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.     

On optimality and duality for multiple-objective optimization under generalized type I univexity

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established.     

Multiobjective evolutionary algorithm based on multimethod with dynamic resources allocation

In the last two decades, multiobjective optimization has become main stream and various multiobjective evolutionary algorithms (MOEAs) have been suggested in the field of evolutionary computing (EC) for solving hard combinatorial and continuous multiobjective optimization problems. Most MOEAs employ single evolutionary operators such as crossover, mutation and selection for population evolution. In this paper, we suggest a multiobjective evolutionary algorithm based on multimethods (MMTD) with dynamic resource allocation for coping with continuous multi-objective optimization problems (MOPs). The suggested algorithm employs two well known population based stochastic algorithms namely MOEA/D and NSGA-II as constituent algorithms for population evolution with a dynamic resource allocation scheme. We have examined the performance of the proposed MMTD on two different MOPs test suites: the widely used ZDT problems and the recently formulated test instances for the special session on MOEAs competition of the 2009 IEEE congress on evolutionary computation (CEC’09). Experimental results obtained by the suggested MMTD are more promising than those of some state-of-the-art MOEAs in terms of the inverted generational distance (IGD)-metric on most test problems.     

Multi-objective optimization algorithm for multi-page invoice order scheduling problem

针对多联票据订单调度问题进行研究,考虑最小化所有订单的最大完成时间、平均完成时间、最大延迟时间和平均延迟时间四个目标函数,提出一种多目标混合遗传算法。基于问题自身的特点提出完整解的构造算法,使用随机变动的权重实现多维多方向的搜索,设计了基于非主导性比较的局部搜索算法以寻找更多更好的非主导解,建立与更新全局非主导解集档案以保留最好的Pareto近似最优解。采用Pareto兼容的衡量参数,将该算法与两种对照算法进行了比较。大量算例的试验结果表明,该算法能够得到更接近于Pareto前沿且多样性分布更好的Pareto近似最优解集。     

Optimal design of dispersive tubular reactors at steady-state using optimal control theory

This paper studies the design of optimal temperature profiles for a class of exothermic, jacketed dispersive tubular reactors under steady-state conditions and subject to maximum temperature constraints. The studied class ranges from perfectly mixed continuous stirred tank reactors to plug flow reactors. The aim is to derive the Pareto optimal set of temperature profiles for conflicting conversion and energy costs, while extracting generic features from the obtained solutions. Hereto, a four step procedure which is based on a weighted sum of both costs and which combines indirect, analytical and direct, numerical optimal control techniques, is employed. The generic features are studied (i) along the Pareto set by varying the weights and (ii) along the reactor class by adapting the dispersion level.     

Multi-objective Phasor Measurement Unit Placement in Electric Power Networks: Integer Linear Programming Formulation

A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.