模糊择近原则在多目标容差设计中的应用

利用模糊数学中的择近原则,以容差-成本模型为基础,通过引入模糊数学中的隶属度函数和贴近度原则,结合实验并设计方法提出了一种模糊容差稳健优化设计方法,较好地解决了多目标容差设计的全局最优问题.最后通过一个实例验证了该方法的合理、有效性.     

改进的NSGA-Ⅱ算法研究风力机叶片多目标优化

将一种采用精英控制策略和动态拥挤方法用于快速非支配排序遗传算法（NSGA-Ⅱ）,并应用到风力机叶片的优化研究中,获得了一种新颖的风力机叶片多目标优化设计方法．作为应用算例,以设计风速下的功率系数最大和叶片质量最小为优化目标,用该方法设计了5 MW大型风力机叶片．优化结果表明,此算法在处理风力机多目标优化问题取得了良好的效果,给出的是一个Pareto最优解集,而不是传统优化方法追求的单个最优解,为风力机多目标优化设计提供新的思路和通用的算法．     

多目标模糊优化设计

多目标优化设计的函数曲面复杂并且缺乏分析理论，这使得多目标优化中的统一权法带有更多的盲目性。为解决这一难题，贴近度方法被用来分析统一权法的模糊学实质，并为多目标优化加权处理提供一有效的方法。     

兼顾效率和成本的ARMA控制图多目标优化设计

ARMA控制图是一种有效的自相关过程质量监控方法,为了能够同时对ARMA控制图监控方案的效率和成本进行优化,本文分别研究了ARMA控制图的平均运行长度和质量成本的计算方法,并由此建立了ARMA控制图的多目标优化设计模型。采用NSGA-Ш智能优化算法,通过一个具体的算例对该模型的计算方法进行了说明,针对不同程度的过程偏移给出了多目标优化设计的非劣解解集。然后通过灵敏度分析的方法研究了模型中的主要设计参数对监控方案的效率和成本的影响程度。最后,通过与其它几种ARMA控制图优化设计方案的比较分析,说明了本文提出的设计方法的优势。     

Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation

In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consider the robustness of the selected Pareto optimal solution in relation to perturbations within weights of the objective functions. For this task we design an integrated approach that can be used in multi-objective discrete and continuous problems using a combination of Monte Carlo simulation and optimization. In the proposed method we introduce measures of robustness for Pareto optimal solutions. In this way we can compare them according to their robustness, introducing one more characteristic for the Pareto optimal solution quality. In addition, especially in multi-objective discrete problems, we can detect the most robust Pareto optimal solution among neighboring ones. A computational experiment is designed in order to illustrate the method and its advantages. It is noteworthy that the Augmented Weighted Tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems, due to the existence of unsupported Pareto optimal solutions.     

A New Pareto Optimal Solution in a Lagrange Decomposable Multi-Objective Optimization Problem

In this paper a committee decision-making process of a convex Lagrange decomposable multi-objective optimization problem, which has been decomposed into various subproblems, is studied. Each member of the committee controls only one subproblem and attempts to select the optimal solution of this subproblem most desirable to him, under the assumption that all the constraints of the total problem are satisfied. This procedure leads to a new solution concept of a Lagrange decomposable multi-objective optimization problem, called a preferred equilibrium set. A preferred equilibrium point of a problem, for a committee, may or may not be a Pareto optimal point of this problem. In some cases, a non-Pareto optimal preferred equilibrium point of a problem, for a committee, can be considered as a special type of Pareto optimal point of this problem. This fact leads to a generalization of the Pareto optimality concept in a problem.     

An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results.     

求解一种带有微分方程约束的条件变分问题的多目标最优化方法

Aiming at the conditional variational problem with the bi-objective functionals and the differential equational constraint in the optimal design of the electrostatic lenses, the conditional variational problem is transformed into multi-objective optimization problem by means of the spline function and the integral transformation. For solving the transformed problem, the analytic representation formula of the optimal solution about the original problem is obtained with regard to the voltage distribution and the electron trajectory. It will provide a new effective method for the design of the electrostatic lenses.     

