An Overview of Optimization Formulations for Multiresponse Surface Problems

Many industrial applications involve more than one quality characteristic. For example, in robust parameter design, the quality characteristics include the process mean and process variance. Such applications lead to multiresponse surface problems in which it is necessary to determine optimal operating conditions according to some specified optimization criterion involving the quality characteristics. The purpose of this article is to address this problem from a multiobjective decision‐making framework. The foremost approaches in multiresponse optimization are categorized and integrated. Guidelines are presented to help select appropriate formulations. Moreover, the applicability and computational aspects of the methods in various decision‐making contexts are discussed. Numerical examples are also provided. Copyright © 2012 John Wiley & Sons, Ltd.     

矿物质粉体对砂浆及混凝土Cl-渗透性的影响

研究了不同水胶比、不同矿物质粉体掺量的砂浆和混凝土，经标准养护至56天、90天时的导电量。在相同水胶比和相同矿物质粉体掺量下，混凝土的导电量远低于砂浆的导电量。含矿物质粉体的砂浆及混凝土的导电量均低于基准砂浆及混凝土的导电量。导电量随水胶比的降低而降低，也随龄期的增长而降低。     

水库优化调度的Pareto强度值SCE-UA算法

提出求解水库优化调度问题的Pareto强度值SCE-UA算法,该方法将水库优化调度的约束优化问题转换成两个目标函数的无约束优化问题,一个为原问题的目标函数,另一个为违反约束条件的程度函数;对上述两个目标函数组成的向量个体,利用Pareto 优于关系和个体Pareto 强度值概念,实现个体的优劣比较和群体的优劣排序,在此基础上使用 SCE-UA算法求解。这种算法不需要人工处理罚函数,具有较强的通用性、稳定性及更好的搜索性能。     

基于正交试验的枕型空气衬垫优选方法

目的 基于正交试验的方法,探究枕型空气衬垫的规格、初始充气压强、温度、压缩速率在准静态压缩试验下对其缓冲性能影响的主次关系,得到一组使衬垫缓冲性能优良稳定的试验变量和一种枕型空气衬垫的优选方法.方法 采用正交试验的方法设计L9=(34)的正交试验,以枕型空气衬垫为研究对象进行准静态压缩试验,将试验结果归纳整理并进行极差分析和综合优选,判断所研究因素对枕型空气衬垫缓冲性能影响的主次关系,综合优选缓冲性能最优的枕型空气衬垫.结果 通过极差分析,得到了影响枕型空气衬垫缓冲性能的主次因素,由主到次依次为枕型空气衬垫规格、初始充气压强、温度、压缩速率,继而结合试验的易操作性综合优选了枕型空气衬垫的规格为100 mm×150 mm,初始充气压强为5 kPa,温度为30℃,压缩速率为100 mm/min,确定了一组使衬垫缓冲性能优良稳定的试验因素.结论 采用正交试验方法综合优选缓冲性能最优的枕型空气衬垫这一方法是可行的,结果也明确了4个试验变量对枕型空气衬垫缓冲性能影响的主次关系,这种思路能够为后续类似缓冲包装试验研究设计提供参考.     

冲裁模凸、凹模零件的优化设计

分析了冲裁模凸、凹模零件传统设计存在的问题,以现代企业实际需求为出发点,引入汽车企业的钢板模设计标准,从冲裁刃口尺寸计算、外形尺寸设计、材料选用等方面陈述了优化设计的思路,对加快模具开发周期,降低模具制造成本,起到十分重要的作用。     

基于Pareto最优解的零件制作方向优化研究

分析了快速成型工艺中零件制作方向对制件表面质量、所需支撑面积和零件制造时间的影响,分别建立了它们的优化数学模型。采用了基于Pareto最优解的多目标优化遗传算法NSGA-II进行优化计算,通过与单目标优化方法求得最优结果的对比,表明用多目标优化方法进行零件制作方向的优化计算,不仅可以求出比单目标方法更优的解,而且通过一次优化计算就可得到多个较优的零件制作方向。     

