Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements

In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method.     

Unified process assessment for resources use and waste emissions by coal-fired power generation

A unified process assessment is carried out to integrate various resources and emissions associated with the life cycle of typical coal-fired power generation systems, based on the thermodynamic concept of exergy as a common objective measure. For a comprehensive assessment of industrial production systems, three indicators termed as ecological efficiency, resources use efficiency and environmental emission intensity are devised to evaluate the overall efficacy. Concretely assessed in the present work are three typical modes of coal-fired power generation systems, i.e., the Average mode that represents the average emissions and efficiency of coal-fired power plants operating in the US in 1999, the New Source Performance Standards (NSPS) mode that meets the New Source Performance Standards, and the low emission boiler system (LEBS) mode as a kind of highly advanced coal-fired power plant utilizing a low emission boiler, as benchmark cases in related NREL (National Renewable Energy Laboratory) report.     

A genetic algorithm based augmented Lagrangian method for constrained optimization

Among the penalty based approaches for constrained optimization, augmented Lagrangian (AL) methods are better in at least three ways: (i) they have theoretical convergence properties, (ii) they distort the original objective function minimally, thereby providing a better function landscape for search, and (iii) they can result in computing optimal Lagrange multiplier for each constraint as a by-product. Instead of keeping a constant penalty parameter throughout the optimization process, these algorithms update the parameters (called multipliers) adaptively so that the corresponding penalized function dynamically changes its optimum from the unconstrained minimum point to the constrained minimum point with iterations. However, the flip side of these algorithms is that the overall algorithm requires a serial application of a number of unconstrained optimization tasks, a process that is usually time-consuming and tend to be computationally expensive. In this paper, we devise a genetic algorithm based parameter update strategy to a particular AL method. The proposed strategy updates critical parameters in an adaptive manner based on population statistics. Occasionally, a classical optimization method is used to improve the GA-obtained solution, thereby providing the resulting hybrid procedure its theoretical convergence property. The GAAL method is applied to a number of constrained test problems taken from the evolutionary algorithms (EAs) literature. The number of function evaluations required by GAAL in most problems is found to be smaller than that needed by a number of existing evolutionary based constraint handling methods. GAAL method is found to be accurate, computationally fast, and reliable over multiple runs. Besides solving the problems, the proposed GAAL method is also able to find the optimal Lagrange multiplier associated with each constraint for the test problems as an added benefit??a matter that is important for a sensitivity analysis of the obtained optimized solution, but has not yet been paid adequate attention in the past evolutionary constrained optimization studies.     

A robust optimization approach to experimental design for model discrimination of dynamical systems

A high-ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization. Quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions. Typically, before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the models up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification. In this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate (worst case) parameter configurations within a parameter range. The design comprises initial values, system perturbations and the optimal placement of measurement time points, the number of measurements as well as the time points are subject to design. The statistical discrimination criterion is worked out rigorously for these settings, a derivation from the Kullback-Leibler divergence as optimization objective is presented for the case of discontinuous Heaviside-functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure. The resulting problem can be classified as a semi-infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated. We present the theoretical framework, algorithmic realization and numerical results.     

Robust mean variance optimization problem under Rényi divergence information

In this paper, we consider the robust mean variance optimization problem where the probability distribution of assets’ returns is multivariate normal and the uncertain mean and covariance are controlled by a constraint involving Rényi divergence. We present the closed-form solutions for the robust mean variance optimization problem and find that the choice of order parameter which is related to the Rényi divergence measure will not impact optimal portfolio strategy under the cases that the mean vector and the covariance matrix are uncertain, respectively. Moreover, we obtain the closed-form solution for the robust mean variance optimization problem under the case that the mean vector and the covariance matrix are both uncertain. We illustrate the efficiency of our results with an example.     

Model-based parameter optimization for arc welding process simulation

This paper presents a model-based parameter optimization for simulating a metal-inert gas welding process. The computational model used in this study is based on computational fluid dynamics methods and implemented using the finite volume approach on a 3D computational domain. The wire electrode, the arc plasma and the workpiece are treated as a self-consistent system. Important welding parameters, including arc current, wire feed rate, workpiece thickness, welding speed and geometry, as well as the metal alloy types used for the wire and workpiece, were implemented as adjustable parameters. By tuning these parameters, the performance of the arc welding can be predicted, and different settings can be compared to optimize welding performance.A benchmarking study of the arc model against experimental measurements is presented to demonstrate the model's capabilities in the prediction of the weld pool changes and thermal dynamics involved in the welding process. Two numerical case studies are presented to demonstrate the use of the model-based optimization to quantify welding pool variations with the change in welding parameters. The first case study is the determination of the optimal arc current and welding speed settings for different workpiece thicknesses. The optimization process shows that the predictions are not only in agreement with established experimental welding experience on the direct relationship between workpiece thickness and arc current, but more importantly quantify this relationship for a given workpiece thickness. The second case study focuses on the welding parameters optimization for different metal alloys. The comparison suggests that the welding parameters suitable for some aluminium alloys are less likely to be successful in welding magnesium alloys. A further model validation of Mg alloy AZ31 welding shows an agreement with experimental measurements. The work presented shows the potential of model-based parameter optimization to assist process engineers in the practical improvement of the welding process.     

