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Optimizations of Multi Optima Problems Using the Genetic Algorithm, Punch-Out Method, and Least Exponent Method


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DOI: https://doi.org/10.15866/ireme.v16i12.22485

Abstract


The Genetic Algorithm (GA) is a very effective global search algorithm. When the dimension of the optimization problem becomes great, it is not a simple task for methods, such as gradient methods. For the accuracy of a given solution, the search frequency of the variables necessary for a variable axis is far greater with the dimension increase of the solution vector. When the smoothness of the problem is good, the small frequency of the variable will do, with the progress of the generations. However, when the problem has many sharp peaks, such as in data regression, several frequencies of the variable in each variable axis are needed to result in a tremendous total number of individuals. In order to resolve this kind of ineffectiveness for many variables with a moderate number of individuals, a punch-out method is proposed for effectively finding the optimum. The least square method is revisited here to suggest least exponent method to take care of the outlier problem in data regression.
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Keywords


Punch-Out Method; Global Search Algorithm; Least Square Method; Least Exponent Method

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References


J. S. Arora, 1989, Introduction to Optimum Design, McGraw-Hill Inc.

R. T. Haftka and Z. Gürdal, 1992, Elements of Structural Optimization, Kluwer Academic Publishers.
https://doi.org/10.1007/978-94-011-2550-5

A. D. Belegundu and T. R. Chandrupatla, 1999, Optimization Concepts and Applications in Engineering, Prentice-Hall Inc.

R. W. Hamming, 1971, Introduction to Applied Numerical Analysis, McGraw-Hill Kogakusha.

Z. Michalewicz, 1996, Genetic Algorithms+Data Structures = Evolution Programs, Springer-Verlag.
https://doi.org/10.1007/978-3-662-03315-9

E. H. L. Aarts and J. Korst, 1989, Simulated Annealing and Boltzmann Machines, John Wiley.

D. E. Goldberg, 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison- Wesley Publishing Co.

K. Krishnakumar, 1989, Micro-genetic Algorithms for Stationary and Non-stationary Function Optimization, SPIEP: Intelligent Control and Adaptive Systems, 1196, pp. 289~296.
https://doi.org/10.1117/12.969927

Y. D. Kwon, S. B. Jin, J. Y. Kim and I. H. Lee, 2004, Local zooming genetic algorithm and its application to radial gate support problems, Structural Engineering and Mechanics, An International Journal, Vol. 17, No. 5, pp. 611~626.
https://doi.org/10.12989/sem.2004.17.5.611

Y. D. Kwon, S. B. Kwon, S. B. Jin and J. Y. Kim, 2003, Convergence enhanced genetic algorithm with successive zooming method for solving continuous optimization problems, Computers and Structures, Vol. 81, Iss. 17, pp. 1715~1725.
https://doi.org/10.1016/S0045-7949(03)00183-4

Y. D. Kwon, H. W. Kwon, J. Y. Kim and S. B. Jin, 2004, Optimization and verification of parameters used in successive zooming genetic algorithm, Journal of Ocean Engineering and Technology, Vol. 18, No. 5, pp. 29~35.

Y. D. Kwon, H. W. Kwon, S. W. Cho, and S. H. Kang, 2006, Convergence rate of the successive zooming genetic algorithm using optimal control parameters, WSEAS Transactions on Computers, Vol. 5, Iss. 6, pp. 1200~1207.

Zainuddin, F., Abd Samad, M., Comparison of Crossover in Genetic Algorithm for Discrete-Time System Identification, (2021) International Review of Mechanical Engineering (IREME), 15 (2), pp. 59-66.
https://doi.org/10.15866/ireme.v15i2.19726

Batayneh, W., Bataineh, A., Jaradat, M., Intelligent Adaptive Fuzzy Logic Genetic Algorithm Controller for Anti-Lock Braking System, (2021) International Review on Modelling and Simulations (IREMOS), 14 (1), pp. 44-54.
https://doi.org/10.15866/iremos.v14i1.19838

Nguyen Ba, N., Nguyen Cong, C., Vuong Quoc, D., Nguyen Thi, N., A Comparison Among Random Search Algorithms for PID Controller Optimization, (2022) International Review of Automatic Control (IREACO), 15 (5), pp. 251-262.
https://doi.org/10.15866/ireaco.v15i5.22562

A. G. James, A. Green, G. M. Simpson, 1975, Strain Energy Functions of Rubber I. Characterization of Gum Vulcanizates, Journal of Applied Polymer Science, Vol. 19, pp. 2033-2058.
https://doi.org/10.1002/app.1975.070190723