Robust multiattribute decision making under risk and uncertainty in engineering design

In this article, the problem of choosing from a set of design alternatives based upon multiple, conflicting, and uncertain criteria is investigated. The problem of selection over multiple attributes becomes harder when risky alternatives exist. The overlap measure method developed in this article models two sources of uncertainties—imprecise or risky attribute values provided to the decision maker and inabilities of the decision-maker to specify an exact desirable attribute value. Effects of these uncertainties are mitigated using the overlap measure metric. A subroutine to this method, called the robust alternative selection method, ensures that the winning alternative is insensitive to changes in the relative importance of the different design attributes. The overlap measure method can be used to model and handle various sources of uncertainties and can be applied to any number of multiattribute decision-making methods. In this article, it is applied to the hypothetical equivalents and inequivalents method, which is a multiattribute selection method under certainty.     

Aggregate Objective Functions and Pareto Frontiers: Required Relationships and Practical Implications

This paper addresses the problem of capturing Pareto optimal points on non-convex Pareto frontiers, which are encountered in nonlinear multiobjective optimization problems in computational engineering design optimization. The emphasis is on the choice of the aggregate objective function (AOF) of the objectives that is employed to capture Pareto optimal points. A fundamental property of the aggregate objective function, the admissibility property, is developed and its equivalence to the coordinatewise increasing property is established. Necessary and sufficient conditions for such an admissible aggregate objective function to capture Pareto optimal points are derived. Numerical examples illustrate these conditions in the biobjective case. This paper demonstrates in general terms the limitation of the popular weighted-sum AOF approach, which captures only convex Pareto frontiers, and helps us understand why some commonly used AOFs cannot capture desirable Pareto optimal points, and how to avoid this situation in practice. Since nearly all applications of optimization in engineering design involve the formation of AOFs, this paper is of direct theoretical and practical usefulness.     

自我框架对即时、延时决策的影响

目的拓展自我框架的相关研究,重点讨论在即时、延迟水平下,自我框架对风险决策的影响。方法以整群抽样的方式,抽取160名大学男生,随机分为即时决策组与延时决策组,采用亚洲疾病问题改编的自我框架问卷进行评测。结果自我框架对风险决策的影响部分显著,在即时决策组,自我框架情绪语气越积极,被试越容易选择确定性方案(χ2=4.17,P<0.05);当自我框架确定方案比风险方案情绪语气更积极,被试偏好确定性方案(χ2=6.72,P<0.01)。在延时决策组,自我框架对决策无显著影响。结论不同延迟水平下,自我框架对风险决策会产生不同的影响。     

Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation

Reliability-based and risk-informed design, operation, maintenance and regulation lead to multiobjective (multicriteria) optimization problems. In this context, the Pareto Front and Set found in a multiobjective optimality search provide a family of solutions among which the decision maker has to look for the best choice according to his or her preferences. Efficient visualization techniques for Pareto Front and Set analyses are needed for helping decision makers in the selection task.In this paper, we consider the multiobjective optimization of system redundancy allocation and use the recently introduced Level Diagrams technique for graphically representing the resulting Pareto Front and Set. Each objective and decision variable is represented on separate diagrams where the points of the Pareto Front and Set are positioned according to their proximity to ideally optimal points, as measured by a metric of normalized objective values. All diagrams are synchronized across all objectives and decision variables. On the basis of the analysis of the Level Diagrams, we introduce a procedure for reducing the number of solutions in the Pareto Front; from the reduced set of solutions, the decision maker can more easily identify his or her preferred solution.     

