Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation

2021 ◽  
pp. 223-243
Author(s):  
Vijaya Lakshmi V. Nadimpalli ◽  
Rajeev Wankar ◽  
Raghavendra Rao Chillarige
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equation ◽  
Search Space ◽  
Regions Of Interest ◽  
New Method ◽  
Real Numbers ◽  
Algorithmic Approach ◽  
Space Reduction ◽  
Complex Zeros ◽  
The Given

In this article, an innovative Genetic Algorithm is proposed to find potential patches enclosing roots of real valued function f:R→R. As roots of f can be real as well as complex, the function is reframed on to complex plane by writing it as f(z). Thus, the problem now is transformed to finding potential patches (rectangles in C) enclosing z such that f(z)=0, which is resolved into two components as real and imaginary parts. The proposed GA generates two random populations of real numbers for the real and imaginary parts in the given regions of interest and no other initial guesses are needed. This is the prominent advantage of the method in contrast to various other methods. Additionally, the proposed ‘Refinement technique' aids in the exhaustive coverage of potential patches enclosing roots and reinforces the selected potential rectangles to be narrow, resulting in significant search space reduction. The method works efficiently even when the roots are closely packed. A set of benchmark functions are presented and the results show the effectiveness and robustness of the new method.

Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation

2017 ◽  
Vol 6 (2) ◽  
pp. 18-37 ◽  
Author(s):  
Vijaya Lakshmi V. Nadimpalli ◽  
Rajeev Wankar ◽  
Raghavendra Rao Chillarige
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equation ◽  
Complex Plane ◽  
Search Space ◽  
Regions Of Interest ◽  
Real Numbers ◽  
Algorithmic Approach ◽  
Space Reduction ◽  
Complex Zeros ◽  
The Given

In this article, an innovative Genetic Algorithm is proposed to find potential patches enclosing roots of real valued function f:R→R. As roots of f can be real as well as complex, the function is reframed on to complex plane by writing it as f(z). Thus, the problem now is transformed to finding potential patches (rectangles in C) enclosing z such that f(z)=0, which is resolved into two components as real and imaginary parts. The proposed GA generates two random populations of real numbers for the real and imaginary parts in the given regions of interest and no other initial guesses are needed. This is the prominent advantage of the method in contrast to various other methods. Additionally, the proposed ‘Refinement technique' aids in the exhaustive coverage of potential patches enclosing roots and reinforces the selected potential rectangles to be narrow, resulting in significant search space reduction. The method works efficiently even when the roots are closely packed. A set of benchmark functions are presented and the results show the effectiveness and robustness of the new method.

Inverse Solution to the Coupled Ordinary Differential Equation

2010 ◽  
Author(s):  
P. Venkataraman
Keyword(s):  
Differential Equation ◽  
Genetic Algorithm ◽  
Differential Equations ◽  
Generic Model ◽  
Real Numbers ◽  
Data Points ◽  
Discrete Values ◽  
Linear Differential ◽  
Discrete Programming ◽  
The Given

The identification of the actual form of the constant coefficient coupled differential equations and their boundary conditions, from two sets of discrete data points, is possible through a unique two-step approach developed in this paper. In the first step, the best Bezier function is fitted to the data. This allows an effective approximation of the data and the required number of derivatives for the entire range of the independent variable. In the second step, the known derivatives are introduced in a generic model of the coupled differential equation. This generic form includes two types of unknowns, real numbers and integers. The real numbers are the coefficients of the various terms in the differential equations, while the integers are exponents of the derivatives. The unknown exponents and coefficients are identified using an error formulation. Two examples are solved. The given data is exact, smooth and they represent solutions to coupled linear differential equations. The solution is obtained through discrete programming. Three methods are presented. The first is limited enumeration, which is useful if the coefficients belong to a limited set of discrete values. The second is global search using the genetic algorithm for a larger choice of coefficient values. The third uses a state space integrator driven by the genetic algorithm, to minimize the error between known data and that obtained from numerical integration.

scholarly journals OBJECTS IMAGES ALIGNMENT WITH THE USE OF GENETIC AND GRADIENT ALGORITHMS

2014 ◽  
pp. 160-169
Author(s):  
Sergiy Balovsyak ◽  
Igor Fodchuk
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Hybrid Method ◽  
Digital Images ◽  
Image Alignment ◽  
Real Numbers ◽  
Accuracy Improvement ◽  
Gradient Algorithms ◽  
Tournament Selection ◽  
The Given

The given paper presents a hybrid method which is a combination of genetic and gradient algorithms used for the comparison of digital images of an object. Aligning the images, their basic transformations are taken into account, namely shift and scale in a width and height, angle, changes in intensity and contrast. The software for image alignment of objects has been created using Delphi environment. The program utilizes modified genetic algorithms where the chromosomes are the vectors of real numbers. The methods of roulette, rank and tournament selection are used for chromosome selection. After the use of the genetic algorithm the object images were compared by the method of coordinate descent that provides an accuracy improvement of image alignment. The efficiency of different methods of chromosome selection in the genetic algorithm for images alignment is researched. The size of chromosome population as well as other parameters of genetic algorithm have been optimized.

