道路连续减速带对重载汽车平顺性影响

道路减速带是目前广泛使用的强制限速设施,对于减缓汽车的行驶速度、减少交通事故的发生有着良好的效果.但是,减速带产品种类繁多,参差不齐,关于不同限速道路上减速带的选择以及汽车通过减速带时的平顺性研究尚不多见.本文建立了道路连续减速带和三轴重型载货汽车模型,以车身垂向加速度和垂向轮胎力作为评价指标,分析了车速、减速带高度和宽度对汽车平顺性的影响.研究发现道路连续减速带的宽度与控制车速成正比,减速带高度与控制车速成反比.     

A new approach for online multiobjective optimization of mechatronic systems

We present a new concept for online multiobjective optimization and its application to the optimization of the operating point assignment for a doubly-fed linear motor. This problem leads to a time-dependent multiobjective optimization problem. In contrast to classical optimization where the aim is to find the (global) minimum of a single function, we want to simultaneously minimize k objective functions. The solution to this problem is given by the set of optimal compromises, the so-called Pareto set. In the case of the linear motor, there are two conflicting aims which both have to be maximized: the degree of efficiency and the inverter utilization factor. The objective functions depend on velocity, force and power, which can be modeled as time-dependent parameters. For a fixed point of time, the entire corresponding Pareto set can be computed by means of a recently developed set-oriented numerical method. An online computation of the time-dependent Pareto sets is not possible, because the computation itself is too complex. Therefore, we combine the computation of the Pareto set with numerical path following techniques. Under certain smoothness assumptions the set of Pareto points can be characterized as the set of zeros of a certain function. Here, path following allows to track the evolution of a given solution point through time.     

Different types of stability of vector integer optimization problem: General approach

The paper relates the stability of a vector (multiobjective) integer optimization problem to the stability of optimal and nonoptimal solutions of this problem. It is shown that the analysis of several types of stability of the problem of searching for Pareto optimal solutions can be reduced to the analysis of two sets consisting of points that stably belong and do not stably belong to the Pareto set. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 142–148, May–June 2008.     

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.     

Selection Based on the Pareto Nondomination Criterion for Controlling Code Growth in Genetic Programming

The rapid growth of program code is an important problem in genetic programming systems. In the present paper we investigate a selection scheme based on multiobjective optimization. Since we want to obtain accurate and small solutions, we reformulate this problem as multiobjective optimization. We show that selection based on the Pareto nondomination criterion reduces code growth and processing time without significant loss of solution accuracy.     

基于精英选择和个体迁移的多目标遗传算法

提出基于遗传算法求解多目标优化问题的方法,将多目标问题分解成多个单目标优化问题,用遗传算法分别在每个单目标种群中并行搜索.在进化过程中的每一代,采用精英选择和个体迁移策略加快多个目标的并行搜索,提出了控制Pareto最优解数量并保持个体多样性的有限精度法,同时还提出了多目标遗传算法的终止条件.数值实验说明所提出的算法能较快地找到一组分布广泛且均匀的Pareto最优解.     

采用遗传算法求解多跳分组无线网服务质量路由优化模型

采用多目标遗传算法来确定多跳无线网服务质量路由优化问题的Pareto最优解集。通过计算表明，多目标遗传算法能够在一次运行中搜索到优化问题的近似Pareto最优解集，这为决策者进行目标折衷决策提供了充分的依据，此算法是有效可行的。     

The normalized normal constraint method for generating the Pareto frontier

The authors recently proposed the normal constraint (NC) method for generating a set of evenly spaced solutions on a Pareto frontier – for multiobjective optimization problems. Since few methods offer this desirable characteristic, the new method can be of significant practical use in the choice of an optimal solution in a multiobjective setting. This papers specific contribution is two-fold. First, it presents a new formulation of the NC method that incorporates a critical linear mapping of the design objectives. This mapping has the desirable property that the resulting performance of the method is entirely independent of the design objectives scales. We address here the fact that scaling issues can pose formidable difficulties. Secondly, the notion of a Pareto filter is presented and an algorithm thereof is developed. As its name suggests, a Pareto filter is an algorithm that retains only the global Pareto points, given a set of points in objective space. As is explained in the paper, the Pareto filter is useful in the application of the NC and other methods. Numerical examples are provided.     

