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.     

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。     

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.     

Improved cat swarm optimization algorithm for solving global optimization problems and its application to clustering

This paper presents a cat swarm optimization (CSO) algorithm for solving global optimization problems. In CSO algorithm, some modifications are incorporated to improve its performance and balance between global and local search. In tracing mode of the CSO algorithm, a new search equation is proposed to guide the search toward a global optimal solution. A local search method is incorporated to improve the quality of solution and overcome the local optima problem. The proposed algorithm is named as Improved CSO (ICSO) and the performance of the ICSO algorithm is tested on twelve benchmark test functions. These test functions are widely used to evaluate the performance of new optimization algorithms. The experimental results confirm that the proposed algorithm gives better results than the other algorithms. In addition, the proposed ICSO algorithm is also applied for solving the clustering problems. The performance of the ICSO algorithm is evaluated on five datasets taken from the UCI repository. The simulation results show that ICSO-based clustering algorithm gives better performance than other existing clustering algorithms.     

Krill herd algorithm based on cuckoo search for solving engineering optimization problems

This paper presents a hybrid krill herd (CSKH) approach to solve structural optimization problems. CSKH improved the Krill herd algorithm (KH) by combining KU/KA operator originated from cuckoo search algorithm (CS) with KH. In CSKH, a greedy selection scheme is used and often overtakes the original KH and CS. In addition, in order to further enhance the assessment of CSKH, a fraction of the worst krill is thrown away and substituted with newly randomly generated ones by KA operator at the end of each generation. The CSKH is applied to five real engineering problems to verify its performance. The experimental results have proven that CSKH algorithm is well capable of solving constrained engineering design problems more efficiently and effectively than the basic CS and KH algorithm.

     

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.     

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.     

CCSA: Conscious Neighborhood-based Crow Search Algorithm for Solving Global Optimization Problems

In this paper, a conscious neighborhood-based crow search algorithm (CCSA) is proposed for solving global optimization and engineering design problems. It is a successful improvement to tackle the imbalance search strategy and premature convergence problems of the crow search algorithm. CCSA introduces three new search strategies called neighborhood-based local search (NLS), non-neighborhood based global search (NGS) and wandering around based search (WAS) in order to improve the movement of crows in different search spaces. Moreover, a neighborhood concept is defined to select the movement strategy between NLS and NGS consciously, which enhances the balance between local and global search. The proposed CCSA is evaluated on several benchmark functions and four applied problems of engineering design. In all experiments, CCSA is compared by other state-of-the-art swarm intelligence algorithms: CSA, BA, CLPSO, GWO, EEGWO, WOA, KH, ABC, GABC, and Best-so-far ABC. The experimental and statistical results show that CCSA is very competitive especially for large-scale optimization problems, and it is significantly superior to the compared algorithms. Furthermore, the proposed algorithm also finds the best optimal solution for the applied problems of engineering design.     

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。     

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.     

HMOSHSSA: a hybrid meta-heuristic approach for solving constrained optimization problems

This paper proposes a novel hybrid multi-objective optimization algorithm named HMOSHSSA by synthesizing the strengths of Multi-objective Spotted Hyena Optimizer (MOSHO) and Salp Swarm Algorithm (SSA). HMOSHSSA utilizes the exploration capability of MOSHO to explore the search space effectively and leader and follower selection mechanism of SSA to achieve global best solution with faster convergence. The proposed algorithm is evaluated on 24 benchmark test functions, and its performance is compared with seven well-known multi-objective optimization algorithms. The experimental results demonstrate that HMOSHSSA acquires very competitive results and outperforms other algorithms in terms of convergence speed, search-ability and accuracy. Additionally, HMOSHSSA is also applied on seven well-known engineering problems to further verify its efficacy. The results reveal the effectiveness of proposed algorithm toward solving real-life multi-objective optimization problems.

     

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.     

Krill herd algorithm for optimal location of distributed generator in radial distribution system

Distributed generator (DG) is recognized as a viable solution for controlling line losses, bus voltage, voltage stability, etc. and represents a new era for distribution systems. This paper focuses on developing an approach for placement of DG in order to minimize the active power loss and energy loss of distribution lines while maintaining bus voltage and voltage stability index within specified limits of a given power system. The optimization is carried out on the basis of optimal location and optimal size of DG. This paper developed a new, efficient and novel krill herd algorithm (KHA) method for solving the optimal DG allocation problem of distribution networks. To test the feasibility and effectiveness, the proposed KH algorithm is tested on standard 33-bus, 69-bus and 118-bus radial distribution networks. The simulation results indicate that installing DG in the optimal location can significantly reduce the power loss of distributed power system. Moreover, the numerical results, compared with other stochastic search algorithms like genetic algorithm (GA), particle swarm optimization (PSO), combined GA and PSO (GA/PSO) and loss sensitivity factor simulated annealing (LSFSA), show that KHA could find better quality solutions.     

Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization

The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail.     

