Stochastic approximation algorithms for the local optimization of functions with nonunique stationary points

The aim of this paper is the provision of a framework for a practical stochastic unconstrained optimization theory. The results are based on certain concepts of stochastic approximation, although not restricted to those procedures, and aim at incorporating the great flexibility of currently available deterministic optimization ideas into the stochastic problem, whenever optimization must be done by Monte Carlo or sampling methods. Hills with nonunique stationary points are treated. A framework has been provided, with which convergence of stochastic versions of conjugate gradient, partan, etc., can be discussed and proved.     

Adaptive management of natural systems using fuzzy logic

Hypotheses about how management practices influence ecosystem services can be tested using a crisp, probability-based, or fuzzy decision rule. The correct decision rule depends on whether: (1) the observed state of an ecosystem service (x) is non-stochastic or stochastic; (2) the true state of the ecosystem service (y) is non-stochastic or stochastic; and (3) the relationship between x and y is deterministic, stochastic, or uncertain. Crisp and probability-based decision rules are not appropriate when the relationship between y and x is uncertain in the sense that the decision maker is unable or unwilling to specify conditional probabilities of y given x. Under these conditions, a fuzzy decision rule is appropriate. A hypothetical case study is used to illustrate how a fuzzy decision rule is used to test hypotheses about whether selective cutting of timber provides greater or less forest biodiversity than clearcutting of timber. The case study describes how to incorporate the decision rule in an active adaptive management framework to sequentially test the extent to which changes over time in other factors influencing ecosystem services, such as greater spread of invasive species due to global warming, alter the efficacy of timber management practices. The fuzzy adaptive management decision rule can be generalized to account for the effects of management practices on multiple ecosystem services.     

基于光伏预测的微电网能源随机优化调度

可再生能源的间歇性和负荷的随机性对微电网能源管理系统（ EMS）产生了巨大的挑战。在随机环境下的能源优化调度问题在微电网的研究中具有重要意义。以微电网中光伏发电系统的功率预测为基础,将光伏预测误差当做随机变量,建立了一种基于期望模型的能源随机优化调度模型。用Monte Carlo模拟方法生成了光伏发电预测误差的情景集,应用粒子群优化算法来解决随机优化调度模型。通过与确定性模型产生的调度方案相对比,证明了随机优化调度模型更加有效。     

Stochastic and global real time optimization of Tennessee Eastman challenge problem

A stochastic real time optimization (SRTO) which has an efficient result has been implemented on the Tennessee Eastman (TE) challenging problem. In this article a novel stochastic optimization method, the so-called heuristic random optimization (HRO) proposed by Li & Rhinehart is used which attempts to rationally combine features of both deterministic and random (stochastic) methods. Further, an on-line nonlinear identifier via extended Kalman filter (EKF) is used to supply the plant model for model-based optimization algorithm. Using the information obtained from EKF an on-line HRO is accomplished by a random search method whose search directions and steps are considerably reduced by some heuristic rules. In order to compare and prove the performance of HRO method, the problem was solved again via sequential quadratic programming (SQP) which is the most efficient algorithms among the deterministic methods. The optimizer initiates every 8 h and determines the optimal set points of the PI controllers in the plant. The calculations are completed in about 15 s by HRO method. Simulations have been done using an Intel P4 2.8 GHz, and 256 MB of RAM.     

Non-probabilistic robust optimization approach for flood control system design

Flood risk management in floodplain systems is a long-standing problem in water resources management. Soft strategies such as land cover change are used to mitigate damages due to flooding. In this approach one chooses the best combination of land covers such that flood damage and the investment costs are minimized. Because of the uncertain nature of the problem, former studies addressed this problem by stochastic programming models which are found to be computationally expensive. In this work, a novel non-probabilistic robust counterpart approach is proposed in which the uncertainty of the rainfall events requires a new formulation and solution algorithms. Non-probabilistic methods, developed in the field of robust optimization were shown to have advantages over classical stochastic methods in several aspects such as: tractability, non-necessity of full probabilistic information, and the ability to integrate correlation of uncertain variables without adding complexity. However, unlike former studies in the field of robust optimization, the resulting optimization model in the flood risk management problem is nonlinear and discontinuous and leads to an intractable robust counterpart model. In this work, a novel iterative linearization scheme is proposed to effectively solve nonlinear robust counterpart models. This work demonstrates the tractability and applicability of non-probabilistic robust optimization to nonlinear problems similar to the flood risk management problem. The results show considerable promise of the robust counterpart approach in terms of showing the tradeoff between flood risk and cost in an efficient manner.     

