An improved krill herd algorithm with global exploration capability for solving numerical function optimization problems and its application to data clustering

Krill herd algorithm is a stochastic nature-inspired algorithm for solving optimization problems. The performance of krill herd algorithm is degraded by poor exploitation capability. In this study, we propose an improved krill herd algorithm (IKH) by making the krill the global search capability. The enhancement comprises of adding global search operator for exploration around the defined search region and thus the krill individuals move towards the global best solution. The elitism strategy is also applied to maintain the best krill during the krill update steps. The proposed method is tested on a set of twenty six well-known benchmark functions and is compared with thirteen popular optimization algorithms, including original KH algorithm. The experimental results show that the proposed method produced very accurate results than KH and other compared algorithms and is more robust. In addition, the proposed method has high convergence rate. The high performance of the proposed algorithm is then employed for data clustering problems and is tested using six real datasets available from UCI machine learning laboratory. The experimental results thus show that the proposed algorithm is well suited for solving even data clustering problems.     

Hybrid krill herd algorithm with differential evolution for global numerical optimization

In order to overcome the poor exploitation of the krill herd (KH) algorithm, a hybrid differential evolution KH (DEKH) method has been developed for function optimization. The improvement involves adding a new hybrid differential evolution (HDE) operator into the krill, updating process for the purpose of dealing with optimization problems more efficiently. The introduced HDE operator inspires the intensification and lets the krill perform local search within the defined region. DEKH is validated by 26 functions. From the results, the proposed methods are able to find more accurate solution than the KH and other methods. In addition, the robustness of the DEKH algorithm and the influence of the initial population size on convergence and performance are investigated by a series of experiments.     

基于近邻套索算子的磷虾群算法

针对标准磷虾群算法（KH）在求解复杂函数优化问题时局部搜索能力差,开采能力不足的问题,提出了一种基于近邻套索算子的磷虾群算法（NLKH）。该算法将一种新的近邻套索算子加入了标准磷虾群算法,使得处理复杂函数优化问题更加有效。近邻套索算子通过比较磷虾个体之间的欧式距离来选取目标磷虾对,然后通过在优质个体附近加速操作产生新磷虾个体和剔除劣质磷虾个体的方式,提高了磷虾个体局部搜索的能力。通过比较PSO算法、KH算法、KHLD算法、NLKH算法在10个测试函数上的结果表明,NLKH算法相较于PSO算法、KH算法和KHLD算法有着更强全局搜索能力,寻优精度更高,收敛速度更快,稳定性更好。并且NLKH算法相较于KH算法和KHLD算法有着更强的局部勘测能力,开采能力更强。     

基于动态压力控制算子的磷虾群算法

针对基础磷虾群（KH）算法在求解复杂函数优化问题时局部搜索能力差、求解精度低、收敛速度慢、容易陷入局部最优等问题,提出一种基于动态压力控制算子的磷虾群算法（DPCKH）。该算法将一种新的动态压力控制算子加入了标准磷虾群算法,使其处理复杂函数优化问题更有效。动态压力控制算子通过欧氏距离量化了多个不同优秀个体对目标个体的诱导效应,进而在优秀个体附近加速产生新磷虾个体,提高了磷虾个体的局部探索能力。通过比较蚁群算法（ACO）、差分进化算法（DE）、磷虾群算法（KH）、改进的磷虾群算法（KHLD）和粒子群算法（PSO）,DPCKH算法在7个测试函数上的结果表明,DPCKH算法与ACO算法、DE算法、KH算法、KHLD算法和PSO算法相比有着更强的局部勘测能力,其开采能力更强。     

