Feedback controlled particle swarm optimization and its application in time-series prediction

Particle swarm optimization (PSO) algorithm is an algorithmic technique for optimization by solving a wide range of optimization problems. This paper presents a new approach of extending PSO to solve optimization problems by using the feedback control mechanism (FCPSO). The proposed FCPSO consists of two major steps. First, by evaluating the fitness value of each particle, a simple particle evolutionary fitness function is designed to control parameters involving acceleration coefficient, refreshing gap, learning probabilities and number of the potential exemplars automatically. By such a simple particle evolutionary fitness function, each particle has its own search parameters in a search environment. Secondly, a local learning method using a competitive penalized method is developed to refine the solution. The FCPSO has been comprehensively evaluated on 18 unimodal, multimodal and composite benchmark functions with or without rotation. Compared with various state-of-the-art algorithms, including traditional PSO algorithms and representative variants of PSO algorithms, the performance of FCPSO is promising. The effects of parameter adaptation, parameter sensitivity and local search method are studied. Lastly, the proposed FCPSO is applied to constructing a radial basis neural network, together with the K-means method for time-series prediction.     

Locating and tracking multiple dynamic optima by a particle swarm model using speciation

This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment. In the proposed species-based particle swam optimization (SPSO), the swarm population is divided into species subpopulations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population, and then adopted as neighborhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize toward multiple optima, regardless of whether they are global or local optima. Our experiments on using the SPSO to locate multiple optima in a static environment and a dynamic SPSO (DSPSO) to track multiple changing optima in a dynamic environment have demonstrated that SPSO is very effective in dealing with multimodal optimization functions in both environments.     

动态多目标免疫算法及其应用

基于生物免疫系统的机理及功能,提出一种动态多目标免疫算法。利用抗体的被控度及浓度设计抗体的亲和力。用环境记忆池保存优秀抗体,并依抗体浓度更新。记忆细胞参与相似或相同环境初始抗体群的生成。借助动态多目标测试问题,与同类算法仿真比较,结果表明,该算法较其他算法表现出更好的性能,能快速跟踪动态Pareto面且分布均匀,具有较强的求解实际动态问题的能力。     

一类带约束动态多目标优化问题的进化算法

动态多目标约束优化问题是一类NP-Hard问题,定义了动态环境下进化种群中个体的序值和个体的约束度,结合这两个定义给出了一种选择算子.在一种环境变化判断算子下给出了求解环境变量取值于正整数集Z+的一类带约束动态多目标优化问题的进化算法.通过几个典型的Benchmark函数对算法的性能进行了测试,其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集.     

基于GA的网络最短路径多目标优化算法研究

针对现有基于遗传算法(GA)优化的网络最短路径算法存在优化目标单一、遗传编码质量低、搜索策略间平衡性差、适应度分配效率与灵活性较低等问题,建立一种多目标优化最短路径自适应GA模型,提出了优先级编码和优先级索引交叉算子,引入了遗传算子参数的模糊控制机制和基于自适应加权的适应度分配方法.实验结果表明,该算法的准确性和稳定性高、复杂度合理,实现了对网络设计优化中多目标最短路径问题的高质量求解.     

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。     

A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems

This paper proposes a self-organized speciation based multi-objective particle swarm optimizer (SS-MOPSO) to locate multiple Pareto optimal solutions for solving multimodal multi-objective problems. In the proposed method, the speciation strategy is used to form stable niches and these niches/subpopulations are optimized to search and maintain Pareto-optimal solutions in parallel. Moreover, a self-organized mechanism is proposed to improve the efficiency of the species formulation as well as the performance of the algorithm. To maintain the diversity of the solutions in both the decision and objective spaces, SS-MOPSO is incorporated with the non-dominated sorting scheme and special crowding distance techniques. The performance of SS-MOPSO is compared with a number of the state-of-the-art multi-objective optimization algorithms on fourteen test problems. Moreover, the proposed SS-MOSPO is also employed to solve a real-life problem. The experimental results suggest that the proposed algorithm is able to solve the multimodal multi-objective problems effectively and shows superior performance by finding more and better distributed Pareto solutions.     