动态多目标优化的预测遗传算法

为了在动态环境中很好地跟踪最优解,考虑动态优化问题的特点,提出一种新的多目标预测遗传算法.首先对 Pareto 前沿面进行聚类以求得解集的质心;其次应用该质心与参考点描述 Pareto 前沿面;再次通过预测方法给出预测点集,使得算法在环境变化后能够有指导地增加种群多样性,以便快速跟踪最优解;最后应用标准动态测试问题进行算法测试,仿真分析结果表明所提出算法能适应动态环境,快速跟踪 Pareto 前沿面.     

基于智能体的多目标社会进化算法

提出了一种基于智能体的多目标社会进化算法用以求解多目标优化问题(multiobjective optimization problems,简称MOPs),通过多智能体进化的思想来完成Pareto 解集的寻优过程.该方法定义可信任度来表示智能体间的历史活动信息,并据此确定智能体的邻域、控制智能体间的行为.针对多目标问题的特点,设计了3 个进化算子分别体现适者生存、弱肉强食、多样性原则以及自学习的特性.同时采用擂台赛法则构造Pareto 解的存储种群.仿真实验结果表明,该算法能够较好地收敛到Pareto 最优解集上,并且具有良好的多样性.另外,通过对智能体局部邻域环境建立方式的分析结果表明引入“关系网模型”可有效提高算法的收敛速度,并能在一定程度上提高解的质量.     

An efficient multiobjective differential evolution algorithm for engineering design

Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints, a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions with good coverage and convergence to true Pareto-optimal fronts.     

Evolutionary multiobjective optimization using an outranking-based dominance generalization

One aspect that is often disregarded in the current research on evolutionary multiobjective optimization is the fact that the solution of a multiobjective optimization problem involves not only the search itself, but also a decision making process. Most current approaches concentrate on adapting an evolutionary algorithm to generate the Pareto frontier. In this work, we present a new idea to incorporate preferences into a multi-objective evolutionary algorithm (MOEA). We introduce a binary fuzzy preference relation that expresses the degree of truth of the predicate “x is at least as good as y”. On this basis, a strict preference relation with a reasonably high degree of credibility can be established on any population. An alternative x is not strictly outranked if and only if there does not exist an alternative y which is strictly preferred to x. It is easy to prove that the best solution is not strictly outranked. For validating our proposed approach, we used the non-dominated sorting genetic algorithm II (NSGA-II), but replacing Pareto dominance by the above non-outranked concept. So, we search for the non-strictly outranked frontier that is a subset of the Pareto frontier. In several instances of a nine-objective knapsack problem our proposal clearly outperforms the standard NSGA-II, achieving non-outranked solutions which are in an obviously privileged zone of the Pareto frontier.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

基于免疫应答原理的多目标优化免疫算法及其应用

基于免疫应答原理，合理地构建免疫算子及引入一种新的小生境技术, 提出一种 解决多目标优化问题的免疫算法. 在此算法中，将优化问题的可行解对应抗体及Pareto最优个体对应抗原，这种抗原存于抗原群中,并应用新的聚类算法不断更新抗原群中的抗原, 进而获大量的Pareto最优解, 这些解能很好地分布在Pareto面（此指由Pareto最优解构成）上. 理论证明了该算法能获Pareto最优解. 最后，将该文的算法与文献\[3\]的算法SPEA进行仿真比较, 获该算法的有效性, 此表明免疫算法解决多目标优化问题具有广阔的前景.     