基于广义反向学习的磷虾群算法及其在数据聚类中的应用

针对磷虾群（KH）算法在寻优过程中因种群多样性降低而过早收敛的问题，提出基于广义反向学习的磷虾群算法GOBL-KH。首先，通过余弦递减策略确定步长因子平衡算法的探索与开发能力；然后，加入广义反向学习策略对每个磷虾进行广义反向搜索，增强磷虾探索其周围邻域空间的能力。将改进的算法在15个经典测试函数上进行测试并与KH算法、步长线性递减的磷虾群（KHLD）算法和余弦递减步长的磷虾群（KHCD）算法比较，实验结果表明:GOBL-KH算法可有效避免早熟且具有较高的求解精度。为体现算法有效性，将GOBL-KH算法与K均值算法结合提出HK-KH算法用于解决数据聚类问题，即在每次迭代后用最优个体或经过K均值迭代一次后的新个体替换最差个体，使用UCI五个真实数据集进行测试并与K均值、遗传算法（GA）、粒子群优化（PSO）算法、蚁群算法（ACO）、KH算法、磷虾群聚类算法（KHCA）、改进磷虾群（IKH）算法进行比较，结果表明:HK-KH算法适用于解决数据聚类问题且具有较强的全局收敛性和较高的稳定性。     

基于对立搜索和混沌变异的磷虾觅食优化算法

针对磷虾觅食算法存在容易陷入局部极值、收敛速度慢的问题, 提出一种新的改进算法. 首先, 给出启发式二次对立点的定义并证明其性能优势, 进而构造一种启发式二次对立搜索算子, 以加快算法的收敛速度, 提高全局探索能力; 然后, 采用分段线性混沌映射(PWLCM) 混沌函数构造一种变尺度混沌变异算子, 以增强算法跳出局部极值的能力. 仿真实验表明, 所提出算法能有效避免陷入局部极值, 在收敛速度和寻优精度上得到大幅改善.

     

一种基于改进KH与KHM聚类的混合数据聚类算法

为解决K-means聚类对初始聚类中心敏感和易陷入局部最优的问题,提出一种基于改进磷虾群算法与K-harmonic means的混合数据聚类算法.提出一种具有莱维飞行和交叉算子的磷虾群算法以改进磷虾群算法易陷入局部极值和搜索效率低的不足,即在每次标准磷虾群位置更新后加入新的位置更新方法进一步搜索以提高种群的搜索能力,同时交替使用莱维飞行与交叉算子对当前群体位置进行贪婪搜索以增强算法的全局搜索能力. 20个标准测试函数的实验结果表明,改进算法不易陷入局部最优解,可在较少的迭代次数下有效地搜索到全局最优解的同时保证算法的稳定性.将改进的磷虾群算法与K调和均值聚类融合,即在每次迭代后用最优个体或经过K调和均值迭代一次后的新个体替换最差个体. 5个UCI真实数据集的测试结果表明:融合后的聚类算法能够克服K-means对初始聚类中心敏感的不足且具有较强的全局收敛性.     

基于改进磷虾群算法的服务组合优化

面向服务的架构（SOA）下,针对服务组合优化过程中易陷入局部最优、时间开销大的问题,提出一种加入自适应交叉算子和随机扰动算子的改进磷虾群算法PRKH。首先基于服务质量（QoS）建立了服务组合优化模型,并给出不同结构下QoS的计算公式和归一化处理方法。然后在磷虾群（KH）算法的基础上加入自适应的交叉概率和基于实际偏移量的随机扰动,从而在磷虾群的全局搜索能力和局部搜索能力之间达到良好平衡。最后通过仿真,把所提算法与KH算法、粒子群优化（PSO）算法、人工蜂群（ABC）算法和花朵授粉算法（FPA）进行对比,实验结果表明,PRKH算法能够更快找到QoS更优的复合服务。     

基于磷虾群算法的并网电动汽车功率优化分配

为提高并网电动汽车(EV)集群的功率优化分配效率,提出基于磷虾群算法的EV集群并网两阶段功率高效分配策略。考虑用户的需求差异,将并网EV细化为不可调度集及可调度集,分别建立充放电控制模型,提出可调度集EV的优先权评估指标。采用动态自适应权重策略及余弦递减步长演进策略改进磷虾群(KH)算法,将可调度集EV的优先权映射为迭代算法的演变步长,通过两阶段交互迭代实现并网EV集群的功率高效分配。仿真实验验证了模型的可行性以及所提策略的高效性。     

A hybrid method based on krill herd and quantum-behaved particle swarm optimization

A novel hybrid Krill herd (KH) and quantum-behaved particle swarm optimization (QPSO), called KH–QPSO, is presented for benchmark and engineering optimization. QPSO is intended for enhancing the ability of the local search and increasing the individual diversity in the population. KH–QPSO is capable of avoiding the premature convergence and eventually finding the function minimum; especially, KH–QPSO can make all the individuals proceed to the true global optimum without introducing additional operators to the basic KH and QPSO algorithms. To verify its performance, various experiments are carried out on an array of test problems as well as an engineering case. Based on the results, we can easily infer that the hybrid KH–QPSO is more efficient than other optimization methods for solving standard test problems and engineering optimization problems.     

