Engineering Optimization: Theory and Practice, Fourth Edition

12.4 Optimality Criteria Methods 683 12.4 Optimality Criteria Methods The optimality criteria methods are based on the derivatio ...

684 Optimal Control and Optimality Criteria Methods determined by other considerations). Assuming that the firstnvariables denot ...

12.4 Optimality Criteria Methods 685 whereJdenotes the number of displacement (equality) constraints,y∗jthe maximum permissible ...

686 Optimal Control and Optimality Criteria Methods The necessary condition of optimality can be expressed as ∂f ∂zi +λ ∂g ∂zi = ...

12.4 Optimality Criteria Methods 687 Figure 12.6 Three-bar truss. whereρis the weight density,Eis Young’s modulus,Umaxthe maximu ...

Table 12.1 Results for Example 12.5 a Starting values g^0 λ Solution from Eq. (12.68) x^1 x^2 [Eq. (12.70)] [Eq. (12.71)] x^1 x^ ...

Review Questions 689 References and Bibliography 12.1 R. S. Schechter,The Variational Method in Engineering, McGraw-Hill, New Yo ...

690 Optimal Control and Optimality Criteria Methods (g)Functional (h)Hamiltonian 12.3 Match the following terms and descriptions ...

Problems 691 Figure 12.7 Circular annular plate under load. whereDis the flexural rigidity of the plate,wthe transverse deflecti ...

692 Optimal Control and Optimality Criteria Methods Figure 12.8 Two-bar truss subjected to horizontal load. 12.8 The problem of ...

13 Modern Methods of Optimization 13.1 Introduction In recent years, some optimization methods that are conceptually different f ...

694 Modern Methods of Optimization 13.2 Genetic Algorithms 13.2.1 Introduction Many practical optimum design problems are charac ...

13.2 Genetic Algorithms 695 String of length 20 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 x 1 x 2 x 3 x 4 In general, if a binary ...

696 Modern Methods of Optimization 13.2.3 Representation of Objective Function and Constraints Because genetic algorithms are ba ...

13.2 Genetic Algorithms 697 Equations (13.7) and (13.8) show that the penalty will be proportional to the square of the amount o ...

698 Modern Methods of Optimization Roulette wheel Fitness values 3 2 1 6 5 4 Pointer 16% 8% 36% 24% 4% 12% String numbers Figure ...

13.2 Genetic Algorithms 699 sizenduring numerical computations,nrandom numbers, each in the range of zero to one, are generated ...

700 Modern Methods of Optimization single-point crossover operator, a crossover site is selected at random along the string leng ...

13.2 Genetic Algorithms 701 The purpose of mutation is (1) to generate a string (design point) in the neigh- borhood of the curr ...

702 Modern Methods of Optimization 5.Carry out the mutation operation using the mutation probabilitypmto find the new generation ...