Çok Amaçlı Kısıtlama Gerçek Dünya Optimizasyon Problemlerini Çok Amaçlı Optimizasyon Algoritmaları ile Çözme

Öz

Gerçek dünya mühendislik optimizasyon problemlerinde, sistemlerin veya süreçlerin kusurlu koşulları nedeniyle birçok kısıtlamanın dikkate alınması gerekir. Bu nedenle, kısıtlama işleme yöntemleri optimizasyon algoritmalarına entegre edilmiştir. Ancak kısıtlamalar algoritma tarafından başarıldığı için değerleri dikkate alınmaz veya izlenmez. Alternatif olarak, kısıtlamaları hedeflere dönüştürmek mümkündür ve bu çok amaçlı kısıtlamalı gerçek dünya optimizasyon problemleri, çok amaçlı optimizasyon problemlerine dönüştürülür. Bu amaçla bu araştırmada, beş gerçek dünya mühendislik tasarım problemi, Dişli Tren Tasarımı, Basınçlı Kap Tasarımı, İki Çubuk Kafes Tasarımı, Disk Fren Tasarımı ve Titreşimli Platform Tasarımı problemleri olan çok amaçlı optimizasyon problemine dönüştürülmüştür. Problemler çok amaçlı optimizasyon algoritmaları (NSGA-II, MOEA/D, MOEA/D-DE, MPSO/D ve MOPSO) kullanılarak çözülmüş ve hiperhacim metriği kullanılarak performansları karşılaştırılmıştır.

Anahtar Kelimeler

• Dişli Treni
• Basınçlı Kap
• İki Çubuk Kafes
• Disk Fren
• Titreşimli Platform
• çok amaçlı optimizasyon
• çok amaçlı optimizasyon
• NSGA-II
• MOEA/D
• MOEA/D-DE
• MPSO/D
• MOPSO.

Solving Many-objective Constraint Real-World Optimization Problems with Multi-objective Optimization Algorithms

Abstract

In real world engineering optimization problems many constraints must be considered due to the imperfect conditions of the systems or process. Therefore, constraint handling methods are integrated into optimization algorithms. However, since the constraints are succeeded by the algorithm, their value is not considered or watched. Alternatively, it is possible to convert constraints to objectives and these many-objective constraint real-world optimization problems are changed to many-objective optimization problems. In this research for this purpose five real world engineering design problems are converted into many-objective optimization problem which are Gear Train Design, Pressure Vessel Design, Two Bar Truss Design, Disc Brake Design and Vibrating Platform Design problems. The problems are solved by using multi-objective optimization algorithms (NSGA-II, MOEA/D, MOEA/D-DE, MPSO/D and MOPSO) and their performance is compared by using the hypervolume metric.

Keywords

• Gear Train
• Pressure Vessel
• Two Bar Truss
• Disc Brake
• Vibrating Platform
• multi-objective optimization
• many-objective optimization
• NSGA-II
• MOEA/D
• MOEA/D-DE
• MPSO/D
• MOPSO

References

1. B. Kannan, S. N. Kramer, “An augmented lagrange multiplier-based method for mixed integer discrete continuous optimization and its applications to mechanical design,” 1994.
2. S. Narayanan, S. Azarm, “On improving multiobjective genetic algorithms for design optimization,” Structural Optimization, vol. 18, pp. 146– 155, 1999.
3. G. Chiandussi, M. Codegone, S. Ferrero, F. E. Varesio, “Comparison of multi-objective optimization methodologies for engineering applications,” Computers & Mathematics with Applications, vol. 63, pp. 912–942, 2012.
4. A. Osyczka, S. Kundu, “A genetic algorithm-based multicriteria optimization method,” Proc. 1st World Congr. Struct. Multidisc. Optim, pp. 909–914, 1995.
5. T. Ray, K. Liew, “A swarm metaphor for multiobjective design optimization,” Engineering optimization, vol. 34, pp. 141–153, 2002.
6. Messac, A. “Physical Programming-Effective Optimization for Computational Design,” AIAA Journal, 34, 149-158. https://doi.org/10.2514/3.13035, 1996.
7. K. Miettinen, “Nonlinear Multiobjective Optimization,” Norwell, MA: Kluwer, 1999.
8. K. Deb, “Multi-Objective Optimization using Evolutionary Algorithms,” New York: Wiley, 2001

9. C.M. Fonseca; P.J. Fleming,” Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation,” IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 28, no. 1, 1998.
10. C. Coello Coello, “Constraint-Handling Using an Evolutionary Multiobjective Optimization Technique,” Civil Engineering and Environmental Systems, vol.17, 2000.
11. U. Ozkaya, and L.Seyfi. "A comparative study on parameters of leaf-shaped patch antenna using hybrid artificial intelligence network models." Neural Computing and Applications, 29.8 pp. 35-45, 2018.
12. Q. Zhang and H. Li “MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition,” IEEE Tran. on Evolutionary Com., vol. 11, no. 6, 2007.
13. Bo Liu; Francisco V. Fernández; Qingfu Zhang; Murat Pak; Suha Sipahi; Georges Gielen,” An enhanced MOEA/D-DE and its application to multiobjective analog cell sizing,” IEEE Congress on Evolutionary Computation, 2010.
14. Wei Peng; Qingfu Zhang, “A decomposition-based multi-objective Particle Swarm Optimization algorithm for continuous optimization problems,” 2008 IEEE International Conference on Granular Computing, 2008.
15. C.A. Coello Coello; M.S. Lechuga, “MOPSO: a proposal for multiple objective particle swarm optimization,” Proceedings of the 2002 Congress on Evolutionary Computation, 2002.