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

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Zaer Abo-Hammour ◽  
Omar Abu Arqub ◽  
Shaher Momani ◽  
Nabil Shawagfeh

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.

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Omar Abu Arqub ◽  
Zaer Abo-Hammour ◽  
Shaher Momani ◽  
Nabil Shawagfeh

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.


Author(s):  
Alok Ranjan Biswal ◽  
Tarapada Roy ◽  
Rabindra Kumar Behera

The current article deals with finite element (FE)- and genetic algorithm (GA)-based vibration energy harvesting from a tapered piezolaminated cantilever beam. Euler–Bernoulli beam theory is used for modeling the various cross sections of the beam. The governing equation of motion is derived by using the Hamilton's principle. Two noded beam elements with two degrees of freedom at each node have been considered in order to solve the governing equation. The effect of structural damping has also been incorporated in the FE model. An electric interface is assumed to be connected to measure the voltage and output power in piezoelectric patch due to charge accumulation caused by vibration. The effects of taper (both in the width and height directions) on output power for three cases of shape variation (such as linear, parabolic and cubic) along with frequency and voltage are analyzed. A real-coded genetic algorithm-based constrained (such as ultimate stress and breakdown voltage) optimization technique has been formulated to determine the best possible design variables for optimal harvesting power. A comparative study is also carried out for output power by varying the cross section of the beam, and genetic algorithm-based optimization scheme shows the better results than that of available conventional trial and error methods.


2013 ◽  
Vol 651 ◽  
pp. 548-552
Author(s):  
Parinya Kaweegitbundit

This paper considers two stage hybrid flow shop (HFS) with identical parallel machine. The objectives is to determine makespan have been minimized. This paper presented memetic algorithm procedure to solve two stage HFS problems. To evaluated performance of propose method, the results have been compared with two meta-heuristic, genetic algorithm, simulated annealing. The experimental results show that propose method is more effective and efficient than genetic algorithm and simulated annealing to solve two stage HFS scheduling problems.


2021 ◽  
Author(s):  
Mohammed Ahmed Al-Janabi ◽  
Omar F. Al-Fatlawi ◽  
Dhifaf J. Sadiq ◽  
Haider Abdulmuhsin Mahmood ◽  
Mustafa Alaulddin Al-Juboori

Abstract Artificial lift techniques are a highly effective solution to aid the deterioration of the production especially for mature oil fields, gas lift is one of the oldest and most applied artificial lift methods especially for large oil fields, the gas that is required for injection is quite scarce and expensive resource, optimally allocating the injection rate in each well is a high importance task and not easily applicable. Conventional methods faced some major problems in solving this problem in a network with large number of wells, multi-constrains, multi-objectives, and limited amount of gas. This paper focuses on utilizing the Genetic Algorithm (GA) as a gas lift optimization algorithm to tackle the challenging task of optimally allocating the gas lift injection rate through numerical modeling and simulation studies to maximize the oil production of a Middle Eastern oil field with 20 production wells with limited amount of gas to be injected. The key objective of this study is to assess the performance of the wells of the field after applying gas lift as an artificial lift method and applying the genetic algorithm as an optimization algorithm while comparing the results of the network to the case of artificially lifted wells by utilizing ESP pumps to the network and to have a more accurate view on the practicability of applying the gas lift optimization technique. The comparison is based on different measures and sensitivity studies, reservoir pressure, and water cut sensitivity analysis are applied to allow the assessment of the performance of the wells in the network throughout the life of the field. To have a full and insight view an economic study and comparison was applied in this study to estimate the benefits of applying the gas lift method and the GA optimization technique while comparing the results to the case of the ESP pumps and the case of naturally flowing wells. The gas lift technique proved to have the ability to enhance the production of the oil field and the optimization process showed quite an enhancement in the task of maximizing the oil production rate while using the same amount of gas to be injected in the each well, the sensitivity analysis showed that the gas lift method is comparable to the other artificial lift method and it have an upper hand in handling the reservoir pressure reduction, and economically CAPEX of the gas lift were calculated to be able to assess the time to reach a profitable income by comparing the results of OPEX of gas lift the technique showed a profitable income higher than the cases of naturally flowing wells and the ESP pumps lifted wells. Additionally, the paper illustrated the genetic algorithm (GA) optimization model in a way that allowed it to be followed as a guide for the task of optimizing the gas injection rate for a network with a large number of wells and limited amount of gas to be injected.


2018 ◽  
Vol 14 (09) ◽  
pp. 190 ◽  
Author(s):  
Shewangi Kochhar ◽  
Roopali Garg

<p>Cognitive Radio has been skillful technology to improve the spectrum sensing as it enables Cognitive Radio to find Primary User (PU) and let secondary User (SU) to utilize the spectrum holes. However detection of PU leads to longer sensing time and interference. Spectrum sensing is done in specific “time frame” and it is further divided into Sensing time and transmission time. Higher the sensing time better will be detection and lesser will be the probability of false alarm. So optimization technique is highly required to address the issue of trade-off between sensing time and throughput. This paper proposed an application of Genetic Algorithm technique for spectrum sensing in cognitive radio. Here results shows that ROC curve of GA is better than PSO in terms of normalized throughput and sensing time. The parameters that are evaluated are throughput, probability of false alarm, sensing time, cost and iteration.</p>


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