动态电源管理的随机切换模型与在线优化

考虑系统参数未知情况下的动态电源管理问题，提出一种基于强化学习的在线策略优化算法. 通过建立事件驱动的随机切换分析模型，将动态电源管理问题转化为带约束的Markov 决策过程的策略优化问题. 利用此模型的动态结构特性，结合在线学习估计梯度与随机逼近改进策略，提出动态电源管理策略的在线优化算法．随机切换模型对电源管理系统的动态特性描述精确，在线优化算法自适应性强，运算量小，精度高，具有较高的实际应用价值．     

结构可靠度随机仿真与试验分析

为了利用可靠度方法对管道进行风险评价,解决可靠度分析变量过多,模型复杂,计算困难的问题,结合管道跨越工程,利用最优化原理,将最优化蒙特卡罗方法与随机有限元方法结合,在确定基本有限元模型和最优化可靠度数学模型后,根据随机过程对基本变量进行正态化处理,确定出基本统计量的数字特征和单元之间的相关系数,合理控制计算精度,进一步确定出失效概率、可靠度值,通过显著性分析找出主因素,为结构参数优化提供合理依据。通过假设检验,验证了分析结果的合理性,为管线的风险评估提供新思路和方法。     

Perturbation analysis and optimization of stochastic flow networks

We consider a stochastic fluid model of a network consisting of several single-class nodes in tandem and perform perturbation analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal perturbation analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in online environments and easily implementable for network management and optimization. This is illustrated by combining the IPA estimators with standard gradient based stochastic optimization methods and providing simulation examples.     

Robust shape optimization of notches for fatigue-life extension

An iterative 2D finite-element-based optimization procedure has been developed which incorporates robust design philosophies. This has been used to determine precise free-form shapes for a hole in a plate example, with the aim of maximizing its fatigue-life when exposed to varying load orientations. Past methods have typically considered only a single nominal load orientation, with empirical approaches to deal with the orientation variability, thus resulting in suboptimal solutions. Here a robust stress method is developed that produces a notch shape that minimizes the peak stress and renders it constant for a range of load orientations. Furthermore, a more sophisticated robust fatigue-damage optimization method is then developed to minimize the peak fatigue damage for a given stochastic distribution of load orientations. Fatigue calculations for an example problem with significant load orientation variation show that the robust optimization methods provide fatigue-life extensions 2 to 8 times better than past methods. It is anticipated that the implementation of robust optimal shapes in metallic components would result in greater fatigue-life extension.     

Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem

Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions.      

A comparison among stochastic optimization algorithms for parameter estimation of biochemical kinetic models

Mathematical models in biochemical engineering field are usually composed by nonlinear kinetic equations, where the number of parameters that must be estimated from a set of experimental measurements is usually very high. In these cases, the estimation of the model parameters comprises numerical iterative methods for minimization of the objective function. Classical methods for minimization of the objective function, like the Newton method, requires a good initial guess for all parameters and differentiation of the objective function and/or model equations with respect to the model parameters. Besides, the use of stochastic optimization methods for parameter estimation has gained attention, since these methods do not require a good initial guesses of all model parameters and neither the evaluation of derivatives. In this work, some stochastic optimization methods (Artificial Bee Colony, Differential Evolution, Particle Swarm Optimization and Simulated Annealing) were used in the estimation of kinetic parameters of a biochemical model for an alcoholic fermentation of cassava hydrolyzed. The results indicated that Differential Evolution provides better results among the stochastic optimization methods evaluated.     

A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm

Genetic algorithms (GAs), which are directed stochastic hill climbing algorithms, are a commonly used optimization technique and are generally applied to single criterion optimization problems with fairly complex solution landscapes. There has been some attempts to apply GA to multicriteria optimization problems. The GA selection mechanism is typically dependent on a single-valued objective function and so no general methods to solve multicriteria optimization problems have been developed so far. In this paper, a new method of transformation of the multiple criteria problem into a single-criterion problem is presented. The problem of transformation brings about the need for the introduction of thePareto set estimation method to perform the multicriteria optimization using GAs. From a given solution set, which is the population of a certain generation of the GA, the Pareto set is found. The fitness of population members in the next GA generation is calculated by a distance metric with a reference to the Pareto set of the previous generation. As we are unable to combine the objectives in some way, we resort to this distance metric in the positive Pareto space of the previous solutions, as the fitness of the current solutions. This new GA-based multicriteria optimization method is proposed here, and it is capable of handling any generally formulated multicriteria optimization problem. The main idea of the method is described in detail in this paper along with a detailed numerical example. Preliminary computer generated results show that our approach produces better, and far more Pareto solutions, than plain stochastic optimization methods.     

A two-stage programming approach for water resources management under randomness and fuzziness

In this study, a fuzzy stochastic two-stage programming (FSTP) approach is developed for water resources management under uncertainty. The concept of fuzzy random variable expressed as parameters’ uncertainties with both stochastic and fuzzy characteristics was used in the method. FSTP has advantages in uncertainty reflection and policy analysis. FSTP integrates the fuzzy robust programming, chance-constrained programming and two-stage stochastic programming (TSP) within a general optimization framework. FSTP can incorporate pre-regulated water resources management policies directly into its optimization process. Thus, various policy scenarios with different economic penalties (when the promised amounts are not delivered) can be analyzed. FSTP is applied to a water resources management system with three users. The results indicate that reasonable solutions were generated, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and different levels of constraint-violation probability. The developed FSTP was also compared with TSP to exhibit its advantages in dealing with multiple forms of uncertainties.     

