一种求解随机期望值模型的有效算法

随机期望值模型是一类有着广泛应用背景的随机规划问题.为了寻找更为有效的求解随机期望值模型的算法,通过采用随机仿真来逼近随机函数,在微粒群算法中利用随机仿真进行适应值估计和实现为了检验解的可行性,从而给出了求解随机期望值模型的新的算法.最后,通过实例仿真说明了算法的正确性和有效性.     

Reliability-based robust assessment for multiobjective optimization design of improving occupant restraint system performance

Optimal performance of vehicle occupant restraint system (ORS) requires an accurate assessment of occupant injury values including head, neck and chest responses, etc. To provide a feasible framework for incorporating occupant injury characteristics into the ORS design schemes, this paper presents a reliability-based robust approach for the development of the ORS. The uncertainties of design variables are addressed and the general formulations of reliable and robust design are given in the optimization process. The ORS optimization is a highly nonlinear and large scale problem. In order to save the computational cost, an optimal sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). Further, to efficiently obtain a robust approximation, the support vector regression (SVR) is suggested to construct the surrogate model in the vehicle ORS design process. The multiobjective particle swarm optimization (MPSO) algorithm is used for obtaining the Pareto optimal set with emphasis on resolving conflicting requirements from some of the objectives and the Monte Carlo simulation (MCS) method is applied to perform the reliability and robustness analysis. The differences of three different Pareto fronts of the deterministic, reliable and robust multiobjective optimization designs are compared and analyzed in this study. Finally, the reliability-based robust optimization result is verified by using sled system test. The result shows that the proposed reliability-based robust optimization design is efficient in solving ORS design optimization problems.     

Optimizing reliability-based robust design model using multi-objective genetic algorithm

Reliability-based robust design optimization (RBRDO) is one of the most important tools developed in recent years to improve both quality and reliability of the products at an early design stage. This paper presents a comparative study of different formulation approaches of RBRDO models and their performances. The paper also proposes an evolutionary multi-objective genetic algorithm (MOGA) to one of the promising hybrid quality loss functions (HQLF)-based RBRDO model. The enhanced effectiveness of the HQLF-based RBRDO model is demonstrated by optimizing suitable examples.     

Reliability-based robust design optimization: A general methodology using genetic algorithm

In this paper, we present an improved general methodology including four stages to design robust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simultaneously to propose the new formulation of reliability-based robust design optimization (RBRDO) problems. In order to generate reliable and robust Pareto-optimal solutions, the combination of genetic algorithm with reliability assessment loop based on the performance measure approach is applied as the second stage. Next, we develop two criteria to select a solution from obtained Pareto-optimal set to achieve the best possible implementation. Finally, the result verification is performed with Monte Carlo Simulations and also the quality improvement during manufacturing process is considered by identifying and controlling the critical variables. The effectiveness and applicability of this new proposed methodology is demonstrated through a case study.     

An efficient strategy for reliability-based multidisciplinary design optimization using BLISS

This paper presents an efficient reliability-based multidisciplinary design optimization (RBMDO) strategy. The conventional RBMDO has tri-level loops: the first level is an optimization in the deterministic space, the second one is a reliability analysis in the probabilistic space, and the third one is the multidisciplinary analysis. Since it is computationally inefficient when high-fidelity simulation methods are involved, an efficient strategy is proposed. The strategy [named probabilistic bi-level integrated system synthesis (ProBLISS)] utilizes a single-level reliability-based design optimization (RBDO) approach, in which the reliability analysis and optimization are conducted in a sequential manner by approximating limit state functions. The single-level RBDO is associated with the BLISS formulation to solve RBMDO problems. Since both the single-level RBDO and BLISS are mainly driven by approximate models, the accuracy of models can be a critical issue for convergence. The convergence of the strategy is guaranteed by employing the trust region–sequential quadratic programming framework, which validates approximation models in the trust region radius. Two multidisciplinary problems are tested to verify the strategy. ProBLISS significantly reduces the computational cost and shows stable convergence while maintaining accuracy.     

随机仿真优化的一类遗传序优化框架

针对仿真优化问题存在随机性、计算费时、解空间巨大、多极小等难点,结合遗传算法的并行遗传搜索、最优计算量分配以及序优化的目标软化和序比较思想提出一类遗传序优化框架,进而讨论了该方法的收敛性和具体实施问题,最后指出了进一步的研究内容.     

A robust dynamic planning strategy for lot-sizing problems with stochastic demands

We consider the question of generating robust plans for production planning problems under uncertainty. In particular, we present an alternative approach to generate robust solutions for lot-sizing problems with stochastic demand. The proposed approach is dynamic and includes a decision rule that guides the planner. The decision rule parameters are determined so that the number of expected planning adaptations and their magnitudes are under control. The robust approach and its related models are presented together with some computational results to show how it performs compared to other approaches.     

