Multiobjective optimization for crash safety design of vehicles using stepwise regression model

In automotive industry, structural optimization for crashworthiness criteria is of special importance. Due to the high nonlinearities, however, there exists substantial difficulty to obtain accurate continuum or discrete sensitivities. For this reason, metamodel or surrogate model methods have been extensively employed in vehicle design with industry interest. This paper presents a multiobjective optimization procedure for the vehicle design, where the weight, acceleration characteristics and toe-board intrusion are considered as the design objectives. The response surface method with linear and quadratic basis functions is employed to formulate these objectives, in which optimal Latin hypercube sampling and stepwise regression techniques are implemented. In this study, a nondominated sorting genetic algorithm is employed to search for Pareto solution to a full-scale vehicle design problem that undergoes both the full frontal and 40% offset-frontal crashes. The results demonstrate the capability and potential of this procedure in solving the crashworthiness design of vehicles.     

The impact of collinearity involving the intercept term on the numerical accuracy of regression

It is well known that multiple linear regression models with ill-conditioning can produce coefficient estimates with degraded numerical accuracy. This study examines the numerical accuracy of regression algorithms in the presence a particular type of ill-conditioning, that arising from collinear relationships that involve the intercept term and the independent variables. A benchmark data set is used to produce ill-conditioned data by introducing near linear relationships among the independent variables and the intercept term. The experiments reported here demonstrate that centering does not prevent a loss in numerical accuracy for this particular type of ill-conditioning. In addition, the ability of commonly used diagnostic checks to detect these problems is studied. As an example of the problems that arise from ignoring the relationships studied here we demonstrate that the regression procedures in two widely used statistical packages, SAS and SPSS-X, fail to detect this type of ill-conditioning and report highly inaccurate coefficient estimates.     

Shape decomposition by collinearity

The analysis of collinearity with semantic considerations in shape decomposition is presented. The method is based on a lot of heuristics satisfying human intuition about collinearity. Man-made objects which often contain many collinear lines are analyzed to verify this approach.     

取证过程的多目标控制

本文研究制订决策的取证问题,对这一问题构造了一个多目标最优控制模型,推导了求解模型的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ－Ｂｅｌｌｍａｎ方程,并讨论了多目标模型解与相应的加权单目标模型解之间的关系和多层取证问题。     

基于多目标优化的控制器设计方法

多目标优化方法对所用的目标函数和约束要进行分析和改进, 为了多个目标的同时实现和分析本文研究了一种新的基于组织型 P 系统的多目标优化算法来设计 PID 控制器. 控制器参数被编码后按照与膜结构相关的规则进化, 组织型 P 系统具有独特的动态膜结构, 整个参数群体被动态膜结构划分成几个子群体计算降低了计算复杂性. 仿真结果表明所提算法收敛快, 解的精度高, 而且在 Pareto 前沿上均匀分布, 所得的控制器具有令人满意的控制性能. 实验结果显示新算法适于研究不同性能指标和调节参数之间的关系, 可以用于设计和评估不同的控制器.     

摄影测量共线方程的单位四元数描述

为探讨四元数在摄影测量共线方程严密解算中的应用问题,从四元数的基本理论出发,详细推导以单位四元数矩阵表达的共线方程的严密线性化公式,该线性化公式无须对旋转矩阵进行微分。以单像后方交会和光束法平差为例采用模拟数据和实际数据实验。结果表明,推导的以四元数矩阵为基础的线性化共线方程具有形式简单、初值无关性和收敛速度快的优点。具有一定的实用价值。     

求解多目标问题的Memetic免疫优化算法

将基于Pareto支配关系的局部下山算子和差分算子引入免疫多目标优化算法之中,提出了一种求解多目标问题的Memetic免疫优化算法(Memetic immune algorithm for multiobjective optimization,简称MIAMO).该算法利用种群中抗体在决策空间上的位置关系设计了两种有效的启发式局部搜索策略,提高了免疫多目标优化算法的求解效率.仿真实验结果表明,MIAMO与其他4种有效的多目标优化算法相比,不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且算法的收敛速度与免疫多目标优化算法相比明显加快.     

Multiobjective evolutionary computation for supersonic wing-shapeoptimization

This paper discusses the design optimization of a wing for supersonic transport (SST) using a multiple-objective genetic algorithm (MOGA). Three objective functions are used to minimize the drag for supersonic cruise, the drag for transonic cruise, and the bending moment at the wing root for supersonic cruise. The wing shape is defined by 66 design variables. A Euler flow code is used to evaluate supersonic performance, and a potential flow code is used to evaluate transonic performance. To reduce the total computational time, flow calculations are parallelized on an NEC SX-4 computer using 32 processing elements. The detailed analysis of the resulting Pareto front suggests a renewed interest in the arrow wing planform for the supersonic wing     

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.     

Multiobjective cuckoo search for design optimization

Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.     

