基于鲁棒优化的多目标共享单车电子围栏选址研究

“双碳”背景下,零排放的共享单车系统可以有效降低公共交通系统的碳排放。将电子围栏作为单车停放点,是应对乱停乱放、保障共享单车行业可持续发展的有效措施。以电子围栏选址总成本最小和用户需求覆盖最大为优化目标,研究了用户需求不确定情形下的多目标电子围栏选址问题。利用预算不确定集来刻画用户需求的不确定性,构建了多目标电子围栏选址的鲁棒优化模型,并利用对偶理论将其转化为鲁棒对等模型,然后采用ε约束法进行求解。现实算例测试结果验证了本文模型和方法的有效性。     

一种改进的广义遗传算法及其在鲁棒优化问题中的应用

提出一种改进的广义遗传算法,算法中引入了异种机制以提高种群的多样性,在保证收敛速度的同时防止了早熟收敛。将该方法应用于复杂载荷作用下结构的鲁棒优化问题,并采用Taguchi望目特性的SN比构造了遗传算法的目标函数。数值算例表明,异种机制能够有效地提高广义遗传算法收敛于全局最优解的概率,加快收敛速度;结合了Taguchi鲁棒设计方法的广义遗传算法能够有效地求解复杂载荷作用下带有不确定参数的结构鲁棒优化问题。     

对光照变化鲁棒的一种运动目标检测方法

鉴于现有的运动目标检测方法对光照变化的敏感性,本文提出了一种在静态场景下对光照变化鲁棒的运动目标检测方法。该方法利用视频当前图像帧的边缘与背景图像的边缘做差分运算,得出运动目标的轮廓,进而对运动目标进行定位与检测。实验证明,本方法在一定程度上能够消除由于环境光照变化引起的"曝光"现象,实时准确地检测出运动目标及其位置,运算速度快,满足实时性的需求。     

振动主动控制系统的一种鲁棒设计方法

本文从控制系统校正的角度出发,提出了一种振动主动控制系统的鲁棒设计方法,并且研究了传感器与作动器的位置对系统鲁捧性的影响,指出传感器与作动器对位有助于提高系统的鲁棒性。最后通过一算例说明了该方法的可行性。     

价格不确定供应链的多目标运作鲁棒模型

建立了由一个制造商和一个供应商构成的多产品、多阶段供应链在原材料和最终产品的市场价格均不确定情况下运作的鲁棒模型.采用区间不确定性描述价格的不确定性.供应链的运作模型为一个多目标规划问题,满足诸如供应链协调运作、所有供应链成员的目标利润尽可能最大、对应于不确定供求价格的决策的鲁棒性等多个相互冲突的目标.数值算例的结果表明,一定范围内的市场价格波动不改变供应链的运作策略,仅对其运作性能产生一定影响,即所提出的模型是鲁棒的.     

一种考虑概率分布的鲁棒优化模型

文章以随机规划中的机会约束思想为指导,根据随机参数的概率分布情况,提出了两种鲁棒性条件约束,并在此基础上建立了一种新的鲁棒优化模型,使模型的可行解控制在一定的鲁棒性指标的范围内。该模型不但可处理约束两端同时含有随机参数的情况,还可以方便地推广到非线性模型中。仿真实例说明了模型的有效性。     

结构动力鲁棒优化设计方法综述

如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。     

鲁棒优化设计方法在结构动力学中的应用

在传统的静力学鲁棒优化设计基础上,考虑时间t参数,通过优化系统目标函数和约束条件的鲁棒性,将鲁棒优化设计方法运用在动力学问题中。通过一个主系统的质量和刚度均有微小波动的二自由度模型减振器设计算例,与传统的优化设计方法相比,显示了鲁棒优化设计的优越性,能使结构具有更稳定的性能。     

低碳政策下基于区间的模糊多式联运路径鲁棒优化研究北大核心

针对不同碳排放政策下模糊需求的路径优化问题,在综合考虑运输成本、转运成本、时间成本及碳排放成本的基础上,建立基于区间的鲁棒优化模型,并在强制碳排放、碳税、碳交易以及碳补偿政策下对模型进行低碳转换,采用基于蒙特卡洛采样的灾变自适应遗传算法求解。以具有15个节点的多式联运网络进行算例研究,比较不同低碳政策下多式联运总成本和碳排放量,并分析不确定参数的影响。结果表明:对于需求鲁棒性的最大保守值的合理设置有助于引导企业运输决策;碳补偿、碳税、碳交易和强制碳排放政策的减排力度逐步减弱;选择不同的碳排放政策并调节最大保守值可以达到控制碳排放且降低总成本的目的。     

复杂产品的多学科鲁棒协同设计优化方法研究

为了处理好复杂产品各子系统之间的耦合关系以及各子系统的异构性问题,以协同优化(CO)算法为基础,结合系统不确定分析(SUA)方法和近似不确定传播(IUP)方法,构建了多学科鲁棒协同设计优化算法框架.在设计变量的不确定性能够被概率分布函数描述的情况下,此算法框架能够解决复杂产品的设计优化问题.通过对梳齿式微加速度计的多学科鲁棒协同优化设计算例的计算,验证了此算法在输入参数存在微小扰动的情况下能够有效提高设计解的鲁棒性.     

