A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems

Modelling of linear dynamical systems is very important issue in science and engineering. The modelling process might be achieved by either the application of the governing laws describing the process or by using the input-output data sequence of the process. Most of the modelling algorithms reported in the literature focus on either determining the order or estimating the model parameters. In this paper, the authors present a new method for modelling. Given the input-output data sequence of the model in the absence of any information about the order, the correct order of the model as well as the correct parameters is determined simultaneously using genetic algorithm. The algorithm used in this paper has several advantages; first, it does not use complex mathematical procedures in detecting the order and the parameters; second, it can be used for low as well as high order systems; third, it can be applied to any linear dynamical system including the autoregressive, moving-average, and autoregressive moving-average models; fourth, it determines the order and the parameters in a simultaneous manner with a very high accuracy. Results presented in this paper show the potentiality, the generality, and the superiority of our method as compared with other well-known methods

A Robust Computational Technique for Model Order Reduction of Two-Time-Scale Discrete Systems via Genetic Algorithms

A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach

Solution of Inverse Kinematics Problem using Genetic Algorithms

In this paper, the solution of inverse kinematics problem of robot manipulators using genetic algorithms (GA) is presented. Two versions of genetic algorithms are used which include the conventional GA and the continuous GA. The inverse kinematics problem is formulated as an optimization problem based on the concept of minimizing the accumulative path deviation in the absence of any obstacles in the workspace. Simulation results show that the continuous GA outperforms the conventional GA from all aspects. The superiority of the continuous GA is seen in that it will always provide smooth and faster solutions as compared with the conventional GA

Continuous Genetic Algorithm as a Novel Solver for Stokes and Nonlinear Navier Stokes Problems

The one-dimensional continuous genetic algorithm (CGA) previously developed by the principal author is extended and enhanced to deal with two-dimensional spaces in this paper. The enhanced CGA converts the partial differential equations into algebraic equations by replacing the derivatives appearing in the differential equation with their proper finite difference formula in 2D spaces. This optimization methodology is then applied for the solution of steady-state two-dimensional Stokes and nonlinear Navier Stokes problems. The main advantage of using CGA for the solution of partial differential equations is that the algorithm can be applied to linear and nonlinear equations without any modification in its structure. A comparison between the results obtained using the 2D CGA and the known Galerkin finite element method using COMSOL is presented in this paper. The results showed that CGA has an excellent accuracy as compared to other numerical solvers

Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm

A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch’s and Bratu’s problems. The underlying idea of the method is to convert the two differential problems into discrete versions by replacing each of the second derivatives by an appropriate difference quotient approximation. The new method has the following characteristics. First, it should not resort to more advanced mathematical tools; that is, the algorithm should be simple to understand and implement and should be thus easily accepted in the mathematical and physical application fields. Second, the algorithm is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical and physical problems. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. The algorithm is tested on different versions of Troesch’s and Bratu’s problems. Experimental results show that the proposed algorithm is effective, straightforward, and simple

An Optimization Algorithm for Solving Systems of Singular Boundary Value Problems

In this paper, an optimization algorithm is presented for solving systems of singular boundary value problems. In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraints boundary conditions, and is then solved using continuous genetic algorithm in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Two numerical experiments are carried out to verify the mathematical results, and the theoretical statements for the solutions are supported by the results of numerical experiments.Meanwhile, the statistical analysis is provided in order to capture the behavior of the solutions and to discover the effect of system parameters on the convergence speed of the algorithm. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving systems of singular boundary value problems

Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple