Engineering Optimization: Theory and Practice, Fourth Edition

13.6 Optimization of Fuzzy Systems 723 The set [0, 1] is called avaluation set.A setAis called afuzzy setif the valuation set is ...

724 Modern Methods of Optimization 0 1 m m 1 m 2 y 2 yn mn (^0) y 1 (a) (b) 1 m y 1 y 2 yn 0 (c) 1 m y Figure 13.5 Crisp and fuz ...

13.6 Optimization of Fuzzy Systems 725 mAUB(y) mB(y) mABU(y) m(y) mA(y) mA(y) (a) A y (b) y (c) y 1 1 1 mB(y) mA(y) A mA–(y) ...

726 Modern Methods of Optimization Constraint 0 x (in.) 1 m Objective function Design (decision) Figure 13.8 Concept of fuzzy de ...

13.7 Neural-Network-Based Optimization 727 subject to λ≤μf(X) λ≤μg(l) j(X) , j= 1 , 2 ,... , m λ≤μg(u) j (X) , j= 1 , 2 ,... , m ...

728 Modern Methods of Optimization processing capability. The neural computing strategies have been adopted to solve optimizatio ...

13.7 Neural-Network-Based Optimization 729 Several neural network architectures, such as the Hopfield and Kohonen networks, have ...

730 Modern Methods of Optimization q 3 r 2 r 3 r 4 q 2 w 2 q 4 w 3 w 4 g h Figure 13.12 Network used to train relationships for ...

References and Bibliography 731 13.4 S. S. Rao, T. S. Pan, A. K. Dhingra, V. B. Venkayya, and V. Kumar, Genetic- evolution-based ...

732 Modern Methods of Optimization 13.23 A. K. Dhingra and S. S. Rao, A neural network based approach to mechanical design optim ...

Review Questions 733 (c)Roulette wheel selection process (d)Pheromone evaporation rate (e)Neural network (f)Fuzzy feasible domai ...

734 Modern Methods of Optimization (b)How is an inequality constrained optimization problem converted into an uncon- strained pr ...

Problems 735 (a)x(l)= 0 , x(u)= 5 (b)x(l)= 0 , x(u)= 10 (c)x(l)= 0 , x(u)= 20 13.4 A design variable, with lower and upper bound ...

736 Modern Methods of Optimization subject to x 12 +x^22 −x^23 ≤ 0 4 −x 12 −x 22 −x^23 ≤ 0 x 3 − 5 ≤ 0 −xi≤ 0 ;i= 1 , 2 , 3 Defi ...

14 Practical Aspects of Optimization 14.1 Introduction Although the mathematical techniques described in Chapters 3 to 13 can be ...

738 Practical Aspects of Optimization 14.2.2 Design Variable Linking Technique When the number of elements or members in a struc ...

14.2 Reduction of Size of an Optimization Problem 739 the relationship betweenZandXcan be expressed as Z 12 × 1 =[T] 12 × 6 X 6 ...

740 Practical Aspects of Optimization 14.3 Fast Reanalysis Techniques 14.3.1 Incremental Response Approach Let the displacement ...

14.3 Fast Reanalysis Techniques 741 Neglecting the term [K]Y 2 , Eq. (14.17) can be used to obtain the second approxi- mation ...

742 Practical Aspects of Optimization 1 4 2 3 1 3 2 4 y 6 y 5 y 2 y 1 y 4 y 8 y 7 y 3 50 in. 25 in. 1000 lb 100 in. 50 in. 100 i ...