An efficient framework for generating robust adversarial examples

Recent studies show that deep neural networks (DNNs) suffer adversarial examples. That is, attackers can mislead the output of a DNN by adding subtle perturbation to a benign input image. In addition, researchers propose new generation of technologies to produce robust adversarial examples. Robust adversarial examples can consistently fool DNN models under predefined hyperparameter space, which can break through some defenses against adversarial examples or even generate physical adversarial examples against real-world applications. Behind these achievements, expectation over transformation (EOT) algorithm plays as the backbone framework for generating robust adversarial examples. Though EOT framework is powerful, we know little about why such a framework can generate robust adversarial examples. To address this issue, we do the first work to explain the principle behind robust adversarial examples. Then, based on the findings, we point out that traditional EOT framework has a performance problem and propose an adaptive sampling algorithm to overcome such a problem. By modeling the sampling process as classic Coupon Collector Problem, we prove that our new framework reduces the cost from $O\text{◂()▸}\left(n\ast \log \mathrm{}\left(n\right)\right)$ to $O\left(n\right)$, where $n$ denotes the number of sampling points. Under the view of computational complexity, the algorithm is optimal for this problem. The experimental results show that our algorithm can save up to 23% overhead in average. This is significant for black-box attack, where the cost is charged by the amount of queries.     

Improved hybrid method as a robust tool for reliability-based design optimization

In the engineering problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of reliability-based design optimization (RBDO), it is the objective to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. The classical RBDO leads to high computing time and weak convergence, but a Hybrid Method (HM) has been proposed to overcome these two drawbacks. As the hybrid method successfully reduces the computing time, we can increase the number of variables by introducing the standard deviations as optimization variables to minimize the error values in the probabilistic model. The efficiency of the hybrid method has been demonstrated on static and dynamic cases with extension to the variability of the probabilistic model. In this paper, we propose a modification on the formulation of the hybrid method to improve the optimal solutions. The proposed method is called, Improved Hybrid Method (IHM). The main benefit of this method is to improve the structure performance by much more minimizing the objective function than the hybrid method. It is also shown to demonstrate the optimality conditions. The improved hybrid method is next applied to two numerical examples, with consideration of the standard deviations as optimization variables (for linear and nonlinear distributions). When integrating the improved hybrid method within the probabilistic model variability, we minimize the objective function more and more.     

Non-derivative algorithm design for efficient routing over unreliable stochastic networks

We study the question of routing for minimum average drop rate over unreliable servers that are susceptible to random buffer failures, which arises in unreliable data or manufacturing networks. Interestingly, we first reveal that the traditional Join-the-Shortest-Queue (JSQ) or optimal Randomized Splitting (RS) strategies are consistently outperformed by the Constant Splitting Rule (CSR) where the incoming traffic is split with a constant fraction towards the available servers.This finding motivates us to obtain the optimal splitting fraction under CSR. However, the objective function to be minimized depends on the mean queue length of the servers, whose closed-form expression is not available and often intractable for general arrival and service processes. Thus, we use non-derivative methods to solve this optimization problem by approximately evaluating the objective value at each iteration. To that end, we explicitly characterize the approximation error by utilizing the regenerating nature of unreliable buffers. By adaptively controlling the precision of this approximation, we show that our proposed algorithm converges to an optimal splitting decision in the almost sure sense. Yet, previous works on non-derivative methods assume continuous differentiability of the objective function, which is not the case in our setup. We relax this strong assumption to the case when the objective function is locally Lipschitz continuous, which is another contribution of this paper.     

An application of multi-objective stochastic optimisation to structural design

An application to structural design of an innovative method for optimising stochastic systems is introduced in the paper. The proposed method allows one to carry out both the multi-objective optimisation of a structural element and to improve the robustness of the design. The innovative method is rather general. To show its effectiveness, an ideal cantilever has been designed in order to minimise both mass and deflection. The cantilever is shaped as a beam and is subject to random loads acting at its free end. The beam geometrical dimensions and material properties vary stochastically due to manufacturing tolerances. Different beam cross sections and two different materials (aluminium alloy and steel) have been considered. From the optimisation, it turned out that the optimal solutions are the O and the I beam, depending on the required lightness and stiffness. Compared to steel, aluminium alloy beams have provided better (or at least equal) performance.     

