Introduction to Optimum Design phần 9 ppsx

... xuiii=+-()[]=25 50 0 01 1 99 23ln . ; to fixuxiixx()=- + - -()ÊËˆ¯1001123expffiixx()=()=Â21 99 xx120, ≥121510 012xx+-£. 590 INTRODUCTION TO OPTIMUM DESIGN ... Optimum Design 591 18.6 (Hock and Schittkowski, 198 1)minimizesubject to 18.7 (Hock and Schittkowski, 198 1)minimizesubject to 18.8 (Hock and Schittkowski, 198 1)minimizesubject to xx2121250-≥xx12700 ... 000 333 257 30 89 715 43 16 768 46 3134 14 585 79 27 371 043 433 7,.,,,.,., $, , .sppwfPWBuspwf=()=183 199 64 0 15 12 99 3 055 42,. .,$, .ACBcrf sfdf=()+-()= 90 0 000 0 15 20...

Introduction to Optimum Design phần 10 ppsx

... 0, 0). 9. 16 x(1)= (-2.7068, 0.88168). 9. 17 x(1)= (3.771567, 0.3355 89) . 9. 18 x(1)= (4 .99 913, 24 .99 085). 9. 19 x(1)= (-1.268 59, -0.7 597 3, 0.73141, 0. 398 33). 9. 22 x(2)=(4, 2). 9. 23 x(2)= ... 2.2835mm. 9. 45 x1= 2.2213mm, x2=1. 897 8mm. 9. 46 x* = 0.6 190 84. 9. 47 x* = 9. 424753. 9. 48 x* = 1.570807. 9. 49 x*= 1. 496 045. 9. 50 x* = (3.667328, 0.7 395 71). 9. 51 x* = (4.000142, 7 .99 9771).Chapter ... 0.173574). 9. 29 x(2)= (3.73707, 0.28550). 9. 30 x(2)= (-1 .91 03, -1 .90 78). 9. 31 DFP: x(2)= (3.113 39, 0.32226, 1.3 499 1, 2.12286); BFGS: x(2)= (3.113 39, 0.32224,1.3 499 1, 2.12286). 9. 44 x1=...

Introduction to Optimum Design phần 1 pdf

... America0405060708 09 987654321Table of ContentsPrefaceixChapter 1 Introduction to Design 11.1 The Design Process 21.2 Engineering Design versus Engineering Analysis 41.3 Conventional versus Optimum Design ... Gradient Vector 310 9. 2.2 Orthogonality of Steepest Descent Directions 314 9. 3 Scaling of Design Variables 315 9. 4 Search Direction Determination: Newton’s Method 318 9. 4.1 Classical Newton’s Method ... Method 318 9. 4.2 Modiﬁed Newton’s Method 3 19 9.4.3 Marquardt Modiﬁcation 323 9. 5 Search Direction Determination: Quasi-Newton Methods 324 9. 5.1 Inverse Hessian Updating: DFP Method 324 9. 5.2 Direct...

Introduction to Optimum Design phần 2 pdf

... of a design problemmay not be linear, in which case curves must be plotted to identify the feasible region, andcontours or iso-cost curves must be drawn to identify the optimum design. To plot ... concepts related to optimum design problems. In the following section, a design optimization problem is formulated andused to describe the solution process. Some concepts related to design optimization ... asPlotg4=ContourPlot[g4,{x1,-1,25},{x2,-1,25}, ContourShadingÆFalse, ContoursÆ{0,.35}, ContourStyleÆ{{Thickness[.01]}, {GrayLevel[.8],Thickness[.02]}}, DisplayFunctionÆIdentity];62 INTRODUCTION TO OPTIMUM...

Introduction to Optimum Design phần 3 pptx

... miijjx0,0 x0,0**;**;1 1to and to 144 INTRODUCTION TO OPTIMUM DESIGN 4.51 Consider the following problem with equality constraints:Minimize (x1- 1)2+ (x2- 1)2subject to x1+ x2- 4 = 0x1- ... of its use.176 INTRODUCTION TO OPTIMUM DESIGN TABLE 5-1 Alternate Form of KKT Necessary ConditionsProblem: minimize f(x) subject to hi(x) = 0, i = 1 to p; gj(x) £ 0, j = 1 to m1. Lagrangian ... are those stationary points that are neither minimumnor maximum). Optimum Design Concepts 167134 INTRODUCTION TO OPTIMUM DESIGN Thus, all the KKT conditions are satisﬁed, and these are candidate...