Time-dependent discrete road network design with both tactical and strategic decisions

This paper aims to model and investigate the discrete urban road network design problem, using a multi-objective time-dependent decision-making approach. Given a base network made up with two-way links, candidate link expansion projects, and candidate link construction projects, the problem determines the optimal combination of one-way and two-way links, the optimal selection of capacity expansion projects, and the optimal lane allocations on two-way links over a dual time scale. The problem considers both the total travel time and the total CO emissions as the two objective function measures. The problem is modelled using a time-dependent approach that considers a planning horizon of multiple years and both morning and evening peaks. Under this approach, the model allows determining the sequence of link construction, the expansion projects over a predetermined planning horizon, the configuration of street orientations, and the lane allocations for morning and evening peaks in each year of the planning horizon. This model is formulated as a mixed-integer programming problem with mathematical equilibrium constraints. In this regard, two multi-objective metaheuristics, including a modified non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective B-cell algorithm, are proposed to solve the above-mentioned problem. Computational results for various test networks are also presented in this paper.     

Availability allocation and multi-objective optimization for parallel–series systems

Availability allocation is required when the manufacturer is obliged to allocate proper availability to various components in order to design an end product to meet specified requirements. This paper proposes a new multi-objective genetic algorithm, namely simulated annealing based multi-objective genetic algorithm (saMOGA), to resolve the availability allocation and optimization problems of a repairable system, specifically a parallel–series system. Compared with a general multi-objective genetic algorithm, the major feature of the saMOGA is that it can accept a poor solution with a small probability in order to enlarge the searching space and avoid the local optimum. The saMOGA aims to determine the optimal decision variables, i.e. failure rates, repair rates, and the number of components in each subsystem, according to multiple objectives, such as system availability, system cost and system net profit. The proposed saMOGA is compared with three other multi-objective genetic algorithms. Computational results showed that the proposed approach could provide higher solution quality and greater computing efficiency.     

Implementation of scatter search for multi-objective optimization: a comparative study

Interest in the design of efficient meta-heuristics for the application to combinatorial optimization problems is growing rapidly. The optimal design of water distribution networks is an important optimization problem which consists of finding the best way of conveying water from the sources to the users, thus satisfying their requirements. The efficient design of looped networks is a much more complex problem than the design of branched ones, but their greater reliability can compensate for the increase in cost when closing some loops. Mathematically, this is a non-linear optimization problem, constrained to a combinatorial space, since the diameters are discrete and it has a very large number of local solutions. Many works have dealt with the minimization of the cost of the network but few have considered their cost and reliability simultaneously. The aim of this paper is to evaluate the performance of an implementation of Scatter Search in a multi-objective formulation of this problem. Results obtained in three benchmark networks show that the method here proposed performs accurately well in comparison with other multi-objective approaches also implemented.     

Multi-level optimization for multi-objective problems

A multi-level solution method is presented for multi-objective optimization of large-scale systems associated with the hierarchical structure of decision-making. The method, consisting of a multi-level problem formulation and an interactive algorithm, has distinct advantages in handling the difficulties which are often experienced in engineering. The method is illustrated by its application to an optimal design of a processing system.     

Robustness of mechanical systems against uncertainties

In this paper, one can propose a method which takes into account the propagation of uncertainties in the finite element models in a multi-objective optimization procedure. This method is based on the coupling of stochastic response surface method (SRSM) and a genetic algorithm provided with a new robustness criterion. The SRSM is based on the use of stochastic finite element method (SFEM) via the use of the polynomial chaos expansion (PC). Thus, one can avoid the use of Monte Carlo simulation (MCS) whose costs become prohibitive in the optimization problems, especially when the finite element models are large and have a considerable number of design parameters.The objective of this study is on one hand to quantify efficiently the effects of these uncertainties on the responses variability or the cost functions which one wishes to optimize and on the other hand, to calculate solutions which are both optimal and robust with respect to the uncertainties of design parameters.In order to study the propagation of input uncertainties on the mechanical structure responses and the robust multi-objective optimization with respect to these uncertainty, two numerical examples were simulated. The results which relate to the quantification of the uncertainty effects on the responses variability were compared with those obtained by the reference method (REF) using MCS and with those of the deterministic response surfaces methodology (RSM).In the same way, the robust multi-objective optimization results resulting from the SRSM method were compared with those obtained by the direct optimization considered as reference (REF) and with RSM methodology.The SRSM method application to the response variability study and the robust multi-objective optimization gave convincing results.     

