Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model

Coupled optimization methods based on multi-objective genetic algorithms and approximation models are widely used in engineering optimizations. In the present paper, a similar framework is proposed for the aerodynamic optimization of turbomachinery by coupling the well known multi-objective genetic algorithm—NSGA-II and back propagation neural network. The verification results of mathematical problems show that the coupled method with the origin NSGA-II cannot get the real Pareto front due to the prediction error of BPNN. A modified crowding distance is proposed in cooperation with a coarse-to-fine approaching strategy based on the iterations between NSGA-II and BPNN. The results of mathematical model problems show the effect of these improving strategies. An industrial application case is implemented on a transonic axial compressor. The optimization objectives are to maximize efficiencies of two working points and to minimize the variation of the choked mass flow. CFD simulation is employed to provide the performance evaluation of initial training samples for BPNN. The optimized results are compared with optimization results of a single objective optimization based on weighting function. The comparison shows that the present framework can provide not only better solutions than the single objective optimization, but also various alternative solutions. The increase of computational costs is acceptable especially when approximation models are used.     

基于偏好的多目标遗传算法

多目标优化问题中,人们往往只是对目标空间的某一区域感兴趣,因此这就需要在这一特定的区域能够得到比较稠密的Pareto解,但传统的方法权值法无法满足这种需求而且不能处理目标空间是非凸的情况,遗传算法虽然是现在公认的处理多目标优化问题比较有效的方法,但遗传算法是在目标空间内进行全空间寻优,因此最终得到的Pareto解是均匀分布的,这样遗传算法也不能满足人们的这一要求。针对这个问题提出了基于偏好的多目标遗传算法,把个人偏好加到优化过程中,利用偏好信息来引导优化方向,通过仿真把该算法和权值法、NSGA-II进行比较,结果证明了该算法的可行性和有效性。     

快速提高NSGA-Ⅱ算法双目标优化效率的方法

NSGA-Ⅱ是一种性能优良的多目标进化算法,近年来非常流行。为了进一步改进NSGA-Ⅱ在双目标优化时的效率,采取了按需分层的策略,提出了一种新的非支配前沿集分层方法以替代NSGA-II原有的分层方法。与NSGA-Ⅱ的时间复杂度O(N2)相比,新方法的时间复杂度减少为O(kN+NlogN),k为所分前沿层数(k<相似文献   

A multi-objective genetic algorithm for simultaneous model and feature selection for support vector machines

The Support Vector Machines (SVM) constitute a very powerful technique for pattern classification problems. However, its efficiency in practice depends highly on the selection of the kernel function type and relevant parameter values. Selecting relevant features is another factor that can also impact the performance of SVM. The identification of the best set of parameters values for a classification model such as SVM is considered as an optimization problem. Thus, in this paper, we aim to simultaneously optimize SVMs parameters and feature subset using different kernel functions. We cast this problem as a multi-objective optimization problem, where the classification accuracy, the number of support vectors, the margin and the number of selected features define our objective functions. To solve this optimization problem, a method based on multi-objective genetic algorithm NSGA-II is suggested. A multi-criteria selection operator for our NSGA-II is also introduced. The proposed method is tested on some benchmark data-sets. The experimental results show the efficiency of the proposed method where features were reduced and the classification accuracy has been improved.     

基于改进的非支配排序遗传算法的无源滤波器设计

工业中的电网谐波不但降低了电能的质量,还可能引起故障甚至事故,因此有必要对电网谐波进行有效地滤除;实际的工程实践中,无源滤波器常被用来滤除该谐波,而其滤波参数的确定是个关键;基于带精英策略的非支配排序遗传算法NSGA-Ⅱ,文中提出了一种新的无源滤波器的参数优化方法,克服了传统的凭个人经验选择滤波器参数的缺陷.利用NSGA-Ⅱ对无源滤波器进行参数优化,不仅能节省初始投资,还能更有效地消除谐波干扰;仿真结果证明了该方法的有效性.     

