基于一种新模型的多目标遗传算法及性能分析

在多目标优化中,各目标通常相互冲突,其最优解往往有无穷多个,如何在最优解集中求出一组分布均匀且数量多的Pareto最优解供决策者选择十分重要.本文给出了多目标优化的一种新解法.首先定义了种群序值的理想方差和种群密度的方差,然后把目标个数任意的多目标函数优化问题Ⅰ转化成了用种群序值的理想方差和种群密度的方差构成的两个目标函数的优化问题Ⅱ,并对转化后的优化问题Ⅱ提出了一种新的多目标遗传算法(RDMOEA).计算机仿真表明RDMOEA算法对不同的实验函数均可求出在最优解集合中分布均匀且数量充足的Pareto最优解.     

解多目标优化问题的新粒子群优化算法

通过定义的粒子序值方差和U-度量方差,把对任意多个目标函数的优化问题转化成为两个目标函数的优化问题。继而把Pareto最优与粒子群优化(PSO)算法相结合,对转化后的优化问题提出了一种新的多目标粒子群优化算法,并证明了其收敛性。新方法用较少计算量便可以求出一组在最优解集合中分布均匀且数量充足的最优解。计算机仿真表明该算法对不同的试验函数均可用较少计算量求出在最优解集合中分布均匀且数量充足的最优解。     

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.     

基于多区域中心点预测的动态多目标优化算法

现实生活中存在很多动态多目标优化问题(DMOPs),这类问题要求算法在环境变化后快速收敛到新的Pareto前沿,并保持解集的多样性,随着Pareto前沿复杂程度的增加,这一问题更加突出.鉴于此,提出一种基于多区域中心点预测的动态多目标优化算法(MCPDMO).首先,根据环境变化的严重程度将种群划分为多个子区域,使得个体的分配更加适应动态变化的环境;然后,分别计算每个子区域的中心点,对不同子区域在不同时刻的中心点建立时间序列,并利用差分模型预测新环境的最优解集,以提高算法对不同环境变化的响应能力;最后,为验证算法的有效性,与3种动态多目标优化算法在10个标准测试函数上进行仿真实验.实验结果表明,所提出算法在具有复杂Pareto前沿的动态问题上表现出更优的收敛性和分布性.     

一种基于新的模型的多目标存档遗传算法

在多目标优化中,如何在最优解集中获得一组分布均匀且质量较好的代表解是十分重要的。文中给出了种群个体的序和解的均匀性分布定义,在此基础上又给出了解的序值方差和U-度量方差,然后把对任意多个目标函数的优化问题转化成对两个目标函数的优化问题,并对转化后的优化问题提出了一种新的多目标存档遗传算法,并证明了其全局收敛性。数据实验比较表明该算法能找到问题的数量更多、分布更广、更均匀的Pareto最优解。     

动态多目标优化:测试函数和算法比较

生活中存在大量的动态多目标优化问题,应用进化算法求解动态多目标优化问题受到越来越多的关注,而动态多目标测试函数对算法的评估起着重要的作用.在已有动态多目标测试函数的基础上,设计一组新的动态多目标测试函数.Pareto最优解集和Pareto前沿面的不同变化形式影响着动态多目标测试函数的难易程度,通过引入Pareto最优解集形状的变化,结合已有的Pareto最优解集移动模式,设计一组测试函数集.基于提出的测试函数集,对3个算法进行测试,仿真实验结果表明,所设计的函数给3个算法带来了挑战,并展现出算法的优劣.     

多子群协同进化的多目标微粒群优化算法

微粒群优化(PSO)算法是一种非常有竞争力的求解多目标优化问题的群智能算法,因其容易陷入局部极值,导致非劣解集的收敛性和正确性不理想。为此提出一种基于多目标分解进化策略的多子群协同进化的多目标微粒群优化算法(MOPSO_MC),算法中每个子群对应于一个多目标分解之后的子问题,并构造了一种新的速率更新策略,每个粒子跟踪自身历史最优值、子群最优值和子群邻域最优值,从而在增强算法的局部寻优能力的同时,也能从邻域子群获得进化信息,实现协同进化。最后通过仿真实验,与现在主流的多目标微粒群算法在ZDT基准测试函数上比较,验证了算法的收敛性,解分布的均匀性和正确性。     

基于正交设计的动态多目标优化算法

提出了一种基于正交设计的动态多目标优化算法（ODMOA）,当环境变化时通过分析动态多目标优化问题的特点,利用历史信息对新环境下的Pareto最优解集进行预测,得到一个新的预测种群;否则在静态环境下使用正交试验法在解空间内进行系统且高效的搜索,使算法能够在当前环境下快速收敛到最优解。进行了多组对比试验,验证了该算法的有效性。     

一种具有全局快速寻优的多学科协同优化方法

针对协同优化算法迭代次数多、易收敛于局部极值点问题,提出一种全局快速寻优的协同优化算法。在系统级一致性等式约束中采用改进后松弛因子,改进动态松弛因子使优化设计点快速收敛于极值点,静态松弛因子使优化设计点跳出局部极值点,确保系统目标函数得到全局最优解;子学科目标函数由一致性目标函数和子学科最优目标函数两个部分以不同权重相加组成,考虑一致性的同时,又兼顾子学科独立性。采用减速器优化案例对改进协同优化算法进行验证。仿真结果表明,改进后算法在保证最大约束值较小的前提下,可快速得到全局最优解且鲁棒性好。     

基于分解的预测型动态多目标粒子群优化算法

针对动态多目标问题求解,提出一种基于分解的预测型动态多目标粒子群优化算法.首先借助分解思想,将目标问题划分为多个不同的子问题,当问题动态变化时,选择对应于不同子问题的优化个体检测环境变化程度,以提高算法对不同动态问题的适应与响应能力;然后,设计一种群体预测策略,通过将目标空间中相同收敛方向上不同时刻的个体位置转换为时间序列,引入时间序列预测方法预测下一刻位置,从而提高预测种群的多样性和有效性,进而有效减少算法在问题变化后的收敛时间;最后,为避免问题发生变化后个体与子问题不匹配,设计一种再匹配策略,以提高预测策略的准确性.实验结果表明,在6个标准动态多目标测试问题上,与2个动态多目标优化算法进行比较,所提出算法在收敛性、分布性与稳定性上均具有显著优势.     

The effect of diversity maintenance on prediction in dynamic multi-objective optimization

There are many dynamic multi-objective optimization problems (DMOPs) in real-life engineering applications whose objectives change over time. After an environmental change occurs, prediction strategies are commonly used in dynamic multi-objective optimization algorithms to find the new Pareto optimal set (POS). Being able to make more accurate prediction means the algorithm requires fewer computational resources to make the population approximate to the Pareto optimal front (POF). This paper proposes a hybrid diversity maintenance method to improve prediction accuracy. The method consists of three steps, which are implemented after an environmental change. The first step, based on the moving direction of the center points, uses the prediction to relocate a number of solutions close to the new Pareto front. On the basis of self-defined minimum and maximum points of the POS in this paper, the second step applies the gradual search to produce some well-distributed solutions in the decision space so as to compensate for the inaccuracy of the first step, simultaneously and further enhancing the convergence and diversity of the population. In the third step, some diverse individuals are randomly generated within the region of next probable POS, which prompts the diversity of the population. Eventually the prediction becomes more accurate as the solutions with good convergence and diversity are selected after the non-dominated sort [1] on the combined solutions generated by the three steps. Compared with three other prediction methods on a series of test instances, our method is very competitive in convergence and diversity as well as the speed at which it responds to environmental changes.     

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Pareto 解集关联与预测的动态多目标进化算法

针对动态多目标优化问题,提出一种基于Pareto解集关联与预测的动态多目标进化算法(LP-DMOEA),设计了基于超块的Pareto解集关联方法.该方法能够动态维护若干描述Pareto解变化规律的时间序列,通过对新环境下的Pareto解集进行预测来生成初始种群.将LP-DMOEA应用于非劣分类遗传算法(NSGA2),并对3类标准测试函数进行了实验,所得结果表明该方法能够有效求解动态优化问题.     

A novel cooperative coevolutionary dynamic multi-objective optimization algorithm using a new predictive model

Dynamic multi-objective optimization problem (DMOP) is quite challenging and it dues to that there are multiple conflicting objects changing over with time or environment. In this paper, a novel cooperative coevolutionary dynamic multi-objective optimization algorithm (PNSCCDMO) is proposed. The main idea of a new cooperative coevolution based on non-dominated sorting is that it allows the decomposition process of the optimization problem according to the search space of decision variables, and each species subcomponents will cooperate to evolve for better solutions. This way derives from nature and can improve convergence significantly. A modified linear regression prediction strategy is used to make rapid response to the new changes in the environment. The effectiveness of PNSCCDMO is validated against various of DMOPs compared with the other four algorithms, and the experimental result indicates PNSCCDMO has a good capability to track the Pareto front as it is changed with time in dynamic environments.     

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods.     

动态多目标优化进化算法研究进展

动态多目标优化问题(Dynamic multi-objective optimization problems, DMOPs)已成为工程优化的研究热点, 其目标函数, 约束函数和相关参数都可能随时间不断变化, 如何利用搜索到的历史最优解对新的环境变化做出快速响应, 是设计动态多目标优化进化算法(Dynamic multi-objective optimization evolutionary algorithm, DMOEA)的重点和难点. 本文在介绍DMOEA的基础上, 分析了近年来基于个体和种群级别的环境响应策略, 多策略混合等的DMOEA主要研究进展, 并介绍了DMOEA的性能测试函数, 评价指标以及在工程优化领域中的应用, 分析了DMOEA研究中仍面临的主要问题, 展望了未来的研究方向.     

时空视角下的动态多目标进化算法研究综述

现实中的多目标优化问题会随着时间或环境的变化而发生改变,因此在全周期优化过程中,环境变化检测和算法响应是求解动态多目标优化问题的两大关键步骤,为此重点对动态多目标进化算法方面的研究进行总结.为有效求解动态多目标优化问题,大量追踪性能优良的动态多目标进化算法在近20年里被提出,但是很少有文献从时空角度对已有研究进行分析和报道,鉴于此,从该视角对动态多目标进化算法研究进行综述.首先介绍动态多目标优化的基本概念、问题和性能指标;然后从时空视角对近5年提出的动态多目标进化算法研究进行分别介绍;最后列出目前动态多目标进化算法方面研究存在的一些挑战,并对未来研究进行展望.     

Exploiting characterization of dynamism for enhancing dynamic multi-objective evolutionary algorithms

Characterization of dynamism is an essential phase for some of the dynamic multi-objective evolutionary algorithms (DMOEAs) in order to improve their performance. Although frequency of change and severity of change are the two main perspectives of characterizing dynamic features of the dynamic multi-objective optimization problems (DMOPs), they do not sufficiently attract attentions of the research community. In this paper, we propose a set of new sensor-based change detection schemes for the DMOPs that significantly outperform the current used change detection schemes. Additionally, a new technique is proposed for detecting the change severity for DMOPs. The experimental evaluation based on different test problems and change severity levels validates performance of our technique. We also propose a novel adaptive algorithm called change-responsive NSGA-II (CR-NSGA-II) algorithm that incorporates the change detection schemes, the technique for change severity and a new response mechanism into the NSGA-II algorithm. Our algorithm demonstrates competitive and significantly better results than the leading DMOEAs on majority of test problems and metrics considered.     

Adaptive weighted-sum method for bi-objective optimization: Pareto front generation

This paper presents a new method that effectively determines a Pareto front for bi-objective optimization with potential application to multiple objectives. A traditional method for multiobjective optimization is the weighted-sum method, which seeks Pareto optimal solutions one by one by systematically changing the weights among the objective functions. Previous research has shown that this method often produces poorly distributed solutions along a Pareto front, and that it does not find Pareto optimal solutions in non-convex regions. The proposed adaptive weighted sum method focuses on unexplored regions by changing the weights adaptively rather than by using a priori weight selections and by specifying additional inequality constraints. It is demonstrated that the adaptive weighted sum method produces well-distributed solutions, finds Pareto optimal solutions in non-convex regions, and neglects non-Pareto optimal solutions. This last point can be a potential liability of Normal Boundary Intersection, an otherwise successful multiobjective method, which is mainly caused by its reliance on equality constraints. The promise of this robust algorithm is demonstrated with two numerical examples and a simple structural optimization problem.