Stochastic optimization methods in engineering

Abstract

Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliabilityoriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability P. of survival. Lower bounds for p. are obtained by selecting certain redundants in the vector of internal forces; moreover, upper bounds for p. are constructed by considering a pair of dual linear programs for the optimizational representation of the yield or safety conditions. Whereas P. can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of P. with respect to input or design variables have yet to be developed. Hence several new techniques are suggested for the numerical computation of derivatives of P •.

The Model of Stochastic Optimization of Production under Uncertainty and Risk

“…Numerous studies (Catoni and Picard, 2004;Spall, 2004;Cao, 2007;Shukla and Mishra, 2014;Marti, 2015;Williams, 2013;Song, 2013;Bertocchi, Consigli and Michael, 2011) showed that the execution of the work is well described by a beta probability distribution. The expectation (average) time performance can be estimated from the formula: To determine the critical path of the project critical path method is used.…”

Вычисление Объединенных Мягких Ограничений В Задачах Проектирования Оптимальных Технологических Систем

“…В зависимости от желания проектировщика и имеющихся возможностей уточнения информации, управления ХТПС во время его эксплуатации, такие задачи принимают различный вид задач стохастической оптимизации [2]. Можно выделить задачи робастной стохастической оптимизации, учитывающие жесткие ограничения [3], и задачи оптимизации с мягкими ограничениями, которые чаще всего представляют в форме вероятностных ограничений [4]. При этом соблюдается весьма высокий уровень выполнения таких ограничений, или малый уровень риска.…”