基于可信性理论的均值-熵-偏度投资组合模型及其算法求解

本文考虑到证券市场的投资者往往面临着随机和模糊两种不确定性的情形,在模糊随机环境下把证券的收益率视作三角模糊变量,在可信性理论基础上建立了带融资约束条件的均值-熵-偏度三目标投资组合决策模型,拓展了基于可信性理论的投资组合决策模型的研究内容,同时通过对约束条件处理方法,外部档案维护方法等关键算子的改良,提出了一种新的约束多目标粒子群算法。本文运用该算法对模型进行求解,把得到的最优解与传统的多目标粒子群算法得到的最优解进行对比,结果表明新算法得到的最优解的质量会显著地优于传统的多目标粒子群算法的最优解,从而验证了算法的有效性和准确性。该算法可以在三维空间中得到一个分布性和逼近性较好的Pareto最优曲面,满足投资者对不同目标的差异需求,为投资者提供合理的投资组合决策方案。     

基于遗传算法的割缝衬管防砂多目标优化

割缝衬管防砂是油田重要的防砂方式之一,过去的研究往往专注于一个目标来设计割缝衬管参数,从而在参数设计上不能使多个参数在整体上达到最优.基于遗传算法中的gamultiobj多目标优化算法,以衬管使用寿命、地层流动阻力、产能和衬管强度为目标,建立了割缝衬管防砂优化设计模型,得出了高产能,长使用寿命,低流动阻力的割缝参数防砂的最优组合.结果表明,制定多目标适应性分析,建立评价模型,在给定的取值范围内得到的工艺参数,该技术有助于优选和优化调整防砂方法,提高防砂成功率,增强油田寿命和降低开采成本.     

Time-cost trade-off via optimal control theory in Markov PERT networks

We develop a new analytical model for the time-cost trade-off problem via optimal control theory in Markov PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. Then, we construct a multi-objective optimal control problem, in which the first objective is the minimization of the total direct costs of the project, in which the direct cost of each activity is a non-decreasing function of the resources allocated to it, the second objective is the minimization of the mean of project completion time and the third objective is the minimization of the variance of project completion time. Finally, two multi-objective decision techniques, viz, goal attainment and goal programming are applied to solve this multi-objective optimal control problem and obtain the optimal resources allocated to the activities or the control vector of the problem     

A numerical method for nonconvex multi-objective optimal control problems

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.     

含定性因子的二阶Scheff′e模型多目标最优设计北大核心

在实际的很多情形中,混料试验都具有多个目标,且响应变量不仅受到各分量的影响,还会受到其他定性因子变量的影响.文中基于一类含定性因子的混料模型,通过求解效率和极值得到多目标最优设计,并证明了该设计满足相应组合最优性.实例证明,该方法同样适用于3个或更多目标优化设计问题.     

Multiphase flow modeling and optimization for online wash systems of gas turbines

Compressor blade fouling in gas turbines could lead to significant loss in power and efficiency. Online wash systems are used to remove fouling without having to shut down the gas turbine. Hence, the design of efficient online wash systems could lead to significant recovery of performance. The present study aims at developing a generalized numerical approach for the optimization of online wash systems for gas turbines. The procedure utilizes a Lagrangian particle-tracking multiphase flow model combined with constrained multi-objective optimization to develop design charts for selecting the optimal nozzle diameter, location, mass flow rate and half-cone angle. The developed approach is used to optimize the design of the online wash system for the General Electric MS5002 gas turbine model. Comparisons and differences between the optimized design and the existing design are highlighted and presented.