Y. D. Kwon, H. W. Kwon, W. J. Kim, S. D. Yeo, Estimation of Rubber Material Property by Successive Zooming Genetic Algorithm, Journal of Solid Mechanics and Materials Engineering, Vol 1, No 6, pp. 815~826.
https://doi.org/10.1299/jmmp.1.815

Kwon, H., Lee, H., Jun, S., Kwon, Y., Long-Term Lives of Residual Strengths of Chloroprene Rubber Parts Under Seasonal Degradation, (2019) International Review of Mechanical Engineering (IREME), 13 (3), pp. 212-217.
https://doi.org/10.15866/ireme.v13i3.16456

A. K. Olson, 2007, Finite element procedures in modelling the dynamic properties of rubber, Ph.D. thesis, Lund University, Sweden.

H. S. Lee, C. Kim, Y.D., Kwon, J.H. Doh, 2013, Long-term life prediction of polyacrylate (ACM) rubber gasket with chlorine cure sites using four-parameter recovery model, Proceedings of the Institution of Mechanical Engineers Part D (J. Auto. Eng.), Vol. 227, No 11, pp. 1536-1545.
https://doi.org/10.1177/0954407013491239

Alnema, Y., Alsabawee, A., Ahmed, J., MRAC Based PID Controller Design with Genetic Algorithm for a Single Joint Robot Arm, (2021) International Journal on Engineering Applications (IREA), 9 (2), pp. 86-93.
https://doi.org/10.15866/irea.v9i2.19863

Rostom, D., Hasanien, H., El Amary, N., Abdelaziz, A., Adaptive PI Control Strategy for Microgrid Performance Enhancement, (2019) International Journal on Energy Conversion (IRECON), 7 (3), pp. 82-92.
https://doi.org/10.15866/irecon.v7i3.17327

Ambaye, G., Lemu, H., Numerical Study of Effect of Backlash on Flash Temperature of Spur Gear, (2020) International Review of Mechanical Engineering (IREME), 14 (11), pp. 684-692.
https://doi.org/10.15866/ireme.v14i11.19763

Rojas, J., Espinel, E., Florez, E., Parametrical Study of Centrifugal Airfoil Fans by Computational Tools, (2020) International Review of Mechanical Engineering (IREME), 14 (12), pp. 750-759.
https://doi.org/10.15866/ireme.v14i12.19281

Bena, W., Lemu, H., Analysis of Thermomechanical Cracks of Disc Brake Used in Heavy Trucks, (2022) International Review of Mechanical Engineering (IREME), 16 (7), pp. 365-372.
https://doi.org/10.15866/ireme.v16i7.22331

N. R. Draper and H. Smith, 2014, Applied regression analysis, John Wiley & Sons, Inc.

Korol, R., Sivakumaran, K., Energy Dissipation Potential of Square Tubular Steel Columns Subjected to Axial Compression, (2019) International Journal on Engineering Applications (IREA), 7 (1), pp. 27-32.
https://doi.org/10.15866/irea.v7i1.17188

Lu, M., Analysis of Various Techniques for Solving the Problem of Big Data Classification, (2021) International Review on Modelling and Simulations (IREMOS), 14 (4), pp. 242-250.
https://doi.org/10.15866/iremos.v14i4.20987

Iben Ammar, I., Doumiati, M., Kassir, S., Machmoum, M., Francis, C., Chaabane, M., New Nonlinear Control Based on Polynomial Approach for Islanded DC Microgrid Robustness and Voltage Stability, (2022) International Review of Automatic Control (IREACO), 15 (5), pp. 263-275.
https://doi.org/10.15866/ireaco.v15i5.22535

D. Ma and P. Xu, 2015, An Energy Distance Aware Clustering Protocol with Dual Cluster Heads Using Niching Particle Swarm Optimization for Wireless Sensor Networks, Journal of Control Science and Engineering, Vol. 2015, No. 11.
https://doi.org/10.1155/2015/849281

A. Passaro and A. Starita, 2008, Particle Swarm Optimization for Multimodal Functions: A Clustering Approach, Journal of Artificial Evolution and Applications, Vol. 2008.
https://doi.org/10.1155/2008/482032

P. K. Senecal, 2000, Numerical Optimization Using the Gen4 Micro-Genetic Algorithm Code, ERC Document.

H. Reismann, 1988, Elastic plates: Theory and application, Wiley-interscience.

J. Arora, 2016, Introduction to optimum design, 4th ed. Academic Press.

A. K. Olsson, Finite element procedures in modelling the dynamic properties of rubber, 2007 Lund University Publications (ISBN: 978-91-628-7130-7).


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