动力吸振器的多目标优化和多属性决策研究

在结构振动控制中,为了最大限度发挥吸振器的耗能减振作用.需要寻找吸振器的最优参数,即最优频率比、最优阻尼比和最优质量比,使得结构在不同的频率激励下获得最好的减振效果.本文将基于进化算法的多目标优化技术与多属性决策方法联合运用,针对主系统存在阻尼的减振系统,研究了动力吸振器的优化和决策同题.对于多目标优化问题,采用改进的非支配解排序的多目标进化算法(NSGA Ⅱ),求出Pareto最优解,由这些Pareto最优解构成决策矩阵,使用客观赋权的信息熵方法对最优解的属性进行权值计算.然后用逼近理想解的排序方法(TOPSIS)进行多属性决策(MADM)研究,对Pareto最优解给出排序.文中给出了4个设计参数、3个目标函数的动力吸振器优化设计算例.     

基于MOABCO的多目标测试用例优先级排序

为了提高回归测试的效率,提出了一种基于多目标人工蜂群优化(Multi-Objective Artificial Bee Colony Optimization, MOABCO)算法的多目标测试用例优先级排序(Multi-Objective Test Case Prioritization, MOTCP)方法.针对标准多目标人工蜂群(Multi-Objective Artificial Bee Colony, MOABC)算法容易陷入局部最优解的问题,将差分变异策略融入到新蜜源更新阶段,且基于信息熵改进新蜜源选择方法,以避免算法陷入局部最优并增强了全局搜索能力;然后,将代码覆盖率和测试用例有效执行时间作为优化目标,并用MOABCO算法求Pareto最优解集,以解决MOTCP问题.实验结果表明, MOABCO算法求得的Pareto最优解集在逼近性和分布均匀性上均优于MOABC算法;在解决MOTCP问题上,相对于NSGA-II算法具有更高的收敛速度和更高的缺陷检测率.     

基于差异演化算法和多属性决策的机电系统可靠性多目标优化设计

针对机电系统可靠性设计问题,以可靠性和费用(或体积等)最优为目标建立可靠性设计的多目标优化模型．提出了自适应多目标差异演化算法,该算法提出了自适应缩放因子和混沌交叉率,采用改进的快速排序方法构造Pareto最优解,采用NSGA-II的拥挤操作对档案文件进行消减．采用自适应多目标差异演化算法获得多目标问题的Pareto最优解,利用TOPSIS方法对Pareto最优解进行多属性决策．实际工程结果表明：自适应多目标差异演化算法调节参数更少,且求得的Pareto最优解分布均匀;采用基于TOPSIS的多属性决策方法得到的结果合理可行．     

带调整时间的多目标流水车间调度的优化算法

为高效地求解带调整时间的多目标流水车间调度问题,提出了一种多目标混合遗传算法,此算法依据基于Pareto优于关系的个体排序数和密度值计算适应度,保持解的多样性,并采用非劣解并行局部搜索策略,提高算法的搜索效率.此外,引入精英策略保证算法的收敛性,在进化过程中通过淘汰掉个别最差个体,进一步加快解的收敛速度.仿真结果表明,新算法能够有效地解决带调整时间的多目标流水车间调度问题.     

平流层飞艇的多目标优化与决策

该文建立了以平流层飞艇阻力最小、自重最轻、极限承载力最大及刚度最大为优化目标的多目标优化模型;采用强度Pareto进化算法(SPEA)进行了多目标优化设计;基于优化所得的Pareto解集,采用基于信噪比的决策方法选择满足实际需要的最终方案。结果表明:采用的SPEA算法是合理有效的,可以得到非劣解分布较均匀的Pareto曲面;通过基于信噪比的决策方法,可从非劣解集中获得满足实际要求的最稳健设计方案。     

基于SPEA2算法的泊位调度多目标优化

为获得使集装箱码头综合利益最大的泊位调度方案,建立了以船舶平均在港时间、码头生产成本和安全质量为目标的多目标优化模型;采用改进的强度Pareto进化算法(SPEA2)进行求解,基本操作中,可行解用三层染色体结构表示,改进的两点交叉算子和基于领域搜索的变异算子可避免出现不可行解,同时给出了靠泊顺序推迟最小的Pareto最优解选择策略。某集装箱码头的试验算例表明,文中提出的优化方法不仅能获得较优的满意解,同时收敛速度较快,可作为集装箱码头泊位调度的有效手段。     

用于约束多目标优化问题的改进蚁群遗传算法

针对多目标蚁群遗传算法(MOAGA)解集边界分布不均的问题,提出改进算法,解决连续空间中带约束条件多目标优化问题.改进算法在基本MOAGA算法的基础上,在选择中引入一定比例的边界决策、单目标最优决策,并提高边界决策的交叉率.实验证明,改进算法解决了基本算法解集分布边界疏中间密的问题,并且能更快的获得散布性较好的Pareto最优解集.     

