Engineering Optimization: Theory and Practice, Fourth Edition

582 Dynamic Programming

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based approach,Engineering Optimization, Vol. 2, pp. 83–95, 1976.

9.18 M. J. Harley and T. R. E. Chidley, Deterministic dynamic programming for long term

reservoir operating policies,Engineering Optimization, Vol. 3, pp. 63–70, 1978.

9.19 S. G. Dhande, Reliability Based Design of Gear Trains: A Dynamic Programming

Approach, Design Technology Transfer, ASME, New York, pp. 413–422, 1974.

9.20 S. S. Rao and G. Das, Reliability based optimum design of gear trains,ASME Journal

of Mechanisms, Transmissions, and Automation in Design, Vol. 106, pp. 17–22, 1984.

9.21 A. C. Palmer and D. J. Sheppard, Optimizing the shape of pin-jointed structures,

Proceedings of the Institution of Civil Engineers, Vol. 47, pp. 363–376, 1970.

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McGraw-Hill, New York, 1981.

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ming, M. Save and W. Prager (eds.), Plenum Press, New York, 1990.

9.24 L. Cooper and M. W. Cooper,Introduction to Dynamic Programming, Pergamon Press,

Oxford, UK, 1981.

9.25 R. E. Larson and J. L. Casti,Principles of Dynamic Programming,Part I—Basic Analytic

and Computational Methods, Marcel Dekker, New York, 1978.

9.26 D. K. Smith,Dynamic Programming: A Practical Introduction, Ellis Horwood, Chich-

ester, UK, 1991.

9.27 W. F. Stoecker,Design of Thermal Systems, 3rd ed., McGraw-Hill, New York, 1989.

Review Questions

9.1 What is a multistage decision problem?

9.2 What is the curse of dimensionality?

9.3 State two engineering examples of serial systems that can be solved by dynamic

programming.

9.4 What is a return function?

9.5 What is the difference between an initial value problem and a final value problem?

9.6 How many state variables are to be considered if an LP problem withnvariables andm

constraints is to be solved as a dynamic programming problem?

9.7 How can you solve a trajectory optimization problem using dynamic programming?

9.8 Why are the components numbered in reverse order in dynamic programming?

9.9 Define the following terms:

(a)Principle of optimality

(b)Boundary value problem

(c)Monotonic function

(d)Separable function

9.10 Answer true or false:

(a)Dynamic programming can be used to solve nonconvex problems.

(b)Dynamic programming works as a decomposition technique.