Application of Genetic Algorithm in Multi-objective Optimization

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Application of Genetic Algorithm in Multi-objective Optimization of an Indeterminate Structure with Discontinuous Space for Support Locations Rahat Sultana A Thesis Submitted to the Graduate Faculty of GRAND VALLEY STATE UNIVERSITY In Partial Fulfillment of the Requirements For the Degree of Master of Science in Engineering Product Design and Manufacturing Engineering August 2016
Dedication To my parents, Engr. Md. Robiul Islam and Mrs. Mahamuda Islam, and my husband M Shahriar Mazid Khan, for their selfless and relentless support to my pursuit of higher studies. 3
Page 1: Grand Valley State University Schol
Page 5 and 6: Abstract In this thesis, an indeter
Page 7 and 8: Table of Content Dedication……
Page 9 and 10: 2.3.2. Genetic Algorithm with Multi
Page 11 and 12: 4.2.1. Continuous Method………
Page 13 and 14: List of Tables Table 3.1: GA parame
Page 15 and 16: GAs have been used in numerous opti
Page 17 and 18: 2. Literature Review: 2.1 Optimizat
Page 19 and 20: other evolutionary operators named
Page 21 and 22: 2.1.3 Differences between Evolution
Page 23 and 24: espectively, and are the constr
Page 25 and 26: equiring a better solution than any
Page 27 and 28: ∗ ≔ | ∈ ∗ Methods for s
Page 29 and 30: to find a set of non-dominated solu
Page 31 and 32: There are some other approaches whi
Page 33 and 34: individual may be selected. And the
Page 35 and 36: 2.3.1.5. Mutation: Mutation is a ra
Page 37 and 38: Multi-objective genetic algorithms
Page 39 and 40: In 1940, Courant [62] first had the
Page 41 and 42: violated constraints. If a problem
Page 43 and 44: of test problems with a conclusion
Page 45 and 46: (Though in figure 3.1, due to 2D dr
Page 47 and 48: GA operators, such as population in
Page 49 and 50: 1 1 1 , where, , ,
Page 51 and 52: 3.2.1.3.1. GA Operator: In the “C
Page 53 and 54:
In reality, objects, similar to the
Page 55 and 56:
So, if there are n supports, the to
Page 57 and 58:
4. Results & Discussion: 4.1. Uncon
Page 59 and 60:
Heuristically, it was assumed that
Page 61 and 62:
The nodal points were generated in
Page 63 and 64:
and , which were the head and the
Page 65 and 66:
These two approaches were also comp
Page 67 and 68:
0.8 MINIMUM VALUE OF OBJECTIVE FUNC
Page 69 and 70:
(a) (b) (c) Figure 4.7: Indetermina
Page 71 and 72:
As one of the objectives was to max
Page 73 and 74:
this thesis work, one of the popula
Page 75 and 76:
Paired t-test ( 5%) was conducted t
Page 77 and 78:
5. Conclusion: In this work, a stan
Page 79 and 80:
Appendices A. Table 4.7 Results of
Page 81 and 82:
C. Paired t-test analysis of Discre
Page 83 and 84:
References [1] Deb, Kalyanmoy. Mult
Page 85 and 86:
[20] Rawlins, Gregory J. E. Foundat
Page 87 and 88:
[39] Deb, Kalyanmoy, et al. "A fast
Page 89 and 90:
[59] Takahama, Tetsuyuki, and Setsu
Page 91:
[87] Hwang, C-L., and Abu Syed Md M
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Application of Genetic Algorithm in Multi-objective Optimization

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