Balancing the Subjective and Objective Weights for Correlated Multiresponse Optimization

Desirability function approach is very popular for multiresponse optimization problems. However, the approach ignores the correlations among multiple responses and does not consider how to reasonably determine the relative weights of multiple responses. In this paper, an integrative desirability function approach is proposed to simultaneously consider the correlations among the responses and the weight determination method. For the proposed approach, the root mean square error performance is regarded as a new response, and then the seemingly unrelated regression estimation is utilized to fit the models. Through balancing the subjective and objective information, the proposed approach can be used to make more reasonable decisions for correlated multiresponse optimization. Two examples are employed to validate the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

信息系统安全方案的多属性决策方法

为解决信息系统安全建设中信息安全方案的选择问题,综合分析信息安全方案对安全等级保护要求的符合程度、信息安全方案的采购成本、运行维护费用和信息安全方案对抗风险的效能等多种因素和指标,并根据这些因素对信息安全方案选择的影响,提出一种多属性决策方法。通过信息安全方案对抗风险的效能指数计算、信息安全方案各影响因素的权重赋值和信息安全方案综合指数的计算,依据综合指数对信息安全方案进行择优排序,实现对信息安全方案的恰当选择。对于符合基本条件（满足安全等级保护要求、成本在限制范围内、对抗风险达到要求等）而难以取舍的几个备选方案,该选择方法是合适和简捷的。     

A Pareto firefly algorithm for multi-objective disassembly line balancing problems with hazard evaluation

The safety hazards existing in the process of disassembling waste products pose potential harms to the physical and mental health of the workers. In this article, these hazards involved in the disassembly operations are evaluated and taken into consideration in a disassembly line balancing problem. A multi-objective mathematical model is constructed to minimise the number of workstations, maximise the smoothing rate and minimise the average maximum hazard involved in the disassembly line. Subsequently, a Pareto firefly algorithm is proposed to solve the problem. The random key encoding method based on the smallest position rule is used to adapt the firefly algorithm to tackle the discrete optimisation problem of the disassembly line balancing. To avoid the search being trapped in a local optimum, a random perturbation strategy based on a swap operation is performed on the non-inferior solutions. The validity of the proposed algorithm is tested by comparing with two other algorithms in the existing literature using a 25-task phone disassembly case. Finally, the proposed algorithm is applied to solve a refrigerator disassembly line problem based on the field investigation and a comparison of the proposed Pareto firefly algorithm with another multi-objective firefly algorithm in the existing literature is performed to further identify the superior performance of the proposed Pareto firefly algorithm, and eight Pareto optimal solutions are obtained for decision makers to make a decision.     

Response Surface Modeling and Optimization in Multiresponse Experiments Using Seemingly Unrelated Regressions

Response surface methodology (RSM) is widely used for optimizing manufacturing processes and product designs. Most applications of RSM involve several response variables. In a typical RSM study, the experimenter will build an empirical model such as the second-order model to each response and use these models to determine settings on the design variables that produce optimal or at least acceptable values for the responses. In most multiple-response RSM problems, the experimenter fits a model to each response using ordinary least squares (OLS). This article illustrates another estimation technique useful in multiple-response RSM problems, seemingly unrelated regressions (SUR). This technique can be very useful when response variables in a multiple-response RSM problem are correlated. Essentially, SUR produces more precise estimates of the model parameters than OLS when responses are correlated. This improved precision of estimation can lead to a more precise estimate of the optimum operating conditions on the process.     

Multiple Response Optimization for Higher Dimensions in Factors and Responses

When optimizing a product or process with multiple responses, a two‐stage Pareto front approach is a useful strategy to evaluate and balance trade‐offs between different estimated responses to seek optimum input locations for achieving the best outcomes. After objectively eliminating non‐contenders in the first stage by looking for a Pareto front of superior solutions, graphical tools can be used to identify a final solution in the second subjective stage to compare options and match with user priorities. Until now, there have been limitations on the number of response variables and input factors that could effectively be visualized with existing graphical summaries. We present novel graphical tools that can be more easily scaled to higher dimensions, in both the input and response spaces, to facilitate informed decision making when simultaneously optimizing multiple responses. A key aspect of these graphics is that the potential solutions can be flexibly sorted to investigate specific queries, and that multiple aspects of the solutions can be simultaneously considered. Recommendations are made about how to evaluate the impact of the uncertainty associated with the estimated response surfaces on decision making with higher dimensions. Copyright © 2016 John Wiley & Sons, Ltd.     