政府促进银行实施绿色信贷的多目标优化策略研究

传统的绿色信贷研究中存在着模型简单、非动态参数以及只能获取纳什均衡点的局限性。为改善这些局限性,研究了一种基于数据驱动多目标优化算法的政府促进银行实施绿色信贷的策略计算方法。首先针对绿色信贷的最优策略求解问题建立数据驱动的多目标优化算法框架,再基于历史数据建立算法框架中的最优策略马可夫状态转移模型,最后使用多目标粒子群优化算法对政府和银行的长远总收益进行最优策略求解。与传统的基于近似模型及博弈论的方法不同,本文提出的方法可以获得历史数据中的经验,从而制定出具有更加长远收益的策略,避免了传统方法中的“短视”现象。分析结果表明,绿色信贷的收益不会在短时间内显现,因此政府在做决策时,必须根据绿色信贷收益的回报周期作出长远的判断。     

果蝇优化最小二乘支持向量机混合预测模型—以我国物流需求量预测为例

为解决最小二乘支持向量机参数设置的盲目性,利用果蝇优化算法对其参数进行优化选择,进而构建了果蝇优化最小二乘支持向量机混合预测模型.以我国物流需求量预测为例,验证了该模型的可行性和有效性.实例验证结果表明:与单一最小二乘支持向量机和模拟退火算法优化最小二乘支持向量机预测模型相比,该模型不仅能够有效选择参数值,而且预测精度更高.     

Optimal location and optimized parameters for robust power system stabilizer using honeybee mating optimization

A honeybee mating optimization technique is used to tune the power system stabilizer (PSS) parameters and find optimal location of PSSs in this article. The PSS parameters and placement are computed to assure maximum damping performance under different operating conditions. One of the main advantages of the proposed approach is its robustness to the initial parameter settings. The effectiveness of the proposed method is demonstrated on two case studies as; 10‐machine 39‐buses New England (NE) power system in comparison with Tabu Search (TS) and 16 machines and 68 buses‐modified reduced order model of the NE New York interconnected system by genetic algorithm through some performance indices under different operating condition. The proposed method of tuning the PSS is an attractive alternative to conventional fixed gain stabilizer design as it retains the simplicity of the conventional PSS and at the same time guarantees a robust acceptable performance over a wide range of operating and system condition. © 2014 Wiley Periodicals, Inc. Complexity 21: 242–258, 2015     

An Unified Computational Framework for Parameter Identification of Material Models in Finite Inelasticity

Parameter identification processes concern the determination of parameters in a material model in order to fit experimental data. We provide a distinct, unified algorithmic setting of a generic class of material models and discuss the associated gradient–based optimization problem. Gradient–based optimization algorithms need derivatives of the objective function with respect to the material parameter vector κ . In order to obtain the necessary derivatives, an analytical sensitivity analysis is pointed out for the unified class of algorithmic material models. The quality of the parameter identification is demonstrated for a representative example.     

Robust Parameter Settings for Variation Operators by Measuring the Resampling Ratio: A Study on Binary Constraint Satisfaction Problems

In this article, we try to provide insight into the consequence of mutation and crossover rates when solving binary constraint satisfaction problems. This insight is based on a measurement of the space searched by an evolutionary algorithm. From data empirically acquired we describe the relation between the success ratio and the searched space. This is achieved using the resampling ratio, which is a measure for the amount of points revisited by a search algorithm. This relation is based on combinations of parameter settings for the variation operators. We then show that the resampling ratio is useful for identifying the quality of parameter settings, and provide a range that corresponds to robust parameter settings.     

On the role of norm constraints in portfolio selection

Several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among them are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in portfolio optimization from several directions. First, it is shown that the norm constraint can be regarded as a robust constraint associated with the return vector. Second, the reformulations of the robust counterparts of the value-at-risk (VaR) and conditional value-at-risk (CVaR) minimizations contain norm terms and are shown to be highly related to the ν-support vector machine (ν-SVM), a powerful statistical learning method. For the norm-constrained VaR and CVaR minimizations, a nonparametric theoretical validation is posed on the basis of the generalization error bound for the ν-SVM. Third, the norm-constrained approaches are applied to the tracking portfolio problem. Computational experiments reveal that the norm-constrained minimization with a parameter tuning strategy improves on the traditional norm-unconstrained models in terms of the out-of-sample tracking error.     