Fuzzy based Quantum Genetic Algorithm for Project Team Formation

2016 ◽  
Vol 12 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Arish Pitchai ◽  
Reddy A. V. ◽  
Nickolas Savarimuthu
Keyword(s):  
Genetic Algorithm ◽  
Personnel Selection ◽  
Optimization Problem ◽  
Selection Process ◽  
Quantum Walk ◽  
Project Team ◽  
Algorithmic Approach ◽  
Quantum Genetic Algorithm ◽  
Requirement Specifications ◽  
The Given

Formation of an effective project team plays an important role in successful completion of the projects in organizations. As the computation involved in this task grows exponentially with the growth in the size of personnel, manual implementation is of no use. Decision support systems (DSS) developed by specialized consultants help large organizations in personnel selection process. Since, the given problem can be modelled as a combinatorial optimization problem, Genetic Algorithmic approach is preferred in building the decision making software. Fuzzy descriptors are being used to facilitate the flexible requirement specifications that indicates required team member skills. The Quantum Walk based Genetic Algorithm (QWGA) is proposed in this paper to identify near optimal teams that optimizes the fuzzy criteria obtained from the initial team requirements. Efficiency of the proposed design is tested on a variety of artificially constructed instances. The results prove that the proposed optimization algorithm is practical and effective.

scholarly journals Urban Drainage Networks Rehabilitation Using Multi-Objective Model and Search Space Reduction Methodology

2019 ◽  
Vol 4 (2) ◽  
pp. 35 ◽  
Author(s):  
Ulrich A. Ngamalieu-Nengoue ◽  
Pedro L. Iglesias-Rey ◽  
F. Javier Martínez-Solano
Keyword(s):  
Genetic Algorithm ◽  
Search Space ◽  
Urban Drainage ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Space Reduction ◽  
Decision Variables ◽  
Drainage Networks ◽  
Search Space Reduction ◽  
Pareto Fronts

The drainage network always needs to adapt to environmental and climatic conditions to provide best quality services. Rehabilitation combining pipes substitution and storm tanks installation appears to be a good solution to overcome this problem. Unfortunately, the calculation time of such a rehabilitation scenario is too elevated for single-objective and multi-objective optimization. In this study, a methodology composed by search space reduction methodology whose purpose is to decrease the number of decision variables of the problem to solve and a multi-objective optimization whose purpose is to optimize the rehabilitation process and represent Pareto fronts as the result of urban drainage networks optimization is proposed. A comparison between different model results for multi-objective optimization is made. To obtain these results, Storm Water Management Model (SWMM) is first connected to a Pseudo Genetic Algorithm (PGA) for the search space reduction and then to a Non-Dominated Sorting Genetic Algorithm II (NSGA-II) for multi-objective optimization. Pareto fronts are designed for investment costs instead of flood damage costs. The methodology is applied to a real network in the city of Medellin in Colombia. The results show that search space reduction methodology provides models with a considerably reduced number of decision variables. The multi-objective optimization shows that the models’ results used after the search space reduction obtain better outcomes than in the complete model in terms of calculation time and optimality of the solutions.

Minimization of total trim loss occurring in pipe cutting in shipbuilding with genetic algorithm

2021 ◽  
pp. 147509022199169
Author(s):  
Abdullah Türk ◽  
Dursun Saral ◽  
Murat Özkök ◽  
Ercan Köse
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Search Space ◽  
Cutting Process ◽  
Genetic Operators ◽  
Critical Stage ◽  
Different Types ◽  
Trim Loss ◽  
Pipe Systems

Outfitting is a critical stage in the shipbuilding process. Within the outfitting, the construction of pipe systems is a phase that has a significant effect on time and cost. While cutting the pipes required for the pipe systems in shipyards, the cutting process is usually performed randomly. This can result in large amounts of trim losses. In this paper, we present an approach to minimize these losses. With the proposed method it is aimed to base the pipe cutting process on a specific systematic. To solve this problem, Genetic Algorithms (GA), which gives successful results in solving many problems in the literature, have been used. Different types of genetic operators have been used to investigate the search space of the problem well. The results obtained have proven the effectiveness of the proposed approach.

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