一种求解多目标组合优化的遗传局部搜索算法

为改善遗传算法求解多目标组合优化问题的搜索效率,提出一种新的遗传局部搜索算法.算法采取非劣解并行局部搜索策略以及基于分散度的精英选择策略,并采用基于NSGA-Ⅱ的适应度赋值方式和二元赌轮选择操作,以提高算法收敛性,保持群体多样性.实验结果表明,新算法能够产生数量较多分布较广的近似Pareto最优解.     

Achieving balance between proximity and diversity in multi-objective evolutionary algorithm

Currently, an alternative framework using the hypervolume indicator to guide the search for elite solutions of a multi-objective problem is studied in the evolutionary multi-objective optimization community very actively, comparing to the traditional Pareto dominance based approach. In this paper, we present a dynamic neighborhood multi-objective evolutionary algorithm based on hypervolume indicator (DNMOEA/HI), which benefits from both Pareto dominance and hypervolume indicator based frameworks. DNMOEA/HI is featured by the employment of hypervolume indicator as a truncation operator to prune the exceeded population, while a well-designed density estimator (i.e., tree neighborhood density) is combined with the Pareto strength value to perform fitness assignment. Moreover, a novel algorithm is proposed to directly evaluate the hypervolume contribution of a single individual. The performance of DNMOEA/HI is verified on a comprehensive benchmark suite, in comparison with six other multi-objective evolutionary algorithms. Experimental results demonstrate the efficiency of our proposed algorithm. Solutions obtained by DNMOEA/HI well approach the Pareto optimal front and are evenly distributed over the front, simultaneously.     

解决多目标优化问题的拟态物理学优化算法

提出一种解决多目标优化问题的多目标拟态物理学优化(MOAPO)算法。该算法利用为每个目标赋予随机权重的方法求得全局总目标,由此选取全局最好及最差适应值,并利用拟态物理学优化算法实现对Pareto最优解集的搜索。通过3个典型多目标优化测试函数对MOAPO和MOPSO进行比较,结果表明了MOAPO算法的有效性,特别是在保持解集分布性方面具有较好的性能。     

Application of dynamic neighborhood small population particle swarm optimization for reconfiguration of shipboard power system

In all-electric navy ships, severe damage or faults may occur during different conditions. As a result, critical loads may suffer from power deficiencies, ultimately leading to a complete system collapse. Therefore, a fast reconfiguration of shipboard power system (SPS) is necessary to serve the critical loads. This work proposes a novel swarm intelligent algorithm based on dynamic neighborhood small population particle swarm optimization (PSO) (DNSPPSO). DNSPPSO is a variant of PSO having fewer numbers of particles and regenerating new solutions within the search space every few iterations. This concept of regeneration in DNSPPSO makes the algorithm fast and greatly enhances its capability. Meanwhile, this algorithm can handle multi-objective problem effectively by using dynamic neighborhood strategy. This technique sorts the objectives and evaluates objectives one by one but retaining the global best solution and fitness so far. Therefore, the strategy converts the multi-objective problem into a single objective optimization problem. The strength of the proposed reconfiguration strategy is demonstrated by an 8-bus test example in Matlab environment comparing with discrete PSO (DPSO), small population PSO (SPPSO) and NSGA-II.     

动态多目标优化进化算法及性能分析

针对动态多目标优化问题提出了一种求解的新进化算法。首先,构建了一种近似估计新环境下动态多目标优化问题的Pareto核迁移估计模型。其次,当探测到问题环境发生改变时,算法利用以前环境搜索到的Pareto核的有效信息通过Pareto核迁移估计模型对新环境下的进化种群进行近似估计;当问题的环境未发生变化时,引入了带区间分割的变异算子和非劣解存档保优策略,以提高算法的搜索效率。最后计算机仿真表明新算法对动态多目标优化问题十分有效。     

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.     

一种基于拟态物理学优化的多目标优化算法

提出一种使用拟态物理学优化(APO)解决多目标优化问题的算法(MOAPO).根据多目标优化问题的特点,借鉴聚集函数法的思想,利用APO算法实现了对多目标优化问题中Pareto最优解集的搜索,并且在搜索过程中动态调整惯性权重与引力因子,以增强非劣解的多样性.实验结果表明了将APO应用于多目标优化问题的有效性.通过与基于微粒群优化(PSO)的多目标优化算法及NSGA-Ⅱ算法的比较,表明了MOAPO算法具有较好的分布性.     