Solving Multiobjective Optimization Problems Using an Artificial Immune System

In this paper, we propose an algorithm based on the clonal selection principle to solve multiobjective optimization problems (either constrained or unconstrained). The proposed approach uses Pareto dominance and feasibility to identify solutions that deserve to be cloned, and uses two types of mutation: uniform mutation is applied to the clones produced and non-uniform mutation is applied to the not so good antibodies (which are represented by binary strings that encode the decision variables of the problem to be solved). We also use a secondary (or external) population that stores the nondominated solutions found along the search process. Such secondary population constitutes the elitist mechanism of our approach and it allows it to move towards the true Pareto front of a problem over time. Our approach is compared with three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, three metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is a viable alternative to solve multiobjective optimization problems.     

基于分解和多策略变异的多目标差分进化算法*

差分进化是一种有效的优化技术,已成功用于多目标优化问题。但也存在Pareto最优集合的收敛慢和多样性差等问题。针对上述不足,本文提出了一种基于分解和多策略变异的多目标差分进化算法(MODE/DMSM)。该算法利用基于分解的方法将多目标优化问题分解为多个单目标优化问题;通过高效的非支配排序方法选择具有良好收敛性和多样性的解来指导差分进化过程;采用了多策略变异方法来平衡进化过程中收敛性和多样性。在ZDT和DTLZ的10个测试函数上的仿真结果表明,本文算法在Parato最优集合的收敛性和多样性优于其他六种代表性多目标优化算法。     

A new perspective on multiobjective optimization by enhanced normalized normal constraint method

In industrial applications, several objectives are often managed simultaneously (e.g., minimizing the cost and the weight of a mechanical structure satisfying some constraints). Although lots of optimization studies deal with only one objective, this approach is often not realistic for engineering optimization. Therefore, improvements in multiobjective optimization methods are required. This paper presents the formulation of a new utopia hyperplane that improves the proposal of the original normalized normal constraint method using two approaches: a redefinition of the anchor points and an exact linear transformation between the design objectives space and the normalized space. Both approaches always produce a normalized space with equal scales that improves the even distribution of the solutions over the Pareto frontier. Examples of the method proposed are presented related with mechanical engineering and structure design including a challenging non-convex Pareto frontier. Partially supported by FEDER DPI2005-07835, FEDER DPI2004-8383-C03-02 projects (MEC—Spain) and GV06/26 (Generalitat Valenciana)     

一种基于粒子群优化的多目标优化算法

论文提出了一种基于粒子群的多目标优化算法,该算法采用Pareto支配关系来更新粒子的个体最优值和局部最优值,用存储池保存搜索过程中发现的非支配解;采用聚类算法裁剪非支配解,以保持解的分布性能;采用动态惯性权重法来平衡粒子群对解空间的局部搜索和全局搜索,以提高算法的全局收敛性能。实验结果表明,论文算法是有效的,能有效的求解多种多目标优化问题。     

On some multiobjective optimization problems arising in biology

In this paper, we discuss modelling and solving some multiobjective optimization problems arising in biology. A class of comparison problems for string selection in molecular biology and a relocation problem in conservation biology are modelled as multiobjective optimization programmes. Some discussions about applications, solvability and different variants of the obtained models are given, as well. A crucial part of the study is based upon the Pareto optimization which refers to the Pareto solutions of multiobjective optimization problems. For such solution, improvement of some objective function can only be obtained at the expense of the deterioration of at least one other objective function.     

Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation

This paper presents an adaptive weighted sum (AWS) method for multiobjective optimization problems. The method extends the previously developed biobjective AWS method to problems with more than two objective functions. In the first phase, the usual weighted sum method is performed to approximate the Pareto surface quickly, and a mesh of Pareto front patches is identified. Each Pareto front patch is then refined by imposing additional equality constraints that connect the pseudonadir point and the expected Pareto optimal solutions on a piecewise planar hypersurface in the -dimensional objective space. It is demonstrated that the method produces a well-distributed Pareto front mesh for effective visualization, and that it finds solutions in nonconvex regions. Two numerical examples and a simple structural optimization problem are solved as case studies. Presented as paper AIAA-2004-4322 at the 10th AIAA-ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, August 30–September 1, 2004