基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

权重自适应clonal选择算法及其应用研究

在求解两个目标以上的多目标优化问题时,基于Pareto支配的多目标进化算法多数需要较长的求解时间.基于固定权重的聚合函数方法求解速度快,但要确定一个适合待求解问题的合理权重是十分困难的,为了解决这一问题,将clonal选择算法与权重自适应方法相结合,提出了一种适用于多目标优化问题的权重自适应clonal选择算法.并将权...     

HMOFA:一种混合型多目标萤火虫算法

现实中不断涌现出数目众多且日益复杂的多目标优化问题,迫切需要发展新型多目标优化算法以应对挑战.将基本萤火虫算法拓展至多目标优化领域,提出一种混合型多目标萤火虫算法HMOFA（hybrid multi-objective firefly algorithm）.该算法提出使用混合水平正交实验设计和连续决策空间量化的方法生成接近于用户指定规模且均匀分布于搜索空间的初始种群,为后续的进化提供良好的起始点;利用外部档案中的精英解个体引导萤火虫移动,促使算法较快收敛;运用3点最短路径方法维持外部档案的多样性.HMOFA算法与另外5种代表性多目标进化算法一同在17个基准多目标测试题上进行性能比较,实验结果表明,HMOFA算法在收敛性、多样性和鲁棒性方面总体上具有较显著的性能优势.     

Learning the Search Range for Evolutionary Optimization in Dynamic Environments

Conventional evolutionary algorithms operate in a fixed search space with limiting parameter range, which is often predefined via a priori knowledge or trial and error in order to ‘guess’ a suitable region comprising the global optimal solution. This requirement is hard, if not impossible, to fulfil in many real-world optimization problems since there is often no clue of where the desired solutions are located in these problems. Thus, this paper proposes an inductive–deductive learning approach for single- and multi-objective evolutionary optimization. The method is capable of directing evolution towards more promising search regions even if these regions are outside the initial predefined space. For problems where the global optimum is included in the initial search space, it is capable of shrinking the search space dynamically for better resolution in genetic representation to facilitate the evolutionary search towards more accurate optimal solutions. Validation results based on benchmark optimization problems show that the proposed inductive–deductive learning is capable of handling different fitness landscapes as well as distributing nondominated solutions uniformly along the final trade-offs in multi-objective optimization, even if there exist many local optima in a high-dimensional search space or the global optimum is outside the predefined search region. Received 15 January 2001 / Revised 8 June 2001 / Accepted in revised form 24 July 2001     

Multi-objective reactive power market clearing in competitive electricity market using HFMOEA

This paper presents an application of a hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) for solving a highly constraint, mixed integer type, complex multi-objective reactive power market clearing (RPMC) problem for the competitive electricity market environment. In HFMOEA based multi-objective optimization approach, based on the output of a fuzzy logic controller crossover and mutation probabilities are varied dynamically. It enhances stochastic search capabilities of HFMOEA. In multi-objective RPMC optimization framework, two objective functions namely the total payment function (TPF) for reactive power support from generators and synchronous condensers and the total real transmission loss (TRTL) are minimized simultaneously for clearing the reactive power market. The proposed HFMOEA based multi-objective RPMC scheme is tested on a standard IEEE 24 bus reliability test system and its performance is compared with five other multi-objective evolutionary techniques such as MOPBIL, NSGA-II, UPS-EMOA and SPEA-2 and a new extended form of NSGA (ENSGA-II). Applying all these six evolutionary techniques, a detailed statistical analysis using T-test and boxplots is carried out on three performance metrics (spacing, spread and hypervolume) data for RPMC problem. The obtained simulation results confirm the overall superiority of HFMOEA to generate better Pareto-optimal solutions with higher convergence rate as compared to above mentioned algorithms. Further, TPF and TRTL values corresponding to the best compromise solutions are obtained using said multi-objective evolutionary techniques. These values are compared with one another to take better market clearing decisions in competitive electricity environment.     

A Novel Quantum - inspired Multi - Objective Evolutionary Algorithm Based on Cloud Theory

In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the non-dominated set as well as the diversity of population in multi-objective problems,in this paper,a Novel Cloud -based quantum -inspired multi-objective evolutionary Algorithm(CQMEA) is proposed.CQMEA is proposed by employing the concept and principles of Cloud theory.The algorithm utilizes the random orientation and stability of the cloud model,uses a self-adaptive mechanism with cloud model of Quantum gates updating strategy to implement global search efficient.By using the self-adaptive mechanism and the better solution which is determined by the membership function uncertainly,Compared with several well-known algorithms such as NSGA-Ⅱ,QMEA.Experimental results show that(CQMEA) is more effective than QMEA and NSGA -Ⅱ.     