Robust optimal experiment design for system identification

This paper develops the idea of min-max robust experiment design for dynamic system identification. The idea of min-max experiment design has been explored in the statistics literature. However, the technique is virtually unknown by the engineering community and, accordingly, there has been little prior work on examining its properties when applied to dynamic system identification. This paper initiates an exploration of these ideas. The paper considers linear systems with energy (or power) bounded inputs. We assume that the parameters lie in a given compact set and optimise the worst case over this set. We also provide a detailed analysis of the solution for an illustrative one parameter example and propose a convex optimisation algorithm that can be applied more generally to a discretised approximation to the design problem. We also examine the role played by different design criteria and present a simulation example illustrating the merits of the proposed approach.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

An inverse-measure-based unilevel architecture for reliability-based design optimization

Reliability-based design optimization (RBDO) is a methodology for finding optimized designs that are characterized with a low probability of failure. Primarily, RBDO consists of optimizing a merit function while satisfying reliability constraints. The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the system or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. During the last few years, a variety of different formulations have been developed for RBDO. Traditionally, these have been formulated as a double-loop (nested) optimization problem. The upper level optimization loop generally involves optimizing a merit function subject to reliability constraints, and the lower level optimization loop(s) compute(s) the probabilities of failure corresponding to the failure mode(s) that govern(s) the system failure. This formulation is, by nature, computationally intensive. Researchers have provided sequential strategies to address this issue, where the deterministic optimization and reliability analysis are decoupled, and the process is performed iteratively until convergence is achieved. These methods, though attractive in terms of obtaining a workable reliable design at considerably reduced computational costs, often lead to premature convergence and therefore yield spurious optimal designs. In this paper, a novel unilevel formulation for RBDO is developed. In the proposed formulation, the lower level optimization (evaluation of reliability constraints in the double-loop formulation) is replaced by its corresponding first-order Karush–Kuhn–Tucker (KKT) necessary optimality conditions at the upper level optimization. Such a replacement is computationally equivalent to solving the original nested optimization if the lower level optimization problem is solved by numerically satisfying the KKT conditions (which is typically the case). It is shown through the use of test problems that the proposed formulation is numerically robust (stable) and computationally efficient compared to the existing approaches for RBDO.     

Maximum principle for the stochastic optimal control problem with delay and application

In this paper, we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay. We obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations. Our results can be applied to a production and consumption choice problem. The explicit optimal consumption rate is obtained.     

最优实验设计的改进随机进化算法

详细阐述构造最优实验设计的原始随机进化算法,并在原始算法的基础上,拓展广度搜索,改进深度搜索,以提高最优实验设计的计算速度。通过不同规模和不同优化准则的拉丁超立方体最优实验设计,验证改进算法的应用效果。算例分析表明,改进算法能够比原始算法节省约30%～60%的机时完成最优实验设计,而且改进算法对应于优化准则的最优值与原始算法最优值的差别仅为1%～3%。可见,改进算法能够兼顾最优实验设计的计算时间和优化质量,明显提高最优实验设计的构造效率。     

An investigation of structural optimization in crashworthiness design using a stochastic approach

In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.     

An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

Stochastic model predictive control hinges on the online solution of a stochastic optimal control problem. This paper presents a computationally efficient solution method for stochastic optimal control for nonlinear systems subject to (time‐varying) stochastic disturbances and (time‐invariant) probabilistic model uncertainty in initial conditions and parameters. To this end, new methods are presented for joint propagation of time‐varying and time‐invariant probabilistic uncertainty and the nonconservative approximation of joint chance constraint (JCC) on the system state. The proposed uncertainty propagation method relies on generalized polynomial chaos and conditional probability rules to obtain tractable expressions for the state mean and covariance matrix. A moment‐based surrogate is presented for JCC approximation to circumvent construction of the full probability distribution of the state or the use of integer variables as required when using the sample average approximation. The proposed solution method for stochastic optimal control is illustrated on a nonlinear semibatch reactor case study in the presence of probabilistic model uncertainty and stochastic disturbances. It is shown that the proposed solution method is significantly superior to a standard random sampling method for stochastic optimal control in terms of computational requirements. Furthermore, the moment‐based surrogate for the JCC is shown to be substantially less conservative than the widely used distributionally robust Cantelli‐Chebyshev inequality for chance constraint approximation.     

Application of discrete event simulation for robust system design of a melt facility

This paper presents a methodology to identify robust operating regions through the selection of controllable factory variables, using discrete event simulation. A casting plant melt facility was used as an industrial test bed to develop these techniques. A robust system design was determined by response surface analysis of key production parameters. Furthermore, robust operating policies that maximise throughput, while minimizing work-in-progress and thus energy consumption were identified.