共查询到19条相似文献,搜索用时 125 毫秒
1.
2.
3.
4.
不同阶段需求不确定情况下,决策者的风险偏好和生产过程中的废品处理影响着供应链生产库存管理和供应链整体效益。本文考虑决策者风险偏好下,构建了包含I个生产者企业,一个库存点和一个废物处理基地的T阶段动态供应链生产库存框架,建立了椭球型需求不确定集下,以追求整体收益最大化为目标的不确定优化模型,并应用鲁棒优化理论得到了数据确定性线性鲁棒对应模型,讨论了模型解的可靠性和有效性。最后的算例表明,只有当决策者风险偏好参数在一定范围内时,才会存在满足条件且具有较高可靠性的鲁棒决策,验证了该鲁棒优化模型的合理性。 相似文献
5.
6.
7.
该文旨在刻画一类约束函数是带有不确定信息的凸多项式的不确定凸优化问题的鲁棒可行性半径的下界.首先借助鲁棒优化方法,引入了该不确定凸优化问题的鲁棒对等问题(Robust counterpart),并给出了其鲁棒可行性半径的定义.随后通过引入一类上图集和借助由不确定集所生成的Minkowski泛函,刻画了该不确定凸优化问题的鲁棒可行性半径的下界.进一步的,在不确定集是仿射不确定集以及约束函数是平方和凸多项式时,得到了该不确定优化问题的鲁棒可行性半径的一个精确公式,推广和改进了文献[10]的相应结果. 相似文献
8.
《数学物理学报(A辑)》2017,(2)
该文旨在研究一类不确定性凸优化问题的鲁棒最优解.借助次微分的性质,首先引入了一类鲁棒型次微分约束品性.随后借助此约束品性,刻划了该不确定性凸优化问题的鲁棒最优解.最后建立了该不确定凸优化问题与其对偶问题之间的Wolfe型鲁棒对偶性. 相似文献
9.
本文研究了一类回报率不确定的投资组合问题.利用鲁棒优化方法,提出了一种鲁棒平均绝对偏差模型.现有的研究通常假设回报率是呈对称分布的不确定数据,本文提出的模型可处理非对称分布的不确定数据,适用范围更广. 相似文献
10.
为提升应急设施的服务质量和抵御中断风险的能力,研究应急设施最大覆盖选址-分配决策问题。扩展无容量限制的固定费用的可靠性选址决策模型,建立考虑共享不确定因素的应急设施最大覆盖选址优化模型,通过在目标和约束中引入budget不确定集刻画共享不确定因素,基于Bertsimas和Sim鲁棒优化方法建立混合整数规划模型,并将非线性问题转化为易于求解的鲁棒等价模型,利用带混沌搜索策略的改进灰狼优化算法求解模型,并对不确定鲁棒水平和中断概率进行敏感性分析。最后通过案例及数据仿真结果的对比分析,验证了模型的合理性和有效性,并给出最优的选址分配布局。 相似文献
11.
In this paper, we consider a nonlinear switched time-delay (NSTD) system with unknown switching times and unknown system parameters, where the output measurement is uncertain. This system is the underling dynamical system for the batch process of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. The uncertain output measurement is regarded as a stochastic vector (whose components are stochastic variables) and the only information about its distribution is the first-order moment. The objective of this paper is to identify the unknown quantities of the NSTD system. For this, a distributionally robust optimization problem (a bi-level optimization problem) governed by the NSTD system is proposed, where the relative error under the environment of uncertain output measurements is involved in the cost functional. The bi-level optimization problem is transformed into a single-level optimization problem with non-smooth term through the application of duality theory in probability space. By applying the smoothing technique, the non-smooth term is approximated by a smooth term and the convergence of the approximation is established. Then, the gradients of the cost functional with respect to switching times and system parameters are derived. A hybrid optimization algorithm is developed to solve the transformed problem. Finally, we verify the obtained switching times and system parameters, as well as the effectiveness of the proposed algorithm, by solving this distributionally robust optimization problem. 相似文献
12.