嵌入式系统动态数据结构优化的并行进化算法

为了更好地解决现代多媒体嵌入式系统动态数据结构优化问题,结合NSGA-II和SPEA2两个多目标进化算法,引入岛屿模型和多线程机制,提出了一种并行多目标进化算法--PMOEA-NS。基于多核计算机系统,使用PMOEA-NS具体的3个不同并行算法和串行NSGA-II、SPEA2,对一个实际动态嵌入式应用程序进行优化实验和计算,结果表明:与串行算法NSGA-II和SPEA2相比,并行算法不但提高了优化过程的速度,而且改善了解的质量和多样性。     

多目标约束处理方法求解泊位岸桥联合分配问题

为了制定合理高效的泊位岸桥联合分配方案,加快船舶周转,本文针对船舶动态到港的连续泊位建立了以船舶总在港时间最短为目标的泊位岸桥联合分配混合整数非线性模型.通过多目标约束处理策略将复杂约束的违反程度转化为另一个目标,从而将原单目标优化模型转化为双目标优化模型,并用基于快速非支配排序的多目标遗传算法(NSGA-II)对其进行求解.同时,针对问题特点,分别设计了基于调整、惩罚函数、可行解优先和综合约束处理策略的单目标遗传算法对原模型进行求解.通过多组不同规模的标准算例对本文的方法进行测试,验证了基于多目标约束处理策略的方法求解效果相较于单目标约束处理策略的方法更加高效和稳定.     

A cooperative negotiation embedded NSGA-II for solving an integrated product family and supply chain design problem with remanufacturing consideration

Product family design is a popular approach adopted by manufacturers to increase their product varieties in order to satisfy the needs of various markets. In recent years, because of increasing environmental concerns in societies and strict regulations of environmental protection, quite a number of manufacturers adopted remanufacturing strategy in their product development in response to the challenges. Remanufacturing of used products unavoidably involves a closed-loop supply chain system. To achieve the best outcomes, the supply chain design should be considered in product family design process. In this research, a multi-objective optimization model of integrated product family and closed loop supply chain design is formulated based on a cooperative game model for minimizing manufacturer’s total cost and maximize suppliers’ total payoffs. Since the optimization problem could be a large- scale one and involves mixed continuous-discrete variables, a new version of nondominated sorting genetic algorithm-II (NSGA-II), namely cooperative negotiation embedded NSGA-II (NSGA-CO), is proposed to solve the optimization model. Simulation tests are conducted to validate the effectiveness of the proposed NSGA-CO. The test results indicate that the proposed NSGA-CO outperforms NSGA-II in solving various scale of multi-objective optimization problems in terms of convergence. With the formulated optimization model and the proposed NSGA-CO, a case study of integrated product family and supply chain design is conducted to investigate the effects of environmental penalty, quantity of demand and marginal cost of remanufacturing on used product return rate, manufacturers’ and suppliers’ profits and joint payoff.     

Pareto frontier for simultaneous structural and manufacturing optimization of a composite part

Optimized design of composite structures requires simultaneous optimization of structural performance and manufacturing process. Such a challenge calls for a multi-objective optimization. Here, a generating multi-objective optimization method called normalized normal constraint method, which attains a set of optimal solutions and allows the designer to explore design alternatives before making the final decision, is coupled with a local-global search called constrained globalized bounded Nelder–Mead method. The proposed approach is applied to the design of a Z-shaped composite bracket for optimization of structural and manufacturing objectives. Comparison of the results with non-dominated sorting genetic algorithm (NSGA-II) shows that when only a small number of function evaluations are possible and a few Pareto optima are desired, the proposed method outperforms NSGA-II in terms of convergence to the true Pareto frontier. The results are validated by an enumeration search and by exploring the neighbourhood of the final solutions.     

基于NSGA-II 的具有多目标子学科的协同优化方法

针对子学科具有物理目标的多目标协同优化问题, 研究基于NSGA-II 的求解策略. 鉴于子学科个体满足约束可行性的进化过程与系统级分配期望值无关, 提出具有良好的可行性和多样性的初始种群生成方法, 以提高多目标子学科的计算效率和计算精度. 为了解决由一致性目标函数与物理目标函数的作用不同而造成的NSGA-II 非支配级排序困难, 提出将子学科一致性目标函数转化为子学科自身约束的策略. 最后, 利用工程算例对所提出方法的有效性进行了验证.