A procedure to design the mainline system in natural gas networks

With the start up of West–East Natural Gas Transmission Project, the construction of natural gas-pipeline will enter on a new era in China. The development tendency will be towards large-diameter, high-pressure and long-distance for natural gas-pipelines. Correspondingly, the life cycle cost of natural gas-pipeline networks is increasing gradually. The mainline system is a vital part of natural gas network systems. The investment required for the mainline system is enormous, usually accounting for 80% of the total investment for this system. In general, the investment required for a gas-pipeline depends on its operating parameters. Therefore, based on the characteristics of gas networks, optimization for investment becomes indispensable to gas networks design. A comprehensive and optimal mathematic model of a gas networks system is established in this paper which considers all the factors influencing the total investment of a gas networks system (e.g. pipe diameter, thickness, pressure, length, compression ratio, etc). From the standpoint of the characteristics of a model comprising both continuous and discrete variables, a new methodology, rank-optimization, is presented. On the basis of this model, a simple and visual high-pressure networks optimization program has been compiled. Furthermore, the developed optimization program has been applied to a practical project and the effects of operating parameters on the total investment have been analyzed. The simulation model in this paper is shown to be an effective method to solve optimization on mainline system in high-pressure gas networks.     

基于PCA和改进的PSO-SVM的机器人移动方向分类

随着人们创新水平的不断提高,为了更加准确的实现机器人的导航任务,提出了一种基于改进的粒子群优化支持向量机中的参数的方法.首先利用主成分分析法对数据进行降维,然后利用改进的粒子群优化算法,对SVM中的惩罚参数c和核函数的参数g进行优化,最后代入到SVM中,以此来达到运用SVM对机器人的导航任务进行分类识别.相对于其他算法,容易发现改进的粒子群优化算法优化后的支持向量机可以达到很好的效果.这种识别分类可以帮助人们很好的对机器人进行导航,对今后机器人的研究具有很大的应用价值.     

Convexity and optimization with copulæ structured probabilistic constraints

Probability constraints play a key role in optimization problems involving uncertainties. These constraints request that an inequality system depending on a random vector has to be satisfied with a high enough probability. In specific settings, copulæ can be used to model the probabilistic constraints with uncertainty on the left-hand side. In this paper, we provide eventual convexity results for the feasible set of decisions under local generalized concavity properties of the constraint mappings and involved copulæ. The results cover all Archimedean copulæ. We consider probabilistic constraints wherein the decision and random vector are separated, i.e. left/right-hand side uncertainty. In order to solve the underlying optimization problem, we propose and analyse convergence of a regularized supporting hyperplane method: a stabilized variant of generalized Benders decomposition. The algorithm is tested on a large set of instances involving several copulæ among which the Gaussian copula. A Numerical comparison with a (pure) supporting hyperplane algorithm and a general purpose solver for non-linear optimization is also presented.     

Weekly self-scheduling,forward contracting,and pool involvement for an electricity producer. An adaptive robust optimization approach

This paper addresses the optimization under uncertainty of the self-scheduling, forward contracting, and pool involvement of an electricity producer operating a mixed power generation station, which combines thermal, hydro and wind sources, and uses a two stage adaptive robust optimization approach. In this problem the wind power production and the electricity pool price are considered to be uncertain, and are described by uncertainty convex sets. To solve this problem, two variants of a constraint generation algorithm are proposed, and their application and characteristics discussed. Both algorithms are used to solve two case studies based on two producers, each operating equivalent generation units, differing only in the thermal units’ characteristics. Their market strategies are investigated for three different scenarios, corresponding to as many instances of electricity price forecasts. The effect of the producers’ approach, whether conservative or more risk prone, is also investigated by solving each instance for multiple values of the so-called budget parameter. It was possible to conclude that this parameter influences markedly the producers’ strategy, in terms of scheduling, profit, forward contracting, and pool involvement. These findings are presented and analyzed in detail, and an attempted rationale is proposed to explain the less intuitive outcomes. Regarding the computational results, these show that for some instances, the two variants of the algorithms have a similar performance, while for a particular subset of them one variant has a clear superiority.     

An extension of the Basic Constraint Qualification to nonconvex vector optimization problems

In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite-dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half-spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite-dimensional vector optimization, specially with the Kurcyuscz-Robinson-Zowe constraint qualification, are also given.     

Application of chaos-based chaotic invasive weed optimization techniques for environmental OPF problems in the power system

This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems.     

Optimal Parameter Tuning for Multiclass Support Vector Machines in Machinery Health State Estimation

The increasing demand for high reliability, safety and availability of technical systems calls for innovative maintenance strategies. The use of prognostic health management (PHM) approach where maintenance action is taken based on current and future health state of a component or system is rapidly gaining popularity in the maintenance industry. Multiclass support vector machines (MC-SVM) has been identified as a promising algorithm in PHM applications due to its high classification accuracy. However, it requires parameter tuning for each application, with the objective of minimizing the classification error. This is a single objective optimization problem which requires the use of optimization algorithms that are capable of exhaustively searching for the global optimum parameters. This work proposes the use of hybrid differential evolution (DE) and particle swarm optimization (PSO) in optimally tuning the MC-SVM parameters. DE identifies the search limit of the parameters while PSO finds the global optimum within the search limit. The feasibility of the approach is verified using bearing run-to-failure data and the results show that the proposed method significantly increases health state classification accuracy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)