Pressure regulation inside a hypersonic wind tunnel using H-infinity optimization control

Hypersonic wind tunnel is a ground-based facility used to study the aerodynamic properties of space vehicles during re-entry. This paper aims at designing an H-infinity controller with krill herd optimization algorithm to regulate pressure inside the settling chamber of a hypersonic wind tunnel. The krill herd algorithm is a novel stochastic algorithm for improving the performance characteristics by optimizing the H-infinity controller parameters. The proposed algorithm minimizes the H-infinity norms by tuning the controller weighing function parameters. The dynamic characteristics of the settling chamber pressure with H-infinity and H-infinity control based on krill herd algorithm is studied by numerical simulations. The proposed algorithm is highly efficient and robust in controlling the settling chamber pressure in terms of performance parameters.     

An enhanced pathfinder algorithm for engineering optimization problems

The pathfinder algorithm (PFA) is a new population-based optimizer, it divides the search agents of the algorithm into leaders and followers, imitating the leadership level of the group movement to find the best food area or prey. In PFA, followers follow the new position according to the position of the leader and their own consciousness makes the algorithm easy to fall into local optimum. To overcome this shortcoming, the following stage is complicated in this paper, and the acceptance operator, the exchange operator and the mutation mechanism are introduced into the algorithm. To further balance the mining ability and exploration ability of the algorithm, the article regards the leader as a guide and introduces a guide mechanism. To verify the performance of the improved algorithm, it is applied to nine real-life engineering case problems. The simulation results of the real-life engineering design problems exhibit the superiority of the improved PFA (IMPFA) algorithm in solving challenging problems with constrained and unknown search spaces when compared to the basic PFA algorithm or other available solutions.

     

自适应磷虾群优化Elman神经网络的目标威胁评估

提出一种自适应磷虾群算法,在基本磷虾群算法中引入遗传繁殖机制,并加入进化算子和优化算子构成自适应环节,提高了算法的全局搜索能力和预测精度;通过自适应磷虾群算法对Elman神经网络的初始权值和阈值进行寻优,并在此基础上建立目标威胁评估模型。仿真实验表明,自适应磷虾群优化Elman神经网络既保证了一定的收敛速度,又能够使寻优精度得到明显提升,其对测试集的预测结果优于传统Elman神经网络和基本磷虾群优化Elman神经网络,从而验证了算法模型在目标威胁评估中的可行性、有效性。     

Incorporating mutation scheme into krill herd algorithm for global numerical optimization

Recently, Gandomi and Alavi proposed a robust meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization. To improve the performance of the KH algorithm, harmony search (HS) is applied to mutate between krill during the process of krill updating instead of physical diffusion used in KH. A novel hybrid meta-heuristic optimization approach HS/KH is proposed to solve global numerical optimization problem. HS/KH combines the exploration of harmony search (HS) with the exploitation of KH effectively, and hence, it can generate the promising candidate solutions. The detailed implementation procedure for this improved meta-heuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most cases, the performance of this hybrid meta-heuristic method (HS/KH) is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, HS, KH, PSO, and SGA. The effect of the HS/FA parameters is also analyzed.     

基于种群特征反馈的布谷鸟搜索算法

布谷鸟搜索(CS) 算法是一种新型的生物启发式算法. 为了提高算法对不同优化问题的适应能力, 根据反馈控制原理提出一种基于种群特征反馈的布谷鸟搜索(SFFCS) 算法, 将年龄结构、变异成功率等种群特征作为反馈信息引入算法框架, 动态调节算法参数, 同时引入双进化策略机制和策略选择概率, 加强算法对局部搜索和全局搜索的平衡能力. 对标准测试函数和电力系统最优潮流问题进行数值实验, 实验结果表明, SFFCS 算法具有较好的收敛性能和适应能力, 验证了所提出算法的有效性和工程应用价值.