Multiobjective decisions analysis for engineering systems

Two decision analysis methodologies are developed and compared for the evaluation and selection of optimal engineering systems, the method of complete orders and the method of dichotomies. The problem is viewed as consisting of seeking to rank a discrete set of engineering alternatives in a decreasing order of attractiveness, as determined on the basis of their performance over a discrete set of criteria. The first methodology proceeds by successive dichotomies of the set of alternatives until the irreducible subset (core) of equally attractive alternatives is isolated, whereas the latter seeks complete (linear) orderings of the alternatives. Both methodologies are based on a probability impact-matrix that reflects the pair-wise comparison of the alternatives. The evaluation of this matrix makes use of the first and second statistical moments of each attribute, with respect to each one of the alternatives. The hypotheses are tested that each alternative consecutively is superior to all other alternatives. The alternatives are ranked according to the relative robustness of these hypotheses. The quality of the ranking is also assessed by the level of inductive entropy achieved. The method of complete orders proved in general to be superior to the method of dichotomies.     

Convergence Acceleration Operator for Multiobjective Optimization

A convergence acceleration operator (CAO) is described which enhances the search capability and the speed of convergence of the host multiobjective optimization algorithm. The operator acts directly in the objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). The suggested improved objective vectors are then mapped into the decision variable space and tested. This method improves upon prior work in a number of important respects, such as mapping technique and solution improvement. Further, the paper discusses implications for many-objective problems and studies the impact of the use of the CAO as the number of objectives increases. The CAO is incorporated with two leading MOEAs, the non-dominated sorting genetic algorithm and the strength Pareto evolutionary algorithm and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm while maintaining the desired distribution of solutions. It is shown that the operator is a transferable component that can be hybridized with any MOEA.      

Multiobjective trajectory optimization for electric trains

This paper develops a method for generating Pareto efficient trajectories that provide optimal tradeoffs between two conflicting attributes-the total energy consumed and the total time taken to complete each trajectory. Straightforward formulations of the multiobjective optimization problem in these attributes are difficult to solve because of certain nonlinearities in train models and certain constraints on train trajectories. A discrete reformulation is developed to circumvent these difficulties and produce computationally feasible algorithms. The results from the algorithms can be used to develop operating strategies for existing systems and to compare hardware alternatives in planning new systems. An illustration is included.     

区域水环境经济系统的多目标递阶规划

本文针对文献[1]提出的以水系水质规划为基础的多子区域多目标水环境经济规划问题,提出了它的相互作用式逐步折衷递阶优化解法,并以两个子区域和五个污水集中处理厂的系统为例进行计算机仿真,说明其有效性.     

两层多目标规划的罚函数法

研究了一类非线性两层多目标规划问题.在下层多目标规划问题的目标函数是严格凸函数、决策变量约束集是凸集的假设下,通过将两层多目标规划问题转化成一系列单层多目标规划问题,建立了两层多目标规划的罚函数理论,并进行了收敛性分析.从而丰富了两层多目标规划的理论,为解决实际中的两层多目标决策问题提供了有力的工具.     

Multiobjective cluster analysis for part family formations

This paper presents an efficient computerized method for forming group technology part families using a goal programming based multiobjective clustering analysis with a group technology classification and coding system.The success of group technology applications rests on the effective formation of part families and subsequent efficient retrieval of part family data for rationalization of design and manufacturing. Due to the magnitude of this task, it is necessary to use a computer. A mathematical model and computer program were developed to improve the efficiency of applying this method in practice. The proposed method was tested and proved using actual industrial data.     

A Genetic Algorithm for Multiobjective Robust Design

The goal of robust design is to develop stable products that exhibit minimum sensitivity to uncontrollable variations. The main drawback of many quality engineering approaches, including Taguchi's ideology, is that they cannot efficiently handle presence of several often conflicting objectives and constraints that occur in various design environments.Classical vector optimization and multiobjective genetic algorithms offer numerous techniques for simultaneous optimization of multiple responses, but they have not addressed the central quality control activities of tolerance design and parameter optimization. Due to their ability to search populations of candidate designs in parallel without assumptions of continuity, unimodality or convexity of underlying objectives, genetic algorithms are an especially viable tool for off-line quality control.In this paper we introduce a new methodology which integrates key concepts from diverse fields of robust design, multiobjective optimization and genetic algorithms. The genetic algorithm developed in this work applies natural genetic operators of reproduction, crossover and mutation to evolve populations of hyper-rectangular design regions while simultaneously reducing the sensitivity of the generated designs to uncontrollable variations. The improvement in quality of successive generations of designs is achieved by conducting orthogonal array experiments as to increase the average signal-to-noise ratio of a pool of candidate designs from one generation to the next.     

两层次多目标规划的优化算法

本文综合了多目标对偶理论与多目标包络面方法,提出了一种解决两层次多目标非线性(BLMOP)问题的新方法。在该方法中,首先求出下级多目标规划以参数形式表示的全部非劣解,在此基础上,用常规的多目标规划方法解决上级多目标决策问题,随后,上级将其优化结果传递给下级,不需要迭代可直接得到下级决策问题的解。文中详细地讨论了BLMOP问题的求解过程和原理,最后,用一个算例说明了本文方法的实施过程和算法的可行性。