Adjustable robust optimization (ARO) generally produces better worst-case solutions than static robust optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we provide conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that when the uncertainty is constraint-wise, the problem is convex with respect to the adjustable variables and concave with respect to the uncertain parameters, the adjustable variables lie in a convex and compact set and the uncertainty set is convex and compact, then robust solutions are also optimal for the corresponding ARO problem. Furthermore, we prove that if some of the uncertain parameters are constraint-wise and the rest are not, then under a similar set of assumptions there is an optimal decision rule for the ARO problem that does not depend on the constraint-wise uncertain parameters. Also, we show for a class of problems that using affine decision rules that depend on all of the uncertain parameters yields the same optimal objective value as when the rules depend solely on the non-constraint-wise uncertain parameters. Finally, we illustrate the usefulness of these results by applying them to convex quadratic and conic quadratic problems. 相似文献
13.
A. Takeda S. Taguchi R. H. Tütüncü 《Journal of Optimization Theory and Applications》2008,136(2):275-295
We study two-period nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are
revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty,
we show that quasiconvexity of the optimal value function of certain subproblems is sufficient for the reducibility of the
resulting robust optimization problem to a single-level deterministic problem. We relate this sufficient condition to the
cone-quasiconvexity of the feasible set mapping for adjustable variables and present several examples and applications satisfying
these conditions.
This work was partially supported by the National Science Foundation, Grants CCR-9875559 and DMS-0139911, and by Grant-in-Aid
for Scientific Research from the Ministry of Education, Sports, Science and Culture of Japan, Grant 16710110. 相似文献
14.
Dashan Huang Shushang Zhu Frank J. Fabozzi Masao Fukushima 《European Journal of Operational Research》2010
Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program. 相似文献
15.
《Optimization》2012,61(7):1033-1040
We identify and discuss issues of hidden over-conservatism in robust linear optimization, when the uncertainty set is polyhedral with a budget of uncertainty constraint. The decision-maker selects the budget of uncertainty to reflect his degree of risk aversion, i.e. the maximum number of uncertain parameters that can take their worst-case value. In the first setting, the cost coefficients of the linear programming problem are uncertain, as is the case in portfolio management with random stock returns. We provide an example where, for moderate values of the budget, the optimal solution becomes independent of the nominal values of the parameters, i.e. is completely disconnected from its nominal counterpart, and discuss why this happens. The second setting focusses on linear optimization with uncertain upper bounds on the decision variables, which has applications in revenue management with uncertain demand and can be rewritten as a piecewise linear problem with cost uncertainty. We show in an example that it is possible to have more demand parameters equal their worst-case value than what is allowed by the budget of uncertainty, although the robust formulation is correct. We explain this apparent paradox. 相似文献
16.
在市场需求、设施开设成本和产品回收率不确定的条件下,采用一种交互式可能性规划方法,研究由多个工厂、分销点、市场和废旧点构成的可持续闭环供应链网络设计问题。基于可持续闭环供应链网络结构,构建以企业运营成本和环境伤害最小、社会效益最大为目标的混合整数规划模型。同时,引入改进Epsilon约束方法将多目标优化问题转化为单目标优化问题,在此基础上提出一种两阶段可能性规划方法,基于TH模糊方法对不确定性参数进行处理。最后,通过数值实例,验证本文所建可持续闭环供应链网络模型的有效性,并对悲观-乐观值、不确定参数最低可接受水平β、可调参数γ进行敏感性分析;通过与其他模糊方法对比表明,采用TH模糊方法能得到稳定的最优解。 相似文献
17.
Zhongfeng Qin 《Fuzzy Optimization and Decision Making》2018,17(4):375-386
Goal programming provides an efficient technique to deal with decision making problems with multiple conflicting objectives. This paper joins the streams of research on goal programming by providing a so-called uncertain random goal programming to model the multi-objective optimization problem involving uncertain random variables. Several equivalent deterministic forms are derived on the condition that the set of parameters consists of uncertain variables and random variables. Finally, an example is given to illustrate the application of the approach. 相似文献
18.
《Optimization》2012,61(7):1099-1116
In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the method. 相似文献
19.
Maria Grazia Scutellà Raffaella Recchia 《4OR: A Quarterly Journal of Operations Research》2010,8(2):113-139
Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are
not known in advance, but can only be forecast or estimated. Several methodologies have therefore, been proposed to handle
the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem
of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness
is provided by Robust Optimization which, given optimization problems with uncertain parameters, looks for solutions that
will achieve good objective function values for the realization of these parameters in given uncertainty sets. Robust Optimization
thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true,
for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance
portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches,
that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology.
We also give an overview of some of the computational results that have been obtained with the described approaches. In addition
we analyse the relationship between the concepts of robustness and convex risk measures. 相似文献