Preference-based multi-objective evolutionary algorithms for power-aware application mapping on NoC platforms

Network-on-chip (NoC) are considered the next generation of communication infrastructure in embedded systems. In the platform-based design methodology, an application is implemented by a set of collaborative intellectual property (IP) blocks. The selection of the most suited set of IPs as well as their physical mapping onto the NoC infrastructure to implement efficiently the application at hand are two hard combinatorial problems that occur during the synthesis process of Noc-based embedded system implementation. In this paper, we propose an innovative preference-based multi-objective evolutionary methodology to perform the assignment and mapping stages. We use one of the well-known and efficient multi-objective evolutionary algorithms NSGA-II and microGA as a kernel. The optimization processes of assignment and mapping are both driven by the minimization of the required silicon area and imposed execution time of the application, considering that the decision maker’s preference is a pre-specified value of the overall power consumption of the implementation.     

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.      

一种求解多目标优化问题的进化算法混合框架

为了提高多目标优化算法的求解性能,提出一种启发式的基于种群的全局搜索与局部搜索相结合的多目标进化算法混合框架.该框架采用模块化、系统化的设计思想,不同模块可以采用不同策略构成不同的算法.采用经典的改进非支配排序遗传算法(NSGA-II)和基于分解的多目标进化算法(MOEA/D)作为进化算法的模块算法来验证所提混合框架的有效性.数值实验表明,所提混合框架具有良好性能,可以兼顾算法求解的多样性和收敛性,有效提升现有多目标进化算法的求解性能.     

基于多目标进化算法的MOEA/D权重向量产生方法

在进化多目标优化研究领域,多目标优化是指对含有2个及以上目标的多目标问题的同时优化,其在近些年来受到越来越多的关注。随着MOEA/D的提出,基于聚合的多目标进化算法得到越来越多的研究,对MOEA/D算法的改进已有较多成果,但是很少有成果研究MOEA/D中权重的产生方法。提出一种使用多目标进化算法产生任意多个均匀分布的权重向量的方法,将其应用到MOEA/D,MSOPS和NSGA-III中,对这3个经典的基于聚合的多目标进化算法进行系统的比较研究。通过该类算法在DTLZ测试集、多目标旅行商问题MOTSP上的优化结果来分别研究该类算法在连续性问题、组合优化问题上的优化能力,以及使用矩形测试问题使得多目标进化算法的优化结果在决策空间可视化。实验结果表明,没有一个算法能适用于所有特性的问题。然而,MOEA/D采用不同聚合函数的两个算法MOEA/D_Tchebycheff和MOEA/D_PBI在多数情况下的性能比MSOPS和NSGA-III更好。     

On the hardness of offline multi-objective optimization

It has been empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. This paper shows that the convergence rate of all comparison-based multi-objective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search under certain conditions. The number of objectives must be very moderate and the framework should hold the following assumptions: the objectives are conflicting and the computational cost is lower bounded by the number of comparisons is a good model. Our conclusions are: (i) the number of conflicting objectives is relevant (ii) the criteria based on comparisons with random-search for multi-objective optimization is also relevant (iii) having more than 3-objectives optimization is very hard. Furthermore, we provide some insight into cross-over operators.     

Evolutionary design and implementation of a hard disk drive servo control system

The ever increasing demand for higher storage capacity and smaller magnetic hard disk drives have driven the need of developing a high performance head positioning servo control system. To meet the challenge, this paper presents the design and real-time implementation of a robust two-degree-of-freedom servo system for physical 3.5-in. hard disk drive with single voice-coil-motor actuator using a multi-objective evolutionary algorithm toolbox. Besides the simplicity in controller structure, such an evolutionary servo control system is capable of meeting various performance specifications of hard disk drives in both the time and frequency domains. It is shown that the servo system optimally moves the magnetic head onto the desired track with minimal control effort, and keeps it on the track robustly against plant uncertainties or runout disturbances. Validation results of the evolutionary servo control system are compared with classical PID and RPT controllers, which show excellent closed-loop response and robustness in the face of practical perturbations in HDD.     

A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.     

高维多目标进化算法研究综述

传统的多目标进化算法能够有效地解决2个或3个目标的优化问题,但当优化目标超过4维即具有高维目标时,其优化效果将大大下降,因此高维多目标进化算法的研究得到了较多的关注.鉴于此,对高维多目标进化算法的研究进展进行系统地分类综述,分析了高维目标对优化算法造成的困难以及改进的可视化技术;总结了各类算法的特点与缺陷,并给出进一步可能的研究方向.     