     

基于多体力学的车辆动力学控制系统仿真及优化

利用多体分析软件ADAMS建立了多自由度汽车整车多体动力学仿真模型,并进一步简化为15自由度非线性模型,结合2自由度线性模型建立PID控制策略,进行了冰面单周正弦工况下的汽车操纵稳定性仿真试验研究,采用自适应模拟退火算法与非线性序列二次规划法相结合的组合优化方法对控制系统的控制参数进行了分析和优化.结果表明,该控制方法能够大幅度提高车辆的操纵稳定性和安全性,能够适应复杂的路面和行驶工况,取得了良好的效果.     

An improved evolutionary algorithm for handling many-objective optimization problems

It has been shown that the multi-objective evolutionary algorithms (MOEAs) act poorly in solving many-objective optimization problems which include more than three objectives. The research emphasis, in recent years, has been put into improving the MOEAs to enable them to solve many-objective optimization problems efficiently. In this paper, we propose a new composite fitness evaluation function, in a novel way, to select quality solutions from the objective space of a many-objective optimization problem. Using this composite function, we develop a new algorithm on a well-known NSGA-II and call it FR-NSGA-II, a fast reference point based NSGA-II. The algorithm is evaluated for producing quality solutions measured in terms of proximity, diversity and computational time. The working logic of the algorithm is explained using a bi-objective linear programming problem. Then we test the algorithm using experiments with benchmark problems from DTLZ family. We also compare FR-NSGA-II with four competitive algorithms from the extant literature to show that FR-NSGA-II will produce quality solutions even if the number of objectives is as high as 20.     

MIJ2K Optimization using evolutionary multiobjective optimization algorithms

This paper deals with the multiobjective definition of video compression and its optimization. The optimization will be done using NSGA-II, a well-tested and highly accurate algorithm with a high convergence speed developed for solving multiobjective problems. Video compression is defined as a problem including two competing objectives. We try to find a set of optimal, so-called Pareto-optimal solutions, instead of a single optimal solution. The two competing objectives are quality and compression ratio maximization. The optimization will be achieved using a new patent pending codec, called MIJ2K, also outlined in this paper. Video will be compressed with the MIJ2K codec applied to some classical videos used for performance measurement, selected from the Xiph.org Foundation repository. The result of the optimization will be a set of near-optimal encoder parameters. We also present the convergence of NSGA-II with different encoder parameters and discuss the suitability of MOEAs as opposed to classical search-based techniques in this field.     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.     

Handling multiple objectives with biogeography-based optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization (BBMO) is introduced, which uses the cluster attribute of islands to naturally decompose the problem. The proposed algorithm makes use of nondominated sorting approach to improve the convergence ability effciently. It also combines the crowding distance to guarantee the diversity of Pareto optimal solutions. We compare the BBMO with two representative state-of-the-art evolutionary multi-objective optimization methods, non-dominated sorting genetic algorithm-II (NSGA-II) and archive-based micro genetic algorithm (AMGA) in terms of three metrics. Simulation results indicate that in most cases, the proposed BBMO is able to find much better spread of solutions and converge faster to true Pareto optimal fronts than NSGA-II and AMGA do.     

改进NSGA-Ⅱ算法的海上搜救调度方法

针对海上搜救资源调度决策困难、干扰多、实时性差、难以实现全局最优问题,本文以黄渤海海域为例,采用改进的非支配排序遗传(NSGA-Ⅱ)算法解决海上船舶搜救资源调度问题.首先,根据AIS以及北斗数据,建立了海上搜救资源的多目标优化模型;其次,改进的NSGA-Ⅱ算法采用基于正态分布交叉(NDX)算子,在扩大搜索范围的基础上,避免陷入局部最优,得到多目标问题完整的Pareto解集;采用综合评价法(TOPSIS)从Pareto解集中求得折衷解,即最终设计的搜救调度方案;最后,在考虑船舶数量约束以及时间约束的条件下,采用改进的NSGA-Ⅱ算法分别与NSGA-Ⅱ算法和贪婪算法进行对比,并采用黄渤海海域船舶采集数据进行仿真.结果表明该算法能够有效解决海上搜救资源调度优化问题.     

