOMPLEKS

2018 ◽  
Vol 18 (2) ◽  
pp. 81
Author(s):  
Ema Fahma Farikha ◽  
Rusli Hidayat ◽  
Muhammad Ziaul Arif
Keyword(s):  
Optimization Algorithm ◽  
Linear Equations ◽  
Food Sources ◽  
Polynomial Equations ◽  
Metaheuristic Algorithm ◽  
Swarm Optimization ◽  
Non Linear Equation ◽  
Complex Roots ◽  
Non Linear ◽  
Newton Raphson

In this paper, we use a metaheuristic algorithm for solving non-linear equations (polynomial equations) which have a set of complex roots (complex numbers). The metaheuristic algorithm is the Cockroach Swarm Optimization Algorithm (CSOA) which imitate various types of natural cockroach behaviors such as chase-swarming, dispersing and ruthlessness when hunting for food sources. In this study, several examples of non-linear polynomial equations were used for evaluating the accuracy of CSOA. In this simulation, the accuracy comparison has been accomplished. It is shown that CSOA results are more accurate compared to the Newton-Raphson results. Keywords: Cockroach Swarm Optimization Algorithm, Complex roots of polynomial, Newton-Raphson, Non-Linear equation.

scholarly journals Performance Assessment Techniques for the 3-Phase IAG

2019 ◽  
Vol 9 (2) ◽  
pp. 2191-2200
Keyword(s):  
Performance Assessment ◽  
Linear Equations ◽  
Optimization Technique ◽  
Advantages And Disadvantages ◽  
Non Linear Equation ◽  
Non Linear ◽  
Assessment Techniques ◽  
Preliminary Study ◽  
Non Linear Equations ◽  
Steady State Performance

This manuscript covers the analytical and optimization based techniques for the performance assessment of 3-phase IAG furnishing 3-phase and 1-phase load. It examines initially the basic phenomenon of voltage build-up and then the steady state performance of 3-phase IAG furnishing 3-phase and 1-phase load. This preliminary study forms the foundation or basis of the design of future controllers. The conventional techniques and MATLAB based optimization technique fsolve is elaborated in detail along-with advantages and disadvantages for attaining the solution of simultaneous non linear equation. The fsolve technique is recommended for the solution of non-linear equations due to its advantages over conventional method.

Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.

Complementary bounds for inner products associated with non-linear equations

1984 ◽  
Vol 96 (1-2) ◽  
pp. 135-142 ◽  
Author(s):  
R. J. Cole ◽  
J. Mika ◽  
D. C. Pack
Keyword(s):  
Real Hilbert Space ◽  
Linear Equations ◽  
Linear Operators ◽  
Inner Product ◽  
Upper And Lower Bounds ◽  
Non Linear Equation ◽  
Non Linear ◽  
Non Linear Operator ◽  
Non Linear Equations ◽  
Unknown Solution

SynopsisFunctionals are found that give upper and lower bounds to the inner product 〈g0, f〉 involving the unknown solution f of a non-linear equation T[f] = f0, with f∈H, a real Hilbert space, g0 a given function in H and f0 a given function in the range of the non-linear operator T. The method depends upon a re-ordering of terms in the expansion of T[f] about a trial function so as to transfer the non-linearity to a secondary problem that requires its own particular treatment and to enable earlier results obtained for linear operators to be used for the main part. First, bivariational bounds due to Barnsley and Robinson are re-derived. The new and more accurate bounds are given under relaxed assumptions on the operator T by introducing a third approximating function. The results are obtained from identities, thus avoiding some of the conditions imposed by the use of variational methods. The accuracy of the new method is illustrated by applying it to the problem of the heat contained in a bar.

scholarly journals A Generic Optimization Algorithm for the Allocation of DP Actuators

2011 ◽  
Author(s):  
E. F. G. van Daalen ◽  
J. L. Cozijn ◽  
C. Loussouarn ◽  
P. W. Hemker
Keyword(s):  
Optimization Algorithm ◽  
Lagrange Multipliers ◽  
Linear Equations ◽  
Exact Expression ◽  
Computational Effort ◽  
Total Power ◽  
Linear Solution ◽  
Multipliers Method ◽  
Non Linear ◽  
The Cost