记忆增强的动态多目标分解进化算法

现实世界中的一些多目标优化问题经常受动态环境影响而不断发生变化,要求优化算法不断地及时跟踪时变的Pareto 最优解集.提出了一种记忆增强的动态多目标分解进化算法.将动态多目标优化问题分解为若干个动态单目标优化子问题并同时优化这些子问题,以便快速逼近Pareto 最优解集.给出了一个改进的环境变化检测算子,以便更好地检测环境变化.设计了一种基于子问题的串式记忆方法,利用过去类似环境下搜索到的最优解来有效地响应新的环境变化.在8 个标准的测试问题上,将新算法与其他3 种记忆增强的动态进化多目标优化算法进行了实验比较.结果表明,新算法比其他3 种算法具有更快的运行速度、更强的记忆能力与鲁棒性能,并且新算法所获得的解集还具有更好的收敛性与分布性.     

基于多点非均匀变异的多目标极值优化算法研究

多目标进化算法因其在解决含有多个矛盾目标函数的多目标优化问题中的强大处理能力,正受到越来越多的关注与研究。极值优化作为一种新型的进化算法,已在各种离散优化、连续优化测试函数以及工程优化问题中得到了较为成功的应用,但有关多目标EO算法的研究却十分有限。本文将采用Pareto优化的基本原理引入到极值优化算法中,提出一种求解连续多目标优化问题的基于多点非均匀变异的多目标极值优化算法。通过对六个国际公认的连续多目标优化测试函数的仿真实验结果表明：本文提出算法相比NSGA-II、 PAES、SPEA和SPEA2等经典多目标优化算法在收敛性和分布性方面均具有优势。     

Effective Linkage Learning Using Low-Order Statistics and Clustering

The adoption of probabilistic models for selected individuals is a powerful approach for evolutionary computation. Probabilistic models based on high-order statistics have been used by estimation of distribution algorithms (EDAs), resulting better effectiveness when searching for global optima for hard optimization problems. This paper proposes a new framework for evolutionary algorithms, which combines a simple EDA based on order 1 statistics and a clustering technique in order to avoid the high computational cost required by higher order EDAs. The algorithm uses clustering to group genotypically similar solutions, relying that different clusters focus on different substructures and the combination of information from different clusters effectively combines substructures. The combination mechanism uses an information gain measure when deciding which cluster is more informative for any given gene position, during a pairwise cluster combination. Empirical evaluations effectively cover a comprehensive range of benchmark optimization problems.      

Adaptive memetic method of multi-objective genetic evolutionary algorithm for backpropagation neural network

Neural Computing and Applications - In recent years, multi-objective evolutionary optimization algorithms have shown success in different areas of research. Due to their efficiency and power, many...     

Hybrid multi-attribute QoS optimization in component based software systems

Design decisions for complex, component-based systems impact multiple quality of service (QoS) properties. Often, means to improve one quality property deteriorate another one. In this scenario, selecting a good solution with respect to a single quality attribute can lead to unacceptable results with respect to the other quality attributes. A promising way to deal with this problem is to exploit multi-objective optimization where the objectives represent different quality attributes. The aim of these techniques is to devise a set of solutions, each of which assures an optimal trade-off between the conflicting qualities. Our previous work proposed a combined use of analytical optimization techniques and evolutionary algorithms to efficiently identify an optimal set of design alternatives with respect to performance and costs. This paper extends this approach to more QoS properties by providing analytical algorithms for availability-cost optimization and three-dimensional availability-performance-cost optimization. We demonstrate the use of this approach on a case study, showing that the analytical step provides a better-than-random starting population for the evolutionary optimization, which lead to a speed-up of 28% in the availability-cost case.     

Preference-based multi-objectivization applied to decision support for High-Pressure Thermal processes in food treatment

Food industry aims to provide healthy products that must satisfy the quality requirements of the considered legislation. To do so, food is treated by using some processing techniques, such as High-Pressure Thermal (HPT) treatments. In this work, we propose a preference-based multi-objectivization methodology to design HPT processes for food treatment. This approach is based on formulating a multi-objective optimization problem, instead of a constrained mono-objective problem, where the constraints are reformulated as separate objective functions. The multi-objective problem is then solved by using preference-based evolutionary optimization algorithms (PMOEAs). PMOEAs focus the search of a numerical solution inside a region of interest defined by the food engineer, avoiding exploring HPT designs that are out of interest. The proposed methodology is validated by considering several particular mono-objective and multi-objective optimization problems related to HPT processing. In particular, we compare the results obtained by two competitive state-of-the-art PMOEAs, called WASF-GA and R-NSGA-II, with the ones returned by a mono-objective algorithm called MLS-GA. As part of this study, the influence of the optimization algorithm parameters on the solutions, their quality and the computing time are discussed. Finally, the best solutions returned by the algorithm that shows a better performance for our problems, which is WASF-GA, are analyzed from a food engineering point of view and a sensitivity analysis regarding the impact of design parameters on the performances of those solutions is carried out.