A novel approach to CNC machining center processing parameters optimization considering energy-saving and low-cost

NC machining is currently a machining method widely used in mechanical manufacturing systems. Reasonable selection of process parameters can significantly reduce the processing cost and energy consumption. In order to realize the energy-saving and low-cost of CNC machining, the cutting parameters are optimized from the aspects of energy-saving and low-cost, and a process parameter optimization method of CNC machining center that takes into account both energy-saving and low -cost is proposed. The energy flow characteristics of the machining center processing system are analyzed, considering the actual constraints of machine tool performance and tool life in the machining process, a multi-objective optimization model with milling speed, feed per tooth and spindle speed as optimization variables is established, and a weight coefficient is introduced to facilitate the solution to convert it into a single objective optimization model. In order to ensure the accuracy of the model solution, a combinatorial optimization algorithm based on particle swarm optimization and NSGA-II is proposed to solve the model. Finally, take plane milling as an example to verify the feasibility of this method. The experimental results show that the multi-objective optimization model is feasible and effective, and it can effectively help operators to balance the energy consumption and processing cost at the same time, so as to achieve the goal of energy conservation and low-cost. In addition, the combinatorial optimization algorithm is compared with the NSGA-II, the results show that the combinatorial optimization algorithm has better performance in solving speed and optimization accuracy.     

A chaotic non-dominated sorting genetic algorithm for the multi-objective automatic test task scheduling problem

Solving a task scheduling problem is a key challenge for automatic test technology to improve throughput, reduce test time, and operate the necessary instruments at their maximum capacity. Therefore, this paper attempts to solve the automatic test task scheduling problem (TTSP) with the objectives of minimizing the maximal test completion time (makespan) and the mean workload of the instruments. In this paper, the formal formulation and the constraints of the TTSP are established to describe this problem. Then, a new encoding method called the integrated encoding scheme (IES) is proposed. This encoding scheme is able to transform a combinatorial optimization problem into a continuous optimization problem, thus improving the encoding efficiency and reducing the complexity of the genetic manipulations. More importantly, because the TTSP has many local optima, a chaotic non-dominated sorting genetic algorithm (CNSGA) is presented to avoid becoming trapped in local optima and to obtain high quality solutions. This approach introduces a chaotic initial population, a crossover operator, and a mutation operator into the non-dominated sorting genetic algorithm II (NSGA-II) to enhance the local searching ability. Both the logistic map and the cat map are used to design the chaotic operators, and their performances are compared. To identify a good approach for hybridizing NSGA-II and chaos, and indicate the effectiveness of IES, several experiments are performed based on the following: (1) a small-scale TTSP and a large-scale TTSP in real-world applications and (2) a TTSP used in other research. Computational simulations and comparisons show that CNSGA improves the local searching ability and is suitable for solving the TTSP.     

基于改进的NSGA-II多目标优化方法研究*

针对传统多目标优化算法在其领域存在的多个子目标不能同时取优的问题,提出了一种基于改进的非支配排序遗传算法（Non-dominated Sorting Genetic Algorithm-II, NSGA-II）多目标优化方法,以多目标优化遗传算法为基础,多输入多输出的反向传播（Back-Propagation, BP）神经网络为适应度函数评价体系,保证算法快速收敛并搜索到全局最优解集,该算法在建模前对实验数据进行主成分分析,降低了运算时间和算法难度,通过在遗传进化过程中引进正态分布交叉算子（Normal Distribution Crossover, NDX）和改进的自适应调整变异算子,实现了多个目标同时取优,保证Pareto最优解集快速、准确地获取。仿真实验使用UCI数据集,通过与其他常用的多目标优化算法对比,验证了改进的NSGA-II算法精确度更高、收敛速度更快、稳定性更强。