广义Pareto分布下风险值估计

采用适当的统计方法来估计广义Pareto的分布参数，对于计算基于极值理论的风险值(VaR)具有重要的理论和现实意义．一般采用最大似然法(MLM)对它的参数进行估计，作者采用和McNeil，Frey相似的方法选择域值后，分别采用最大似然法、概率权重矩法(PWM)和矩法(MoM)对广义Pareto分布的参数进行了估计．并对上证指数的VaR进行了相应计算，最后对结果进行后验比较分析，探讨了不同估计方法的适用规律．     

Multi-objective optimal design of vertical natural circulation steam generator

In this work, a hybrid non-dominated sorting genetic algorithm was proposed and utilized to perform the multi-objective optimization design of a natural circulation steam generator, which included minimizing of the weight, the volume and the reactor coolant flow-rate. Sensitivity analysis of the design variables was carried out to study the relationships between the optimization variables and the objective functions, which was also helpful for the explanation of the optimization results. The mathematical model of the steam generator was validated by the RELAP5 code. The results show that the mathematical model has a good agreement with the RELAP5 model after modifying the boiling correlation in the secondary side; the proposed hybrid non-dominated sorting genetic algorithm is able to find much better spread of solutions and better convergence near the true Pareto optimal front compared to the non-dominated sorting genetic algorithm; reactor inlet temperature is the most important variable which influences the distribution of Pareto optimal solutions.     

A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its Pareto Frontier

The DC optimal power flow (DC-OPF) plays an important role in the operation and planning of modern power systems. In this paper, a bi-objective DC-OPF model minimizing both network losses and generation costs is introduced, which can further be converted into a single objective model via the weighted sum method. Furthermore, the Pareto Frontier is employed to solve this problem. In the mathematical view, the model is a special non-convex quadratic constraints quadratic programming problem. In order to obtain a continuous Pareto Frontier, the original non-convex feasible region is relaxed to its convex hull using a linear relaxation-based second order cone programming method. Compared with the semi-definite relaxation method, the proposed method can greatly reduce the number of dummy variables and the complexity of solutions. Finally, simulations on eight small systems and four practical, large systems are performed, in addition to the comparison of a Monte Carlo simulation. The results verify the effectiveness of the proposed algorithm.     

COMMENTS ON ZELENÝ'S PAPER CONCERNING COGNITIVE EQUILIBRIA

Bivariate Pareto distributions arise naturally when it comes to comparing the performances of two systems. In this note, explicit expressions are derived for a relative measure of performance for every known bivariate Pareto distribution. The calculations involve the use of Gauss hypergeometric function.     

Reducing CO2 emission from exhaust gases using molten carbonate fuel cells: a new approach

The aim of this study is to couple molten carbonate fuel cell (MCFC) stack with integrated gasification combined cycle fed by refinery residues, to remove CO₂ from gas turbine exhaust gases that have CO₂ emission rate of 14,200 ton/year. By applying multi-objective optimisation (MOO) using genetic algorithm, the optimal values of operating load and the corresponding values of objective functions are obtained. The MOO of the MCFC system regarding two scenarios is performed. The first scenario is minimisation of cost of electricity (COE) and CO₂ emission rate. Objective functions of the second scenario are the same as in the first scenario while CO₂ tax is taken into account. Results show that the second scenario has 29.5% lower average optimal COE and 2.5% lower average emission rate in comparison with the first scenario. A sensitivity analysis is also performed to study the effect of fuel price and CO₂ tax variations on optimal solutions.     

Tail Estimation for Window-Censored Processes

This article develops methods to estimate the tail and full distribution of the lengths of the 0-intervals in a continuous time stationary ergodic stochastic process that takes the values 0 and 1 in alternating intervals. The setting is that each of many such 0–1 processes has been observed during a short time window. Thus, the observed 0-intervals could be noncensored, right-censored, left-censored, or doubly-censored, and the lengths of 0-intervals that are ongoing at the beginning of the observation window have a length-biased distribution. We exhibit parametric conditional maximum likelihood estimators for the full distribution, develop maximum likelihood tail estimation methods based on a semiparametric generalized Pareto model, and propose goodness-of-fit plots. Finite sample properties are studied by simulation, and asymptotic normality is established for the most important case. The methods are applied to estimation of the length of off-road glances in the 100-car study, a big naturalistic driving experiment. Supplementary materials that include MatLab code for the estimation routines and a simulation study are available online.     

基于决策空间变换最近邻方法的Pareto支配性预测

为提高在决策空间运用最近邻方法预测多目标优化Pareto支配性的精度，提出一种基于决策空间变换的最近邻预测方法.在分析目标函数与决策分量相关性的基础上，提出属性变化趋势模型的构造方法，建立低计算成本的属性趋势代理模型.通过属性趋势模型引入决策空间到目标空间的映射知识，对多目标问题的决策空间进行变换，使决策空间的最近邻更有效反映目标空间的最近邻.选取具有不同相关系数特征的典型多目标优化问题，进行Pareto支配性预测的可对比实验，结果表明在新空间中运用最近邻方法可显著提高分类准确性.     

Bayesian threshold selection for extremal models using measures of surprise

Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold. However, in practice a suitable threshold is unknown and must be determined for each analysis. While there are many threshold selection methods for univariate extremes, there are relatively few that can be applied in the multivariate setting. In addition, there are only a few Bayesian-based methods, which are naturally attractive in the modelling of extremes due to data scarcity. The use of Bayesian measures of surprise to determine suitable thresholds for extreme value models is proposed. Such measures quantify the level of support for the proposed extremal model and threshold, without the need to specify any model alternatives. This approach is easily implemented for both univariate and multivariate extremes.     

Comprehensive Pareto Efficiency in robust counterpart optimization

In this paper, an innovative concept named Comprehensive Pareto Efficiency is introduced in the context of robust counterpart optimization, which consists of three sub-concepts: Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). Different algorithms are developed for computing robust solutions with respect to these three sub-concepts. As all sub-concepts are based on the Probability of Constraint Violation (PCV), formulations of PCV under different probability distributions are derived and an alternative way to calculate PCV is also presented. Numerical studies are drawn from two applications (production planning problem and orienteering problem), to demonstrate the Comprehensive Pareto Efficiency. The numerical results show that the Comprehensive Pareto Efficiency has important significance for practical applications in terms of the evaluation of the quality of robust solutions and the analysis of the difference between different robust counterparts, which provides a new perspective for robust counterpart optimization.     

Preference adjustable multi-objective NMPC: An unreachable prioritized point tracking method

This paper proposes a new preference adjustable multi-objective model predictive control (PA-MOMPC) law for constrained nonlinear systems. With this control law, a reasonable prioritized optimal solution can be directly derived without constructing the Pareto front by solving a minimal optimization problem, which is a novel development of recently proposed utopia tracking approaches by additionally considering objective preferences with more flexible terminal and stability constraints. The tracking point of the proposed PA-MOMPC law is represented by a parametric vector with the parameters adjustable on the basis of objective preferences. The main result of this paper is that the solution obtained through the proposed PA-MOMPC law is demonstrated to have two important properties. One is the inherent Pareto optimality, and the other is the priority consistency between the solution and the tuning parametric vector. This combination makes the objective priorities tuning process transparent and efficient. The proposed PA-MOMPC law is supported by feasibility analyses, proof of nominal stability, and a numerical case study.