Engineering Optimization: Theory and Practice, Fourth Edition
1.2 Historical Development 3 Table 1.1 Methods of Operations Research Mathematical programming or Stochastic process optimizatio ...
4 Introduction to Optimization sufficiency conditions for the optimal solution of programming problems laid the foun- dations fo ...
1.3 Engineering Applications of Optimization 5 1.3 Engineering Applications of Optimization Optimization, in its broadest sense, ...
6 Introduction to Optimization 1.4 Statement of an Optimization Problem An optimization or a mathematical programming problem ca ...
1.4 Statement of an Optimization Problem 7 Figure 1.3 Gear pair in mesh. thedesign variable spaceor simplydesign space. Each poi ...
8 Introduction to Optimization 1.4.3 Constraint Surface For illustration, consider an optimization problem with only inequality ...
1.4 Statement of an Optimization Problem 9 1.4.4 Objective Function The conventional design procedures aim at finding an accepta ...
10 Introduction to Optimization Figure 1.5 Contours of the objective function. has to be solved purely as a mathematical problem ...
1.4 Statement of an Optimization Problem 11 i Figure 1.6 Tubular column under compression. The behavior constraints can be expre ...
12 Introduction to Optimization Thus the behavior constraints can be restated as g 1 (X)= 2500 πx 1 x 2 − 005 ≤ 0 (E 6 ) g 2 (X) ...
1.4 Statement of an Optimization Problem 13 Figure 1.7 Graphical optimization of Example 1.1. x 1 2 4 6 8 10 12 14 x 2 2.41 0.71 ...
14 Introduction to Optimization Next, the contours of the objective function are to be plotted before finding the optimum point. ...
1.5 Classification of Optimization Problems 15 1.5.2 Classification Based on the Nature of the Design Variables Based on the nat ...
16 Introduction to Optimization Here the design variables are functions of the length parametert. This type of problem, where ea ...
1.5 Classification of Optimization Problems 17 Figure 1.9 Control points in the path of the rocket. SOLUTION Let points (or cont ...
18 Introduction to Optimization or xi−mig−k 1 vi=miai (E 1 ) where the massmican be expressed as mi=mi− 1 −k 2 s (E 2 ) andk 1 a ...
1.5 Classification of Optimization Problems 19 Thus the problem can be stated as an OC problem as FindX= x 1 x 2 x ...
20 Introduction to Optimization Figure 1.10 Step-cone pulley. SOLUTION The design vector can be taken as X= ...
1.5 Classification of Optimization Problems 21 To have the belt equally tight on each pair of opposite steps, the total length o ...
22 Introduction to Optimization Finally, the lower bounds on the design variables can be taken as w≥ 0 (E 8 ) di≥ 0 , i= 1 , 2 , ...
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