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.     

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.     

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.     

一种基于“探测"与“开采"的多目标进化算法

针对实践中多目标优化问题(MOPs)的Pareto解集(PS)未知且比较复杂的特性,提出了一种基于"探测"(Exploration)与"开采"(Exploitation)的多目标进化算法(MOEA)——MOEA/2E。该算法在进化过程中采用"探测"与"开采"相结合的方法,用进化操作不断地探测新的搜索区域,用局部搜索充分开采优秀的解区域,并用隐最优个体保留机制保存每一代的最优个体。与目前最流行且有效的多目标进化算法NSGA-Ⅱ及SPEA-Ⅱ进行的比较实验结果表明,MOEA/2E获得的Pareto最优解集具有更好的收敛性与分布性。     

一种基于遗传算法的多目标优化算法研究

对一般的无约束多目标优化问题的求解进行讨论,提出一种基于遗传算法的求解方法,该方法区别于传统遗传算法的求解模式,它采用带性别标志的编码、子群体的选择、保留Pareto最优解,并对解集进行共享函数的处理,最后得到较高质量的Pareto最优解集,给出的两个算例也充分说明此方法在处理多目标问题的可行性和实用性。     

基于遗传算法的辊筒棒磨机多目标优化设计

为了优化辊筒棒磨机的磨矿过程,选取影响磨矿性能的主要因素,利用量纲分析法对磨矿特征进行描述,并结合实验数据,建立磨矿过程的多目标优化模型;利用遗传算法对模型进行求解,得到Pareto最优解集,采用优劣解距离(TOPSIS)法寻得多目标优化问题的一组最优解,并对结果进行分析。结果表明:进行多目标优化后,棒磨机产率提高了5. 46%,能源利用率提升5. 04%,磨矿产物的均一性指数增大1. 088,有效地提升了辊筒棒磨机的综合性能。     

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。     

基于NSGA-Ⅱ&DEA混合算法的高速铁路桥梁风屏障高度多目标优化研究

为探究高速铁路桥梁风屏障高度的多目标优化问题,基于计算流体动力学理论,采用数值模拟方法计算设置有不同高度风障时,列车及桥梁各自的气动力系数。以车辆侧倾稳定性力矩系数及桥梁阻力系数为优化目标,风屏障高度为设计变量,采用多目标遗传算法(NSGA-II)求解Pareto最优解集,采用数据包络分析方法(DEA)评价Pareto解集中各个解的相对效率,得到最优风屏障高度。结果表明:采用NSGA-IIDEA混合算法对风屏障高度进行多目标优化是可行的。该优化设计方法为风屏障高度优化问题提供了一种新思路。     

用于结构优化设计的改进多目标群搜索算法

在多目标群搜索算法（multi-objective group search optimization, MGSO）基本原理的基础上,结合Pareto最优解理论,提出了基于约束改进的多目标群搜索算法（IMGSO）,并应用于多目标的结构优化设计．算法的改进主要有3个方面：第一,引入过渡可行域的概念来处理约束条件;第二,利用庄家法来构造非支配解集;最后,结合禁忌搜索算法和拥挤距离机制来选择发现者,以避免解集过早陷入局部最优,并提高收敛精度．采用IMGSO优化算法分别对平面和空间桁架结构进行了离散变量的截面优化设计,并与MGSO优化算法的计算结果进行了比较,结果表明改进的多目标群搜索优化算法IMGSO与MGSO算法相比具有更好的收敛精度.通过算例表明：IMGSO算法得到的解集中的解能大部分支配MGSO算法的解,在复杂高维结构中IMGSO算法的优越性更加明显,且收敛速度也有一定的提高,可有效应用于多目标的实际结构优化设计．     

Practical solutions for multi-objective optimization: An application to system reliability design problems

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.     

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.     

Microgenetic multiobjective reconfiguration algorithm considering power losses and reliability indices for medium voltage distribution network

This study proposes and applies an evolutionary-based approach for multiobjective reconfiguration in electrical power distribution networks. In this model, two types of indicators of power quality are minimised: (i) power system's losses and (ii) reliability indices. Four types of reliability indices are considered. A microgenetic algorithm ('GA) is used to handle the reconfiguration problem as a multiobjective optimisation problem with competing and non-commensurable objectives. In this context, experiments have been conducted on two standard test systems and a real network. Such problems characterise typical distribution systems taking into consideration several factors associated with the practical operation of medium voltage electrical power networks. The results show the ability of the proposed approach to generate well-distributed Pareto optimal solutions to the multiobjective reconfiguration problem. In the systems adopted for assessment purposes, our proposed approach was able to find the entire Pareto front. Furthermore, better performance indexes were found in comparison to the Pareto envelope-based selection algorithm 2 (PESA 2) technique, which is another well-known multiobjective evolutionary algorithm available in the specialised literature. From a practical point of view, the results established, in general, that a compact trade-off region exists between the power losses and the reliability indices. This means that the proposed approach can recommend to the decision maker a small set of possible solutions in order to select from them the most suitable radial topology.     

Multi-objective scheduling problems: Determination of pruned Pareto sets

There are often multiple competing objectives for industrial scheduling and production planning problems. Two practical methods are presented to efficiently identify promising solutions from among a Pareto optimal set for multi-objective scheduling problems. Generally, multi-objective optimization problems can be solved by combining the objectives into a single objective using equivalent cost conversions, utility theory, etc., or by determination of a Pareto optimal set. Pareto optimal sets or representative subsets can be found by using a multi-objective genetic algorithm or by other means. Then, in practice, the decision maker ultimately has to select one solution from this set for system implementation. However, the Pareto optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially as the number of objectives increase. Our research involves the post Pareto analysis phase, and two methods are presented to filter the Pareto optimal set to determine a subset of promising or desirable solutions. The first method is pruning using non-numerical objective function ranking preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Pareto optimal set. The clustered data allows the decision maker to have just k general solutions from which to choose. These methods are general, and they are demonstrated using two multi-objective problems involving the scheduling of the bottleneck operation of a printed wiring board manufacturing line and a more general scheduling problem.     

Compromise design of stochastic dynamical systems: A reliability-based approach

This paper presents a procedure for obtaining compromise designs of structural systems under stochastic excitation. In particular, an effective strategy for determining specific Pareto optimal solutions is implemented. The design goals are defined in terms of deterministic performance functions and/or performance functions involving reliability measures. The associated reliability problems are characterized by means of a large number of uncertain parameters (hundreds or thousands). The designs are obtained by formulating a compromise programming problem which is solved by a first-order interior point algorithm. The sensitivity information required by the proposed solution strategy is estimated by an approach that combines an advanced simulation technique with local approximations of some of the quantities associated with structural performance. An efficient Pareto sensitivity analysis with respect to the design variables becomes possible with the proposed formulation. Such information is used for decision making and tradeoff analysis. Numerical validations show that only a moderate number of stochastic analyses (reliability estimations) has to be performed in order to find compromise designs. Two example problems are presented to illustrate the effectiveness of the proposed approach.     

Multi-objective genetic algorithm for solving N-version program design problem

N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently.We formulate the optimal design problem of NVP as a bi-objective 0–1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process.The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.     

Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

Trade-off analysis approach for interactive nonlinear multiobjective optimization

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.     

MONSS: A multi-objective nonlinear simplex search approach

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.