Introduction to Optimum Design phần 4 pdf

... 06.67 Maximize z = x1+ 4x2subject to x1+ 2x2£ 52x1+ x2= 4254 INTRODUCTION TO OPTIMUM DESIGN 232 INTRODUCTION TO OPTIMUM DESIGN 1. For 2x1+ x2£ 9: y1= 1.6 (c¢3in column x3)2. ... 18x2subject to x1- 3x2£-32x1+ 2x2≥ 5x1, x2≥ 06.11 Minimize f = 20x1- 6x2subject to 3x1- x2≥ 3Linear Programming Methods for Optimum Design 247228 INTRODUCTION TO OPTIMUM DESIGN TABLE ... when 00,RcaBr rkrm=¢=Â1cBBB BmTcc c=[]12 242 INTRODUCTION TO OPTIMUM DESIGN Linear Programming Methods for Optimum Design 233(d)(e)where x3is a slack variable, x4is a surplus...

Introduction to Optimum Design phần 5 pptx

... positive.300 INTRODUCTION TO OPTIMUM DESIGN 322 INTRODUCTION TO OPTIMUM DESIGN FIGURE 9- 7 Iteration history for Example 9. 7 with Newton’s method.TABLE 9- 2 Optimum Solution for Example 9. 7 with Modiﬁed ... applications.TABLE 9- 3 Evaluation of Three Methods for Example 9. 8: f(x) = 50(x2- x21)2+ (2 - x1)2Steepest descent Conjugate gradient Modiﬁed Newtonx11 .99 41 2.0000 2.0000x23 .97 65 3 .99 98 3 .99 99 f ... called the DFP (Davidon-Fletcher-Powell) method:324 INTRODUCTION TO OPTIMUM DESIGN 290 INTRODUCTION TO OPTIMUM DESIGN In general, we continue to evaluate the function at the points(8.14)Let us...

Introduction to Optimum Design phần 6 potx

... Exercise 2.14 at the point P1= 2 and P2= 1.376 INTRODUCTION TO OPTIMUM DESIGN ...

Introduction to Optimum Design phần 7 pot

... 2.27873E+01 7.87500E+02 9. 9438E+00 9. 9438E+00 1.0000E-013 1.25020E-02 1.3 199 3E+00 7.13063E+02 9. 0133E+00 9. 0133E+00 1.0000E-014 2. 199 48E-02 1.03643E-01 6 .99 734E+02 7. 693 3E+00 1.0000E+01 1.0000E-015 ... 9. 0828E+00 9 CCC 4.2 495 0E-04 1.67623E-02 1.27 298 E-02 5.3485E-02 4.0151E-01 9. 0831E+0010 CCS 1.0 895 7E-04 1.67623E-02 1.27 290 E-02 5.3 395 E-02 3 .99 16E-01 9. 1854E+0011 CR 0.00000E+00 5. 490 55E-05 1.27300E-02 ... constraints.458 INTRODUCTION TO OPTIMUM DESIGN 11 10 9 8 7 6 5 4 3 2 1 0123Iteration no. Design variable value4567 891 011121314FIGURE 13-5 History of design variables for the spring design...

Introduction to Optimum Design phần 8 pot

... references cited there (Arora et al., 199 4; Arora and Huang, 199 6; Huang and Arora, 199 5, 199 7a,b; Huang et al., 199 7; Arora, 199 7, 2002; Kocer and Arora 199 6a,b, 199 7, 199 9, 2002). These references contain ... 16100 895 15.00 1010 123 3.750W36 ¥ 230 67.60 35 .90 0.760 16.470 1.260 15000 837 14 .90 94 0 114 3.730W36 ¥ 210 61.80 36. 69 0.830 12.180 1.360 13200 7 19 14.60 411 67.5 2.580W36 ¥ 194 57.00 36. 49 ... for optimum design of electric transmission line structures are given in Kocer andArora ( 199 6, 199 7, 199 9, 2002).Exercises for Chapter 16*Solve the following problems using a genetic algorithm.16.1...

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