A New Uncertain Optimization Method Based on Intervals and An Approximation Management Model
C. Jiang; and X. Han;

doi:10.3970/cmes.2007.022.097
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 2, pp. 97-118, 2007
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Keywords uncertain optimization; interval; approximation model; trust region; possibility degree of interval
Abstract A new uncertain optimization method is developed based on intervals and an approximation management model. A general uncertain optimization problem is considered in which the objective function and constraints are both nonlinear and uncertain, and intervals are used to model the uncertainty existing in the system. Based on a \textit {possibility degree of interval}, a \textit {nonlinear interval number programming} (NINP) method is proposed. A deterministic objective function is constructed to maximize the possibility degree of the uncertain objective function, and the uncertain constraints are changed into deterministic ones by introducing some possibility degree levels. If the optimal possibility degree of the objective function reaches 1.0, a robustness criterion is introduced and a corresponding robustness optimization is performed for the uncertain objective function. To improve the optimization efficiency, the NINP method is combined with an approximation management model to form an efficient uncertain optimization method. The trust region method is employed to manage a sequence of NINP problems which are based on the approximation models of the uncertain objective function and constraints within the uncertainty space and current design space. Two numerical examples are investigated to demonstrate the effectiveness of the present method.
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