A decision support system for strategic asset allocation

Strategic asset allocation is a crucial activity for any institutional or individual investor. Given a set of asset classes, the problem concerns the definition and management over time of the best asset mix to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. Although a considerable attention has been placed by the scientific community to address this problem by proposing sophisticated optimization models, limited effort has been devoted to the design of integrated framework that can be systematically used by financial operators. The paper presents a decision support system which integrates simulation techniques for forecasting future uncertain market conditions and sophisticated optimization models based on the stochastic programming paradigm. The system has been designed to be accessed via web and takes advantages of the increased computational power offered by high performance computing platforms. Real-world instances have been used to assess the performance of the decision support system also in comparison with more traditional portfolio optimization strategies.     

A new stochastic search algorithm bundled honeybee mating for solving optimization problems

This paper presents a new stochastic search technique to solve optimization problems. The new stochastic search of parallel vector evaluated honeybee mating optimization (VEHBMO) technique mimics the honeybee’s mating. The effectiveness of the proposed technique is compared with other stochastic optimization methods through standard benchmark functions. Also, the proposed VEHBMO is applied over real engineering problems of economic load dispatch and environmental/economic power dispatch problems. Obtained results confirm the validity of the proposed stochastic search technique.     

模拟退火法在钟手表机芯布局中的应用

布局问题,特别是三维物体的布局问题在工业界有着广泛的用途,由于该问题在理论上已属于ＮＰ完全问题,很难用传统优化算法求解,钟手表机芯设计中的传动件布局是具有强约束的三维物体布局问题,根据退火法是一种用于解决连续,有序离散和多模态优化问题的随机优化技术,本文利用根据退火法成功地解决了钟手表机芯设计中的难题,该文还提供了解决一般物体布局问题的框架。     

Optimization and Filtering for Human Motion Capture

Local optimization and filtering have been widely applied to model-based 3D human motion capture. Global stochastic optimization has recently been proposed as promising alternative solution for tracking and initialization. In order to benefit from optimization and filtering, we introduce a multi-layer framework that combines stochastic optimization, filtering, and local optimization. While the first layer relies on interacting simulated annealing and some weak prior information on physical constraints, the second layer refines the estimates by filtering and local optimization such that the accuracy is increased and ambiguities are resolved over time without imposing restrictions on the dynamics. In our experimental evaluation, we demonstrate the significant improvements of the multi-layer framework and provide quantitative 3D pose tracking results for the complete HumanEva-II dataset. The paper further comprises a comparison of global stochastic optimization with particle filtering, annealed particle filtering, and local optimization.     

Biogeography-based optimization for constrained optimization problems

Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm and it has so far been successfully applied in a variety of fields, especially for unconstrained optimization problems. The present paper shows how BBO can be applied for constrained optimization problems, where the objective is to find a solution for a given objective function, subject to both inequality and equality constraints.     

基于自抗扰控制的随机扰动库存系统优化模型

针对随机扰动造成的企业库存系统缺货、库存水平增加和订货波动增大的问题,提出一种基于自抗扰控制（ADRC）的随机扰动库存系统优化模型。首先,根据进销存产品流和信息流的运营管理逻辑,通过拉普拉斯变换得到了库存系统的传递函数并将其转换成一类二阶状态空间标准式;然后,设计了一种包括跟踪微分器、扩张状态观测器和非线性状态误差反馈控制率的基于ADRC的随机扰动库存系统优化模型,从而在保证系统稳定的前提下,控制补偿随机扰动对库存系统的影响;最后,利用行业数据进行仿真实验,以验证ADRC优化模型对随机扰动库存系统优化的有效性。仿真实验结果表明,与无ADRC的库存反馈控制模型相比,基于ADRC的随机扰动库存系统优化模型可减少40%的库存剩余,减小47.4%的订货量均值,降低39.3%的订货量波动,并极大地改善随机扰动下企业库存系统的缺货现象。由此可见,基于ADRC的随机扰动库存系统优化模型能够指导企业合理订货,降低企业库存水平,从动态的角度提高库存系统的稳定性,为企业的实际生产运营提供科学的理论借鉴和应对方法。     

机器学习随机优化方法的个体收敛性研究综述

随机优化方法是求解大规模机器学习问题的主流方法,其研究的焦点问题是算法是否达到最优收敛速率与能否保证学习问题的结构。目前,正则化损失函数问题已得到了众多形式的随机优化算法,但绝大多数只是对迭代进行 平均的输出方式讨论了收敛速率,甚至无法保证最为典型的稀疏结构。与之不同的是,个体解能很好保持稀疏性,其最优收敛速率已经作为open问题被广泛探索。另外,随机优化普遍采用的梯度无偏假设往往不成立,加速方法收敛界中的偏差在有偏情形下会随迭代累积,从而无法应用。本文对一阶随机梯度方法的研究现状及存在的问题进行综述,其中包括个体收敛速率、梯度有偏情形以及非凸优化问题,并在此基础上指出了一些值得研究的问题。