考虑决策者风险偏好的微电网多目标区间优化

为使包含可再生能源在内的微电网的发电成本和气体污染物排放量最小，首先，建立了日前24小时多目标区间优化模型，同时引入区间可能度以处理不确定性变量，并转换该模型以满足决策者的风险偏好。其次，根据模型特点，设计解的初始化和修正元启发式策略，并提出一种基于模糊隶属度和切比雪夫函数混合分解的多目标进化算法MOEA/HD求解该模型。最后，通过算例仿真，验证了与其他算法相比，MOEA/HD算法效率更高，能得到质量更好、范围更广、分布更均匀的非劣解集。     

采用Pareto人工鱼群算法的结构健康监测传感器位置多目标优化EI北大核心CSCD

发展基于Pareto多目标人工鱼群算法(Multi⁃Objective Artificial Fish Swarm Algorithm,MO⁃AFSA),解决结构健康监测中传感器位置多目标优化的问题。构建与观测模态线性独立性、结构损伤灵敏度和损伤信息冗余性有关的传感器位置多目标优化目标函数;改进人工鱼群算法的追尾和觅食行为,并引入外部档案集以处理寻优过程中的互不支配解,结合Pareto概念选取与理想点欧式距离最近的Pareto解为最优解;以三层平面钢框架结构为数值算例,用基于Pareto人工鱼群算法求解传感器位置多目标优化方案,并进行结构损伤识别。研究结果表明:用所提方法得到的传感器测点在结构中均匀分布,获取的结构损伤信息更为全面,冗余性低,振型独立性好,能够较精确地识别损伤位置和损伤程度,并且抗噪性能好。     

考虑准备时间的多目标混合流水车间调度

本文研究了一个带有不可预期发生且准备时间顺序相关的混合流水车间调度问题,以最小化制造期和总拖期为多目标进行Pareto求解。首先建立了一个混合整数线性规划模型,然后提出了一种NEH-Pareto档案模拟退火(NEH-pareto archive simulated annealing,NEH-PASA)融合算法,算法采用一种改进的NEH算法产生高质量的初始解,设计了一种基于Pareto最优的混合扰动策略生成邻域解,并引入一种Pareto搜索机制以获取Pareto解集。最后通过计算实验,验证了算法的优越性。     

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

Optimal reservoir flood operation using a decomposition-based multi-objective evolutionary algorithm

Reservoir flood control operation (RFCO) is a challenging optimization problem with interdependent decision variables and multiple conflicting criteria. By considering safety both upstream and downstream of the dam, a multi-objective optimization model is built for RFCO. To solve this problem, a multi-objective optimizer, the multi-objective evolutionary algorithm based on decomposition–differential evolution (MOEA/D-DE), is developed by introducing a differential evolution-inspired recombination into the algorithmic framework of the decomposition-based multi-objective optimization algorithm, which has been proven to be effective for solving complex multi-objective optimization problems. Experimental results on four typical floods at the Ankang reservoir illustrated that the suggested algorithm outperforms or performs as well as the comparison algorithms. It can significantly reduce the flood peak and also guarantee the dam’s safety.     

Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods

Different constraint handling techniques have been used with multi-objective evolutionary algorithms (MOEA) to solve constrained multi-objective optimization problems. It is impossible for a single constraint handling technique to outperform all other constraint handling techniques always on every problem irrespective of the exhaustiveness of the parameter tuning. To overcome this selection problem, an ensemble of constraint handling methods (ECHM) is used to tackle constrained multi-objective optimization problems. The ECHM is integrated with a multi-objective differential evolution (MODE) algorithm. The performance is compared between the ECHM and the same single constraint handling methods using the same MODE (using codes available from http://www3.ntu.edu.sg/home/EPNSugan/index.htm). The results show that ECHM overall outperforms the single constraint handling methods.     

An entropy-based three-stage approach for multi-objective system reliability optimization considering uncertainty

This article presents a three-stage approach for solving multi-objective system reliability optimization problems considering uncertainty. The reliability of each component is considered in the formulation as a component reliability estimate in the form of an interval value and discrete values. Component reliability may vary owing to variations in the usage scenarios. Uncertainty is described by defining a set of usage scenarios. To address this problem, an entropy-based approach to the redundancy allocation problem is proposed in this study to identify the deterministic reliability of each component. In the second stage, a multi-objective evolutionary algorithm (MOEA) is applied to produce a Pareto-optimal solution set. A hybrid algorithm based on k-means and silhouettes is performed to select representative solutions in the third stage. Finally, a numerical example is presented to illustrate the performance of the proposed approach.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

Highly reliable optimal solutions to multi-objective problems and their evolution by means of worst-case analysis

In the current article, high reliability in the presence of uncertainty is of interest. Therefore, no violation of constraints by any solution, although uncertainty exists, is mandatory. The article studies uncertainties in which the boundaries of uncertainty are known. To allow a high reliability, the notion of worst-violation set is introduced. Moreover, two possible measures to assess the extent of the violation of the constraints by a solution, which is subjected to uncertainty, are suggested. One of these measures is then introduced into a multi-objective evolutionary algorithm (MOEA) in order to search for optimal reliable solutions. It is shown that the approach applies a search towards solutions with optimal performances while taking into account high reliability. The suggested approach is the only one available so far (to the authors’ best knowledge), which treats reliability through evolutionary multi-objective search, while not assuming any probability distribution of the uncertainty.     

Optimum plate-fin heat sinks by using a multi-objective evolutionary algorithm

This article demonstrates the practical applications of a multi-objective evolutionary algorithm (MOEA) namely population-based incremental learning (PBIL) for an automated shape optimization of plate-fin heat sinks. The computational procedure of multi-objective PBIL is detailed. The design problem is posed to find heat sink shapes which minimize the junction temperature and fan pumping power while meeting predefined constraints. Three sets of shape design variables used in this study are defined as: vertical straight fins with fin height variation, oblique straight fins with steady fin heights, and oblique straight fins with fin height variation. The optimum results obtained from using the various sets of design variables are illustrated and compared. It can be said that, with this sophisticated design system, efficient and effective design of plate-fin heat sinks is achievable and the best design variables set is the oblique straight fins with fin height variation.     

一种快速构造非支配集的方法--擂台法则

多目标进化算法是用来解决多目标优化问题的,为了提高多目标算法的效率,提出了一种快速构造非支配集的方法——擂台法则。它的时间耗费要低于Deb和Jensen提出的构造非支配集的方法。在实验中将擂台法则同Deb和Jensen的方法进行了比较,最后实验结果证明前者在运行时间上要优于后两者。     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.