     

求解约束化工优化问题的混合布谷鸟搜索算法

针对布谷鸟搜索算法存在收敛速度慢和易陷入局部最优等缺陷,提出一种基于Rosenbrock搜索和柯西变异的混合布谷鸟搜索算法用于求解约束化工优化问题。该算法首先采用佳点集方法对鸟窝位置进行初始化,为全局搜索的多样性奠定基础;然后利用Rosenbrock搜索算法对当前最优位置进行局部搜索,以提高算法的收敛速度;最后对当前最优解进行柯西变异以避免算法陷入局部最优。两个约束化工优化问题的实验结果表明了该混合算法的有效性。     

Hybrid clustering analysis using improved krill herd algorithm

In this paper, a novel text clustering method, improved krill herd algorithm with a hybrid function, called MMKHA, is proposed as an efficient clustering way to obtain promising and precise results in this domain. Krill herd is a new swarm-based optimization algorithm that imitates the behavior of a group of live krill. The potential of this algorithm is high because it performs better than other optimization methods; it balances the process of exploration and exploitation by complementing the strength of local nearby searching and global wide-range searching. Text clustering is the process of grouping significant amounts of text documents into coherent clusters in which documents in the same cluster are relevant. For the purpose of the experiments, six versions are thoroughly investigated to determine the best version for solving the text clustering. Eight benchmark text datasets are used for the evaluation process available at the Laboratory of Computational Intelligence (LABIC). Seven evaluation measures are utilized to validate the proposed algorithms, namely, ASDC, accuracy, precision, recall, F-measure, purity, and entropy. The proposed algorithms are compared with the other successful algorithms published in the literature. The results proved that the proposed improved krill herd algorithm with hybrid function achieved almost all the best results for all datasets in comparison with the other comparative algorithms.     

A self-adaptive differential evolution algorithm for continuous optimization problems

This paper proposes a new self-adaptive differential evolution algorithm (DE) for continuous optimization problems. The proposed self-adaptive differential evolution algorithm extends the concept of the DE/current-to-best/1 mutation strategy to allow the adaptation of the mutation parameters. The control parameters in the mutation operation are gradually self-adapted according to the feedback from the evolutionary search. Moreover, the proposed differential evolution algorithm also consists of a new local search based on the krill herd algorithm. In this study, the proposed algorithm has been evaluated and compared with the traditional DE algorithm and two other adaptive DE algorithms. The experimental results on 21 benchmark problems show that the proposed algorithm is very effective in solving complex optimization problems.     

基于改进磷虾群算法的SVDD参数优化

支持向量数据描述（SVDD）是构造单类数据描述的分类算法,惩罚参数[C]和核参数[σ]作为影响SVDD分类效果的关键,其合理选取一直是个难点。针对这一问题,提出了一种基于改进磷虾群算法的SVDD参数优化算法（IKH-SVDD）。依据仿真实验,分析参数[C]和[σ]对描述边界的影响;引入磷虾群算法并分析其优劣,通过在随机扩散行为中定义扰动因子,增强算法的全局搜索能力;将一种新的精英选择和保留策略引入迭代过程,提高算法的收敛精度;将改进的磷虾群算法引入SVDD参数优化过程,构建了IKH-SVDD参数优化模型。基于UCI标准数据库进行实验并与其他几种参数优化算法进行比较,结果表明了IKH-SVDD算法具有更高的分类准确性。     

趋磁性细菌多目标优化算法

提出趋磁性细菌多目标优化算法(MTBMO).该算法以趋磁性细菌优化算法(MBOA)中磁小体(MTSs)的生成机制为基础,设计适用于多目标优化的新型MTSs磁矩调节机制,确保群体的收敛性;同时采用基于混沌变异的替换方法取代MBOA中的磁小体替换机制来增强群体的多样性.通过标准函数测试和与现有多目标优化算法的比较表明,MTBMO对于求解多目标优化问题(MOPs)是可行且有效的.