In this paper we present a generic optimization algorithm for the allocation of dynamic positioning actuators, such as azimuthing thrusters and fixed thrusters. The algorithm is based on the well-known Lagrange multipliers method. In the present approach the Lagrangian functional represents not only the cost function (the total power delivered by all actuators), but also all constraints related to thruster saturation and forbidden zones for azimuthing thrusters. In the presented approach the application of the Lagrange multipliers method leads to a nonlinear set of equations, because an exact expression for the total power is applied and the actuator limitations are accounted for in an implicit manner, by means of nonlinear constraints. It is solved iteratively with the Newton-Raphson method and a step by step implementation of the constraints related to the actuator limitations. In addition, the results from the non-linear solution method were compared with the results from a simplified set of linear equations, based on an approximate (quadratic) expression for the thruster power. The non-linear solution was more accurate, while requiring only a slightly higher computational effort. An example is shown for a thruster configuration with 8 azimuthing thrusters, typical for a DP semi-submersible. The results show that the optimization algorithm is very stable and efficient. Finally, some options for improvements and future enhancements — such as including thruster-thruster and thruster-hull interactions and the effects of current — are discussed.

Adaptive Neuro-Fuzzy Control Approach Based on Particle Swarm Optimization

2012 ◽  
pp. 81-98
Author(s):  
Gomaa Zaki El-Far
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Fuzzy Controller ◽  
Particle Swarm ◽  
Search Space ◽  
Swarm Optimization ◽  
Control Approach ◽  
Search Spaces ◽  
Neuro Fuzzy ◽  
Non Linear

This paper proposes a modified particle swarm optimization algorithm (MPSO) to design adaptive neuro-fuzzy controller parameters for controlling the behavior of non-linear dynamical systems. The modification of the proposed algorithm includes adding adaptive weights to the swarm optimization algorithm, which introduces a new update. The proposed MPSO algorithm uses a minimum velocity threshold to control the velocity of the particles, avoids clustering of the particles, and maintains the diversity of the population in the search space. The mechanism of MPSO has better potential to explore good solutions in new search spaces. The proposed MPSO algorithm is also used to tune and optimize the controller parameters like the scaling factors, the membership functions, and the rule base. To illustrate the adaptation process, the proposed neuro-fuzzy controller based on MPSO algorithm is applied successfully to control the behavior of both non-linear single machine power systems and non-linear inverted pendulum systems. Simulation results demonstrate that the adaptive neuro-fuzzy logic controller application based on MPSO can effectively and robustly enhance the damping of oscillations.

New Algorithm for Solution of the Non-Linear Equation Systems Occurring in the Design of Thermal Systems

1993 ◽  
Author(s):  
Halil Ibrahim Saraç ◽  
Hasan Riza Güven ◽  
Nedim Sözbir ◽  
Ünal Uysal
Keyword(s):  
Linear Equation ◽  
Linear Systems ◽  
Linear Equations ◽  
Thermal Systems ◽  
Seidel Method ◽  
Non Linear Equation ◽  
Non Linear ◽  
Air Compression ◽  
Non Linear Equations ◽  
Linear Equation Systems

Abstract Models used for the design of thermal systems often lead to non-linear equations which can be converted to linear systems. In this paper, a new algorithm is described for the solution of linear equation systems which have normal or ill-conditioned form A new algorithm and the Gauss-Seidel method were used for two-stage air compression with an inter-cooler. The solutions obtained by using two different methods are compared.

Improved Self-Adaptive Glowworm Swarm Optimization Algorithm

2014 ◽  
Vol 519-520 ◽  
pp. 798-801 ◽  
Author(s):  
Rong Zheng Chen
Keyword(s):  
Optimization Algorithm ◽  
Linear Equations ◽  
Experimental Results ◽  
Swarm Optimization ◽  
Slow Convergence ◽  
Solution Of Equations ◽  
Glowworm Swarm Optimization ◽  
Lower Accuracy ◽  
Adaptive Step ◽  
Self Adaptive

The sparse sets of linear equations are produced in electrical surveying, how to raise the efficiency of the solution of equations is the key to Object-probed. Glowworm swarm optimization algorithm (GSO) algorithm put forward to solve linear equations.To overcome slow convergence and lower accuracy solution, independent movement and self-adaptive step was proposed to improve the GSO (IGSO). The experimental results prove that, IGSO has a better performance than GSO.

Sign in / Sign up

Export Citation Format

Share Document