Evolutionary state-based novel multi-objective periodic bacterial foraging optimization algorithm for data clustering

Clustering divides objects into groups based on similarity. However, traditional clustering approaches are plagued by their difficulty in dealing with data with complex structure and high dimensionality, as well as their inability in solving multi-objective data clustering problems. To address these issues, an evolutionary state-based novel multi-objective periodic bacterial foraging optimization algorithm (ES-NMPBFO) is proposed in this article. The algorithm is designed to alleviate the high-computing complexity of the standard bacterial foraging optimization (BFO) algorithm by introducing periodic BFO. Moreover, two learning strategies, global best individual (gbest) and personal historical best individual (pbest), are used in the chemotaxis operation to enhance the convergence speed and guide the bacteria to the optimum position. Two elimination-dispersal operations are also proposed to prevent falling into local optima and improve the diversity of solutions. The proposed algorithm is compared with five other algorithms on six validity indexes in two data clustering cases comprising nine general benchmark datasets and four credit risk assessment datasets. The experimental results suggest that the proposed algorithm significantly outperforms the competing approaches. To further examine the effectiveness of the proposed strategies, two variants of ES-NMPBFO were designed, and all three forms of ES-NMPBFO were tested. The experimental results show that all of the proposed strategies are conducive to the improvement of solution quality, diversity and convergence.     

Improved global-best-guided particle swarm optimization with learning operation for global optimization problems

In this paper, an improved global-best-guided particle swarm optimization with learning operation (IGPSO) is proposed for solving global optimization problems. The particle population is divided into current population, historical best population and global best population, and each population is assigned a corresponding searching strategy. For the current population, the global neighborhood exploration strategy is employed to enhance the global exploration capability. A local learning mechanism is used to improve local exploitation ability in the historical best population. Furthermore, stochastic learning and opposition based learning operations are employed to the global best population for accelerating convergence speed and improving optimization accuracy. The effects of the relevant parameters on the performance of IGPSO are assessed. Numerical experiments on some well-known benchmark test functions reveal that IGPSO algorithm outperforms other state-of-the-art intelligent algorithms in terms of accuracy, convergence speed, and nonparametric statistical significance. Moreover, IGPSO performs better for engineering design optimization problems.     

一类求解最大独立集问题的混合神经演化算法

提出一类求解最大独立集问题(MIS)的混合型神经演化算法．该算法基于空间剖分与“排除”策略，有效综合了神经网络快速收敛及遗传算法稳健全局搜索的特别优点．与标准遗传算法和神经网络算法相比，该算法显示了极高的全局优化性态与计算效率．     

A novel quasi-oppositional chaotic antlion optimizer for global optimization

This paper proposes a novel quasi-oppositional chaotic antlion optimizer (ALO) (QOCALO) for solving global optimization problems. ALO is a population based algorithm motivated by the unique hunting behavior of antlions in nature and exhibits strong influence in solving global and engineering optimization problems. In the proposed QOCALO algorithm of the present work, the initial population is generated using the quasi-opposition based learning (QOBL) and the concept of QOBL based generation jumping is utilized inside the main searching strategy of the proposed algorithm. Utilization of QOBL ensures better convergence speed of the proposed algorithm and it also provides better exploration of the search space. Alongside the QOBL, a chaotic local search (CLS) is also incorporated in the proposed QOCALO algorithm. The CLS guides local search around the global best solution that provides better exploitation of the search space. Thus, a better trade-off between exploration and exploitation holds for the proposed algorithm which makes it robust. It is observed that the proposed algorithm offers better results than the original ALO in terms of solution quality and convergence speed. The proposed QOCALO algorithm is implemented and tested, successfully, on nineteen mathematical benchmark test functions of varying complexities and the experimental results are compared to those offered by the basic ALO and some other recently developed nature inspired algorithms. The efficacy of the proposed algorithm is further utilized to solve three real world engineering optimization problems viz. (a) the placement and sizing problem of distributed generators in radial distribution networks, (b) the congestion management problem in power transmission system and (c) the optimal design of pressure vessel.     

Modified firefly algorithm for multidimensional optimization in structural design problems

An enhanced nature-inspired metaheuristic optimization algorithm, called the modified firefly algorithm (MFA) is proposed for multidimensional structural design optimization. The MFA incorporates metaheuristic components, namely logistic and Gauss/mouse chaotic maps, adaptive inertia weight, and Lévy flight with a conventional firefly algorithm (FA) to improve its optimization capability. The proposed MFA has several advantages over its traditional FA counterpart. Logistic chaotic maps provide a diverse initial population. Gauss/mouse maps allow the tuning of the FA attractiveness parameter. The adaptive inertia weight controls the local exploitation and the global exploration of the search process. Lévy flight is used in the exploitation of the MFA. The proposed MFA was evaluated by comparing its performance in solving a series of benchmark functions with those of the FA and other well-known optimization algorithms. The efficacy of the MFA was then proven by its solutions to three multidimensional structural design optimization problems; MFA yielded the best solutions among the observed algorithms. Experimental results revealed that the proposed MFA is more efficient and effective than the compared algorithms. Therefore, the MFA serves as an alternative algorithm for solving multidimensional structural design optimization problems.