一种改进的鲁棒多目标优化方法

针对在解决某些复杂多目标优化问题过程中,所得到的Pareto最优解易受设计参数或环境参数扰动的影响,引入了鲁棒的概念并提出一种改进的鲁棒多目标优化方法,它利用了经典的基于适应度函数期望和方差方法各自的优势,有效地将两种方法结合在一起。为了实现该方法,给出一种基于粒子群优化算法的多目标优化算法。仿真实例结果表明,所给出的方法能够得到更为鲁棒的Pareto最优解。     

迭代粒子群算法及其在间歇过程鲁棒优化中的应用

针对无状态独立约束和终端约束的间歇过程鲁棒优化问题，将迭代方法与粒子群优化算法相结合，提出了迭代粒子群算法．对于该算法，首先将控制变量离散化，用标准粒子群优化算法搜索离散控制变量的最优解．然后在随后的迭代过程中将基准移到刚解得的最优值处，同时收缩控制变量的搜索域，使优化性能指标和控制轨线在迭代过程中不断趋于最优解．算法简洁、可行、高效，避免了求解大规模微分方程组的问题．对一个间歇过程的仿真结果证明了迭代粒子群算法可以有效地解决无状态独立约束和终端约束的间歇过程鲁棒优化问题．     

基于混合粒子群算法的动态鲁棒优化

动态鲁棒优化问题广泛存在于各个领域,且难以求解。动态鲁棒粒子群优化(PSO)算法是一种有效的求解方法。但是,现有算法存在全局搜索能力弱和无法对个体进行综合评价的问题。为有效求解动态鲁棒优化问题,在研究的基础上提出一种混合差分进化的动态鲁棒粒子群(DRPSO-DE)算法。该算法不仅使用差分进化(DE)算法的变异策略提升粒子群算法的全局搜索能力,还提出一种综合指标来对种群个体进行评价。此外,为提高动态鲁棒粒子群算法的搜索效率,采用一种基于排序的选择策略挑选最佳个体,并将它们用于指引种群进化。为验证DRPSO-DE的有效性,选取五个动态标准测试函数对其进行测试。从试验结果来看,所提出算法的整体性能要优于原有算法,能够有效求解动态鲁棒优化问题。     

吸引子权重改变内嵌区域震荡搜索粒子群算法

针对粒子群算法搜索精度不高、搜索最优解较慢的问题,提出了一种改进的粒子群算法。该算法通过调整全局最优解和个体最优解,形成一个新的全局吸引子解指导粒子收敛,优化种群粒子来搜索解空间的最优值。再将优化方案融入到内嵌区域震荡搜索的粒子群算法（RSPSO）中,仿真结果表明,改进的粒子群算法在寻优能力及搜索精度方面都得到了进一步的提高。     

多向学习自适应的粒子群算法

粒子群优化算法（PSO）是一种群体智能算法,通过粒子间的竞争和协作以实现在复杂搜索空间中寻找全局最优点。但基本PSO算法存在进化后期收敛速度慢、易陷入局部最优点的缺点,提出了一种多向学习型的粒子群优化算法,该算法中粒子通过同时追随自己找到的最优解、随机的其他粒子同维度的最优解和整个群的最优解来完成速度更新,通过判别区域边界来完成位置优化更新,通过对全局最优位置进行小范围扰动,以增强算法跳出局部最优的能力。对几种典型函数的测试结果表明：改进后的粒子群算法明显改善了全局搜索能力,并且能够有效避免早熟收敛问题。算法使高维优化问题中全局最优解相对搜索空间位置的鲁棒性得到了明显提高,适合于求解同类问题,计算结果能满足实际工程的要求。     

一种改进的禁忌-粒子群算法及应用

针对粒子群优化算法(PSO)的局部搜索能力差和存在早熟收敛的问题,将禁忌搜索(TS)思想融入到粒子群算法中,提出一种新的禁忌搜索的粒子群优化算法.新算法结合了PSO和TS各自的优点,在寻优前期利用粒子群算法得到较好的初始值,同时将个体极值pbest放人禁忌表,在寻优后期,当粒子的搜索能力减弱时,利用禁忌搜索算法中禁忌表的短期记忆功能,使其跳出局部最优解,并且在搜索过程中允许接受劣解.将改进的算法应用于函数的优化,仿真结果表明,改进算法具有计算精度高、稳定性强的特点,是一种非常有效的计算智能方法.     

多目标进化算法搜索鲁棒最优解效率研究

鲁棒最优解是进化计算研究的重要方面,同时也是研究难点。多目标进化算法搜索鲁棒最优解时,通常要用蒙特卡罗积分（MCI）近似估计有效目标函数（EOF）,而已有求解方法近似精度不高,使得算法搜索鲁棒最优解的性能较差。提出用拟蒙特卡罗方法（Q-MC）来估计有效目标函数方法,其所引入的Q-MC方法——Korobov点阵能更精确地估计EOF。实验结果表明,与现有的原始蒙特卡罗方法（C-MC）相比,拟蒙特卡罗方法（Q-MC）可以较大地提高多目标进化算法搜索鲁棒最优解的效率。     

粒子群Memetic算法求解多峰函数优化

针对目前多峰函数优化问题较难找到全部局部最优解的情况,提出了一种粒子群Memetic算法。算法结合了粒子群优化的全局搜索能力和爬山法的局部搜索能力,增强了算法搜索最优解的能力。实验结果表明,该算法求解精度较高,且收敛速度较快。     

带自适应感知能力的粒子群优化算法

提出一种求解约束优化问题的改进粒子群优化算法。它利用可行性判断规则处理约束条件,更新个体最优解和全局最优解。通过为粒子赋予自适应感知能力,算法能较好地平衡全局和局部搜索,且有能力跳出局部极值,防止早熟。边界附近粒子的感知结果被用来修正其飞行速度以加强算法对约束边界的搜索。实验结果表明,新算法收敛速度快,寻优能力强,能很好地求解约束优化问题。     

一种改进的多目标粒子群优化算法及其应用

为提高多目标粒子群优化 (MOPSO)算法处理多目标优化问题的性能, 降低计算复杂度, 改善算法的收敛性, 提出了一种改进的多目标粒子群优化算法。通过运用比例分布及跳数改进机制策略的方法, 使该算法不仅继承了MOPSO算法的优点, 而且具有很强的局部搜索能力和较好的鲁棒性能, 使非劣解集均匀分布, 尽可能逼近真实的非劣前沿。通过对多连杆悬架空间结构硬点的多目标优化, 进一步验证了该算法的实用性及其优越性。     

基于正交设计求解动态鲁棒问题的新算法*

设计了一个基于正交设计法求解动态鲁棒优化问题的新算法(RODEA).该算法把目标搜索区域划分成很多小邻域(小生境),每个小生境都有一个代表,对每个小生境用正交设计法(构造正交矩阵进行抽样)搜索可能成为小生境代表的潜在优解.还设计了一个基准测试函数用来测试动态鲁棒优化问题.实验数据表明RODEA用来求解动态鲁棒问题具有很好的效果.     

Noise analysis compact differential evolution

This article proposes a compact algorithm for optimisation in noisy environments. This algorithm has a compact structure and employs differential evolution search logic. Since it is a compact algorithm, it does not store a population of solutions but a probabilistic representation of the population. This kind of algorithmic structure can be implemented in those real-world problems characterized by memory limitations. The degree of randomization contained in the compact structure allows a robust behaviour in the presence of noise. In addition the proposed algorithm employs the noise analysis survivor selection scheme. This scheme performs an analysis of the noise and automatically performs a re-sampling of the solutions in order to ensure both reliable pairwise comparisons and a minimal cost in terms of fitness evaluations. The noise analysis component can be reliably used in noise environments affected by Gaussian noise which allow an a priori analysis of the noise features. This situation is typical of problems where the fitness is computed by means of measurement devices. An extensive comparative analysis including four different noise levels has been included. Numerical results show that the proposed algorithm displays a very good performance since it regularly succeeds at handling diverse fitness landscapes characterized by diverse noise amplitudes.     

Maximal covering location problem (MCLP) with fuzzy travel times

This paper presents a fuzzy maximal covering location problem (FMCLP) in which travel time between any pair of nodes is considered to be a fuzzy variable. A fuzzy expected value maximization model is designed for such a problem. Moreover, a hybrid algorithm of fuzzy simulation and simulated annealing (SA) is used to solve FMCLP. Some numerical examples are presented, solved and analyzed to show the performance of the proposed algorithm. The results show that the proposed SA finds solutions with objective values no worse than 1.35% below the optimal solution. Furthermore, the simulation-embedded simulated annealing is robust in finding solutions.     

Self-adaptive fitness formulation for constrained optimization

A self-adaptive fitness formulation is presented for solving constrained optimization problems. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions. The performance of the method has been examined by its application to a set of eleven test cases from the specialized literature. The results have been compared with previously published results from the literature. It is shown that the method is able to find the optimum solutions. The proposed method requires no parameter tuning and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution.     

Periodical switching between related goals for improving evolvability to a fixed goal in multi-objective problems

Evolutionary computation plays a principal role in intelligent design automation. Evolutionary approaches have discovered novel and patentable designs. Nonetheless, evolutionary techniques may lead to designs that lack robustness. This critical issue is strongly connected to the concept of evolvability. In nature, highly evolvable species tend to be found in rapidly changing environments. Such species can be considered robust against environmental changes. Consequently, to create robust engineering designs it could be beneficial to use variable, rather than fixed, fitness criteria. In this paper, we study the performance of an evolutionary programming algorithm with periodical switching between goals, which are selected randomly from a set of related goals. It is shown by a dual-objective filter optimization example that altering goals may improve evolvability to a fixed goal by enhancing the dynamics of solution population, and guiding the search to areas where improved solutions are likely to be found. Our reference algorithm with a single goal is able to find solutions with competitive fitness, but these solutions are results of premature convergence, because they are poorly evolvable. By using the same algorithm with switching goals, we can extend the productive search length considerably; both the fitness and robustness of such designs are improved.     

Evolutionary robust optimization in production planning – interactions between number of objectives,sample size and choice of robustness measure

We aim to find robust solutions in optimization settings where there is uncertainty associated with the operating/environmental conditions, and the fitness of a solution is hence best described by a distribution of outcomes. In such settings, the nature of the fitness distribution (reflecting the performance of a particular solution across a set of operating scenarios) is of potential interest in deciding solution quality, and previous work has suggested the inclusion of robustness as an additional optimization objective. However, there has been limited investigation of different robustness criteria, and the impact this choice may have on the sample size needed to obtain reliable fitness estimates. Here, we investigate different single and multi-objective formulations for robust optimization, in the context of a real-world problem addressed via simulation-based optimization. For the (limited evaluation) setting considered, our results highlight the value of an explicit robustness criterion in steering an optimizer towards solutions that are not only robust (as may be expected), but also associated with a profit that is, on average, higher than that identified by standard single-objective approaches. We also observe significant interactions between the choice of robustness measure and the sample size employed during fitness evaluation, an effect that is more pronounced for our multi-objective models.     

面向多目标优化的适应度共享免疫克隆算法

多目标优化的日标在于使得解集能够快速的逼近真实Pareto前沿.针对解的分布性问题,以免疫克隆算法为框架,引入适应度共享策略,提出了一种新的具有良好分布性保持的多目标优化进化算法;算法建立外部群体以保存非支配解,以Pareto优和共亨适应度作为外部群体更新与激活抗体选择的双重标准.为了增强算法对决策空间的开发能力,引入...     

Robust validity index for a modified subtractive clustering algorithm

A novel robust validity index is proposed for subtractive clustering (SC) algorithm. Although the SC algorithm is a simple and fast data clustering method with robust properties against outliers and noise; it has two limitations. First, the cluster number generated by the SC algorithm is influenced by a given threshold. Second, the cluster centers obtained by SC are based on data that have the highest potential values but may not be the actual cluster centers. The validity index is a function as a measure of the fitness of a partition for a given data set. To solve the first problem, this study proposes a novel robust validity index that evaluates the fitness of a partition generated by SC algorithm in terms of three properties: compactness, separation and partition index. To solve the second problem, a modified algorithm based on distance relations between data and cluster centers is designed to ascertain the actual centers generated by the SC algorithm. Experiments confirm that the preferences of the proposed index outperform all others.     

An efficient differential evolution using speeded-up k-nearest neighbor estimator

In evolutionary algorithm, one of the main issues is how to reduce the number of fitness evaluations required to obtain optimal solutions. Generally a large number of evaluations are needed to find optimal solutions, which leads to an increase of computational time. Expensive cost may have to be paid for fitness evaluation as well. Differential evolution (DE), which is widely used in many applications due to its simplicity and good performance, also cannot escape from this problem. In order to solve this problem a fitness approximation model has been proposed so far, replacing real fitness function for evaluation. In fitness approximation, an ability to estimate accurate value with compact structure is needed for good performance. Therefore in this paper we propose an efficient differential evolution using fitness estimator. We choose k-nearest neighbor (kNN) as fitness estimator because it does not need any training period or complex computation. However too many training samples in the estimator may cause computational complexity to be exponentially high. Accordingly, two schemes with regard to accuracy and efficiency are proposed to improve the estimator. Our proposed algorithm is tested with various benchmark functions and shown to find good optimal solutions with less fitness evaluation and more compact size, compared with DE and DE-kNN.