Review Questions 77114.44 W. Stadler, Ed.,Multicriteria Optimization in Engineering and in the Sciences, Plenum
Press, New York, 1988.
14.45 The Rand Corporation,A Million Random Digits with 100,000 Normal Deviates, The
Free Press, Glencoe, IL, 1955.
14.46 C. A. Coello Coello, D. A. Van Veldhuizen, and G. B. Lamont,Evolutionary Algorithms
for Solving Multi-objective Problems, Kluwer Academic/Plenum, New York, 2002.Review Questions
14.1 What is a reduced basis technique?
14.2 State two methods of reducing the size of an optimization problem.
14.3 What is design variable linking? Can it always be used?14.4 Under what condition(s) is the convergence of the quantity (^) iYiin the fast reanalysis
method ensured?
14.5 How do you compute the derivatives of the stiffness matrix with respect to a design
variable,∂[K]/∂xi?
14.6 What is a MIMD computer?
14.7 Indicate various ways by which parallel computations can be performed in a large-scale
optimization problem.
14.8 How are the goals determined in the goal programming method?
14.9 Answertrueorfalse:
(a)The computation of the derivatives of a particularλirequires other eigenvalues
besidesλi.
(b)The derivatives of theith eigenvector can be found without knowledge of the eigen-
vectors other thanYi.
(c)There is only one way to derive expressions for the sensitivity of optimal objective
function with respect to problem parameters.
(d)Multilevel optimization is same as decomposition.
(e)In multilevel optimization, the suboptimization problems are to be solved iteratively.
(f)All multiobjective optimization methods find only a Pareto optimum solution.
(g)All multiobjective optimization techniques convert the problem into a single objec-
tive problem.
(h)A vector optimization problem is same as a multiobjective optimization problem.
(i)Only one Pareto optimal solution exists for a multiobjective optimization problem.
(j)The weighting function method can be considered as the utility function method.
(k)It is possible to achieve the optimum value of each objective function simultaneously
in a multiobjective optimization problem.
14.10 Define the following terms:
(a)Pareto optimal point
(b)Utility function method
(c)Weighting function method
(d)Global criterion function method