Research On Efficient Algorithms Of Interval-based Optimization Under Uncertainty And Its Applications

Uncertainty widely exists in practical engineering problems. Studies on theories and algorithms of optimization under uncertainty are significant for development of industrial complex products and systems. Uncertainty is commonly quantified by probabilistic model and fuzzy set model. Probabilistic model can easily address the aleatory type of uncertainty, and the fuzzy set model is quite suitable for representing the epistemic type of uncertainty or decision-making uncertainty. These two classes of models, however, are rarely applied in practical engineering problems, due to some limitations and deficiencies, such as low computational efficiency and the inability of handling the uncertainty with incomplete information. Interval models are applicable to problems with incomplete information. It considers only the lower and upper bounds of the uncertain parameters without assuming their precise probability distribution functions. In recent years, the interval-based optimization method has been attracting more and more attentions, and shown a high application potential for practical engineering problems. However, some difficulties in interval-based optimization methods should be undertaken. For instance, uncertainty quantification in interval-based optimization problem results in a two-level deterministic optimization process, thus high requirment for computational efficiency, as well as the validity of optimal result pose a great challenge to the development of interval-based optimization algorithms.For this reason, this dissertation is dedicated to a systematical research on the computational efficiency and validity of optimal result in interval-based optimization problems, aiming at making some useful contribution and progress to the improvement. According to the features of interval-based optimization problem, this paper tries to deal with the trade-off between computational efficiency and validity of optimal result by using surrogate model technique under the effective model management framework. Based upon this concept, the following studies are carried out in this dissertation:(1) The general interval-based optimization problem under uncertainty is transformed into a two-level optimization process, such that it can be solved effectively and easily. The surrogate model technique is used to promote the computational efficiency by replacing the time-comsuming simulation model in the two-level optimization process. In order to diminish the untrustworthiness of the optimal result introduced by the approximation error of surrogate model, a local-densifying model management strategy is suggested, based upon which, high computational efficiency and low approximation error can be achieved simultaneously. The interval-based optimization method using surrogate model technique is then applied to an optimization design problem of penetration of multi-layer concrete target. Results indicate that the present method is very encouraging in design of penetration.(2) An improved global search strategy is proposed to ensure the "extremum" of uncertainty analysis in the lower level optimization. The interval-based optimization method combining with this global search strategy can be used to solve time-consuming problems with highly nonlinearity and large uncertain level. The improved global search strategy is established by using the surrogate model as the sampling guide according to the surrogate model’s features. This strategy also gives an effective stopping criterion for the iterations. As a result, an efficienct and trustworthy interval-based optimization method is formed.(3) Different robust measurement and reliability measurement are suggested to transform the interval-based optimization problem, so that the two-level optimization can be decoupled accordingly. An uncertain sphere with allowable degree and minimum tolerance sphere are used to quantify the reliability of constraints, and the sensitivity information is used to measure the robustness of objective function. Based on the above uncertainty measurement, constraint shift method can decouple the two-level optimization process into a sequential optimization process, so that the computational efficiency would increase significantly.(4) High dimensional model representation technique supplements the deficiency of ordinary surrogate model for modeling the high dimensional problems. Combined with a direct decoupling method, a new interval-based method is developed to tackle the high dimensional optimization problems under uncertainty. The direct decoupling method can cope with the robustness of objective and reliability of constraints simultaneously by transformed the two-level optimization process into a sequential optimization process. It improves the constraint shift method from the last chapter which is merely suitable for handling the problems of constraint reliability. Last but not least, an improved high dimensional model representation method is suggested to balance the trade-off between approximation capacity and computational efficiency, for the reason that first order high dimensional model representation does not have enough nonlinear modeling ability, while second order high dimensional model representation needs too much amount of computation.