A robust optimization methodology for preliminary aircraft design

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.     

基于鞍点逼近的机械结构可靠性稳健优化设计

将可靠性优化设计理论与可靠性灵敏度分析方法相结合,讨论了机械零部件稳健优化设计的问题.系统地推导了基于鞍点逼近的可靠性灵敏度公式,并把可靠性灵敏度计算结果融入可靠性稳健优化设计模型之中,将可靠性稳健优化设计归结为满足可靠性要求的多目标优化问题.在基本随机参数概率分布已知的前提下,应用鞍点逼近技术,得到极限状态函数的分布函数与概率密度函数,并且将此结果应用到机械零部件的可靠性灵敏度分析中,进而实现了机械零部件的可靠性稳健优化设计.通过与Monte-Carlo方法计算所得的结果相比可知,应用鞍点逼近技术可以迅速、准确地得到机械零部件可靠性稳健设计信息．     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Gearbox design for uncertain load requirements using active robust optimization

Design and optimization of gear transmissions have been intensively studied, but surprisingly the robustness of the resulting optimal design to uncertain loads has never been considered. Active Robust (AR) optimization is a methodology to design products that attain robustness to uncertain or changing environmental conditions through adaptation. In this study the AR methodology is utilized to optimize the number of transmissions, as well as their gearing ratios, for an uncertain load demand. The problem is formulated as a bi-objective optimization problem where the objectives are to satisfy the load demand in the most energy efficient manner and to minimize production cost. The results show that this approach can find a set of robust designs, revealing a trade-off between energy efficiency and production cost. This can serve as a useful decision-making tool for the gearbox design process, as well as for other applications.     

Multi-objective robust design optimization of fatigue life for a welded box girder

To reduce the scatter of fatigue life for welded structures, a robust optimization method is presented in this study based on a dual surrogate modelling and multi-objective particle swam optimization algorithm. Considering the perturbations of material parameters and environment variables, the mean and standard deviation of fatigue life are fitted using dual surrogate modelling and selected as the objective function to be minimized. As an example, a welded box girder is presented to reduce the standard deviation of fatigue life. A set of non-dominated solutions is produced through a multi-objective particle swam optimization algorithm. A cognitive approach is used to select the optimum solution from the Pareto sets. As a comparative study, traditional single objective optimizations are also presented in this study. The results reduced the standard deviation of the fatigue life by about 16.5%, which indicated that the procedure improved the robustness of the fatigue life.     

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

基于GA-NLP的剪刀式折叠桥梁展桥机构多目标优化设计

针对新型剪刀式折叠桥梁展桥机构的优化设计问题,首先建立了展桥机构的运动学和静力学模型,然后以展桥机构关键铰点位置和岸桥节与竖直方向所成夹角为优化设计变量,以展桥机构的空间位置为主要约束条件,以展桥油缸、连杆、关键铰点受力峰值最小为优化目标,通过正规化和加权处理构造了展桥机构多目标优化分析模型,并采用遗传算法（genetic algorithm, GA）和非线性规划(nonlinear programming, NLP)混合算法对该优化分析模型进行求解。最后,利用ADAMS（automatic dynamic analysis of mechanical systems,机械系统动力学自动分析）软件验证了展桥机构多目标优化分析模型的正确性。结果表明,优化后展桥油缸承载的拉力与推力峰值分别减小了57.9%和25.3%,连杆承载的拉力与压力峰值分别减小了26.1%和55.2%,展桥机构2个关键铰点受力峰值分别减小了23.5%和26.8%。研究结果可为展桥机构的改进设计提供理论依据。     

结构主动控制的一体化多目标优化研究

基于Pareto多目标遗传算法提出了结构主动控制系统的一体化多目标优化设计方法,对作动器位置与主动控制器进行同步优化设计.外界激励采用平稳过滤白噪声来模拟,在状态空间下通过求解Lyapunov方程,得到结构响应和主动控制力的均方值.主动控制器采用LQG控制算法来进行设计.以结构位移和加速度均方值最大值与相应无控响应均方值的最大值之比,以及所需控制力均方值之和作为多目标同步优化的目标函数.优化过程还考虑了结构与激励参数对优化结果的影响.最后以某6层平面框架有限元模型为例进行了计算机仿真分析,结果表明所提出的主动控制系统多目标一体化优化方法简单,高效,实用,具有较好的普适性.     

Simulated variance optimization for robust design

A method to aid robust design in the presence of design parameter uncertainty is described. For a given relationship between a performance measure (or output parameter) and the uncertain design parameters a probabilistic simulation is used to obtain the variance of the performance measure as a function of the nominal design parameter values. The optimum values of the latter are then obtained as those corresponding to a minimum of the computed variance, determined by means of a particular non-linear optimization algorithm in the presence of constraints. The latter are in the form of limits on the nominal values of the design parameters and a specified value for the performance measure at the nominal design point, i.e. the deterministic design target. Some problems inherent in this type of procedure are discussed and methods of solution are described. A specific example is studied and the results from the present method are compared with those previously obtained by use of another procedure. © 1998 John Wiley & Sons, Ltd.