基于供应链金融的银行决策分析

根据需求模型,建立了包含银行在内的供应链决策模型,研究分散决策模型下的收益问题,分别得到供应链各个参与者的期望收益,并通过数值仿真,得到银行在供应链中产生的影响。从供应链金融的角度出发,研究零售商订购量、制造商批发价格、银行利率的关系。并利用Stackelberg博弈的理论,以银行为主导者,制造商和零售商为跟随者,求出均衡最优解。研究发现当市场需求较小时,三者收益函数趋势一致;当市场需求较大时,银行利率对零售商订购量没有影响并且银行的收益最后逐渐平稳达到一个固定值。     

A MULTIOBJECTIVE INTERACTIVE SEQUENTIAL HYBRID OPTIMIZATION TECHNIQUE FOR DESIGN DECISION MAKING

The paper proposes an interactive method for obtaining a solution to a multiple objective design decision making problem. The focus is on generating Pareto solutions including those that are in the non-convex region, and are desirable to obtain in an engineering design context. After the generation of a small subset of the Pareto solutions, the designer's feedback is elicited in order to eliminate part of the subset. The process is repeated until il iteratively narrows down the Pareto solution set to a size small enough so that the designer is able to easily select a final solution. The advantage of this approach is that the designer can view a few sample points from the Pareto set before zooming into the region preferred and without expending computation time in generating a complete Pareto set. The process has been demonstrated with the help of an example, the design of a fleet of ships, that has mixed-discrete variables and hence a genetic algorithm is used as the optimizer.     

A Modeling Approach to Maintenance Decisions Using Statistical Quality Control and Optimization

Maintenance concerns impact systems in every industry and effective maintenance policies are important tools. We present a methodology for maintenance decision making for deteriorating systems under conditions of uncertainty that integrates statistical quality control (SQC) and partially observable Markov decision processes (POMDPs). We use simulation to develop realistic maintenance policies for real‐world environments. Specifically, we use SQC techniques to sample and represent real‐world systems. These techniques help define the observation distributions and structure for a POMDP. We propose a simulation methodology for integrating SQC and POMDPs in order to develop and valuate optimal maintenance policies as a function of process characteristics, system operating and maintenance costs. A two‐state machine replacement problem is used as an example of how the method can be applied. A simulation program developed using Visual Basic for Excel yields results on the optimal probability threshold and on the accuracy of the decisions as a function of the initial belief about the condition of the machine. This work lays a foundation for future research that will help bring maintenance decision models into practice. Copyright © 2005 John Wiley & Sons, Ltd.     

Microstructural Analysis and Multiresponse Optimization During ECM of Inconel 825 Using Hybrid Approach

In the current study, electrochemical machining of Inconel 825, a Ni-based super alloy, was carried out using tungsten as a tool electrode material and NaCl as electrolyte. The present investigation attaches particular emphasis on explaining the mechanism of material removal of Ni-based super alloys in the ECM process. The influence of various ECM parameters such as voltage (V), concentration (C), and tool feed (F) has been investigated on the evolution of the surface morphology of Inconel 825 after ECM. Different performance measures in ECM such as material removal rate (MRR), surface roughness (SR), and radial overcut (ROC) have been measured. Grey relational analysis that uses grey relational grade as performance index has been adopted to simultaneously optimize multiple performance characteristics and determine optimal combination of ECM parameters. Moreover, principal component analysis is utilized to determine the weighting values corresponding to various output responses so that their relative importance can be adequately expressed. Optimal condition was found to be V = 16 V, C = 45 g/L, and F = 0.3 mm/min. Confirmation test was further performed to authenticate the approach applied for determining the optimal conditions that resulted in MRR of 20.867 mm³/min, SR of 0.156 µm, and ROC of 0.0697 mm, which were superior to those corresponding to all previous experimental runs.