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Books > Business & Economics > Business & management > Management & management techniques > Operational research
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Optimization Under Stochastic Uncertainty - Methods, Control and Random Search Methods (Hardcover, 1st ed. 2020)
Loot Price: R2,938
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Optimization Under Stochastic Uncertainty - Methods, Control and Random Search Methods (Hardcover, 1st ed. 2020)
Series: International Series in Operations Research & Management Science, 296
Expected to ship within 18 - 22 working days
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This book examines application and methods to incorporating
stochastic parameter variations into the optimization process to
decrease expense in corrective measures. Basic types of
deterministic substitute problems occurring mostly in practice
involve i) minimization of the expected primary costs subject to
expected recourse cost constraints (reliability constraints) and
remaining deterministic constraints, e.g. box constraints, as well
as ii) minimization of the expected total costs (costs of
construction, design, recourse costs, etc.) subject to the
remaining deterministic constraints. After an introduction into the
theory of dynamic control systems with random parameters, the major
control laws are described, as open-loop control, closed-loop,
feedback control and open-loop feedback control, used for iterative
construction of feedback controls. For approximate solution of
optimization and control problems with random parameters and
involving expected cost/loss-type objective, constraint functions,
Taylor expansion procedures, and Homotopy methods are considered,
Examples and applications to stochastic optimization of regulators
are given. Moreover, for reliability-based analysis and optimal
design problems, corresponding optimization-based limit state
functions are constructed. Because of the complexity of concrete
optimization/control problems and their lack of the mathematical
regularity as required of Mathematical Programming (MP) techniques,
other optimization techniques, like random search methods (RSM)
became increasingly important. Basic results on the convergence and
convergence rates of random search methods are presented. Moreover,
for the improvement of the - sometimes very low - convergence rate
of RSM, search methods based on optimal stochastic decision
processes are presented. In order to improve the convergence
behavior of RSM, the random search procedure is embedded into a
stochastic decision process for an optimal control of the
probability distributions of the search variates (mutation random
variables).
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