云环境下基于DO-GAPSO的任务调度算法

为了找到合理的云计算任务调度方案,仅从单一方面来优化调度策略已不能满足用户需求,但从多个方面优化调度策略又面临着权重分配问题。针对上述问题,从任务完成时间、任务完成成本、服务质量3个方面考虑,提出一种基于遗传与粒子群算法相融合的动态目标任务调度算法,在算法的适应度评价函数建模中引入线性权重动态分配策略。通过CloudSim平台进行云环境仿真实验,并将此算法与经典的双适应遗传算法(DFGA)、离散粒子群优化算法(DPSO)进行比较。实验结果表明,在相同的设置条件下,该算法在执行效率、寻优能力等方面优于其他两个算法,是一种云计算环境下有效的任务调度算法。     

多模态多目标差分进化算法求解非线性方程组

针对当前算法在求解非线性方程组时面临解的个数不完整、精确度不高、收敛速度慢等问题进行了研究,提出一种多模态多目标差分进化算法。首先将非线性方程组转换为多模态多目标优化问题,初始化一个随机种群并对种群中全部个体进行评价;然后通过非支配解排序和决策空间拥挤距离选择机制,挑选种群中的一半优质个体进行变异;接着在变异过程中采用一种新的变异策略和边界处理方法以增加解的多样性;最后通过交叉和选择机制使优质个体进行进化,直到搜索到全部最优解。在所选测试函数集和工程实例上的实验结果表明,该算法能有效地搜索到非线性方程组的解,并通过与当前四个算法进行比较,该算法在解的数量和成功率上具有优越性。     

DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems

The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [Hernández-Díaz AG, Santana-Quintero LV, Coello Coello C, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough set theory. In: 2006 genetic and evolutionary computation conference (GECCO’2006). Seattle, Washington, USA: ACM Press; July 2006], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.     

A single front genetic algorithm for parallel multi-objective optimization in dynamic environments

This paper proposes a new parallel evolutionary procedure to solve multi-objective dynamic optimization problems along with some measures to evaluate multi-objective optimization in dynamic environments. These dynamic optimization problems appear in quite different real-world applications with actual socio-economic relevance. In these applications, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online whilst the size of the changes is unknown. Although parallel processing could be very useful in these problems to meet the solution quality requirements and constraints, to date, not many parallel approaches have been reported in the literature. Taking this into account, we introduce a multi-objective optimization procedure for dynamic problems that are based on PSFGA, a parallel evolutionary algorithm previously proposed by us for multi-objective optimization. It uses an island model where a process divides the population among the remaining processes and allows the communication and coordination among the subpopulations in the different islands. The proposed algorithm makes an exclusive use of non-dominating individuals for the selection and variation operator and applies a crowding mechanism to maintain the diversity and the distribution of the solutions in the Pareto front. We also propose a model to understand the benefits of parallel processing in multi-objective problems and the speedup figures obtained in our experiments.     

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.     

基于分类的多策略预测方法求解动态多目标优化问题

实际生活中存在很多动态多目标优化问题,一旦环境发生变化,就要求进化算法能快速地跟踪优化问题随时间移动的Pareto前沿或Pareto解集.对此,提出一种基于分类的多策略预测方法(CMSP).首先,利用优化得到的近似最优解来检测Pareto解集(PS)的变化类型:不变、平移和其他.然后,针对不同的变化类型,采取不同的应对策略:若为不变,则保留精英个体,并保证多样性;若为平移,则对最优解集的中心点建立时间序列,通过预测梯度策略更新种群,将预测的个体与从旧种群中保留下来的个体进行比较,以保证预测的准确性;若为其他,则对多个特殊点建立时间序列以预测新环境中个体的位置.最后,引入种群保留策略和记忆恢复策略,有利于更充分地利用历史信息.实验结果表明,CMSP可以很好地进行动态多目标优化.