Local Optima Issues Research Articles

Multi-Search Strategy-based Improved Water Flow Optimizer Algorithm for Cluster Analysis

Clustering is a popular technique that has proven its capability in diverse fields like data analytics, business intelligence, social mining, image recognition, document clustering and bioinformatics. This technique determines the valuable information from a pre-defined set of data and groups similar information into the same cluster. In literature, many algorithms have been presented based on several clustering approaches. It is observed that partitional clustering algorithms are widely popular due to there simplicity and easy implementation such as k-means, k-medoids, and k-harmonic means. However, traditional algorithms suffer from several limitations like being trapped in local optima and depending on the initial solution quality. Heuristic algorithms are also proposed to alleviate the problems of traditional clustering algorithms. But, sometimes, these algorithms also get stuck in local minima and exhibit a lack of balance between search mechanisms. Hence, this work presents an improved water flow optimizer (IWFO) algorithm for cluster analysis that can address the issues of traditional and heuristic algorithms. In the proposed IWFO algorithm, the initial solution is generated based on the logistic chaotic map instead of random initialization, and in turn, an optimal quality solution is generated. The search mechanism of the WFO algorithm is enhanced based on an improved search mechanism which is the combination of non-linear functions and the previous best solution. Further, the local optima issue is alleviated using a multi-start search mechanism. The efficacy of the proposed IWFO algorithm is evaluated using twelve benchmark clustering datasets and results are compared with seventeen clustering algorithms. The simulation results are assessed using intra-cluster distance (intra), standard deviation (SD), rank, accuracy rate (AR) and detection rate (DR) parameters. Further, a statistical test is also conducted to validate the efficacy of the proposed IWFO algorithm. The results showed that proposed IWFO algorithms obtain superior quality results on most of the datasets.

An improved K-Means clustering based on differential evolution

Randomly selecting the initial cluster center point in the K-means clustering algorithm can lead to the issue of local optima. The paper introduces an enhanced differential evolution algorithm for optimizing K-means clustering. Experimental results demonstrate the superiority of the improved K-means clustering, based on the proposed differential evolution, over other comparison algorithms. Notably, the optimized version exhibits exceptional performance in clustering Iris, Wine, and Glass datasets. The initial clustering center can improve the clustering accuracy in the later stage. Therefore, the proposed algorithm is more superior.

NDPD: an improved initial centroid method of partitional clustering for big data mining

PurposeThe K-means (KM) clustering algorithm is extremely responsive to the selection of initial centroids since the initial centroid of clusters determines computational effectiveness, efficiency and local optima issues. Numerous initialization strategies are to overcome these problems through the random and deterministic selection of initial centroids. The random initialization strategy suffers from local optimization issues with the worst clustering performance, while the deterministic initialization strategy achieves high computational cost. Big data clustering aims to reduce computation costs and improve cluster efficiency. The objective of this study is to achieve a better initial centroid for big data clustering on business management data without using random and deterministic initialization that avoids local optima and improves clustering efficiency with effectiveness in terms of cluster quality, computation cost, data comparisons and iterations on a single machine.Design/methodology/approachThis study presents the Normal Distribution Probability Density (NDPD) algorithm for big data clustering on a single machine to solve business management-related clustering issues. The NDPDKM algorithm resolves the KM clustering problem by probability density of each data point. The NDPDKM algorithm first identifies the most probable density data points by using the mean and standard deviation of the datasets through normal probability density. Thereafter, the NDPDKM determines K initial centroid by using sorting and linear systematic sampling heuristics.FindingsThe performance of the proposed algorithm is compared with KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms through Davies Bouldin score, Silhouette coefficient, SD Validity, S_Dbw Validity, Number of Iterations and CPU time validation indices on eight real business datasets. The experimental evaluation demonstrates that the NDPDKM algorithm reduces iterations, local optima, computing costs, and improves cluster performance, effectiveness, efficiency with stable convergence as compared to other algorithms. The NDPDKM algorithm minimizes the average computing time up to 34.83%, 90.28%, 71.83%, 92.67%, 69.53% and 76.03%, and reduces the average iterations up to 40.32%, 44.06%, 32.02%, 62.78%, 19.07% and 36.74% with reference to KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms.Originality/valueThe KM algorithm is the most widely used partitional clustering approach in data mining techniques that extract hidden knowledge, patterns and trends for decision-making strategies in business data. Business analytics is one of the applications of big data clustering where KM clustering is useful for the various subcategories of business analytics such as customer segmentation analysis, employee salary and performance analysis, document searching, delivery optimization, discount and offer analysis, chaplain management, manufacturing analysis, productivity analysis, specialized employee and investor searching and other decision-making strategies in business.

Modified honey badger algorithm based global MPPT for triple-junction solar photovoltaic system under partial shading condition and global optimization

In the recent era, Metaheuristic Algorithms (MHs) are developed to tackle many and different optimization problems. The merit of the MHs is not only its simplicity to understand but also its easiness of implementation which helps in tackling different and various real-world applications. Honey Badger Algorithm (HBA) is one of the recent MHs. Although the success of the HBA algorithm in solving complex problems with high dimensions, it suffers from several drawbacks such as; 1) being trapped in local optima issue, 2) low convergence, and 3) the imbalance between exploration and exploitation stages. Therefore, an efficient local search called Dimensional Learning Hunting (DLH) is injected to the HBA to tackle these drawbacks, the proposed method named mHBA. On the other side, the demand of the PV systems (PVSs)’ installations is rapidly increasing from a day to the next. Due to the intermittency of the weather, the PV array performs as a nonlinear component in terms of its output characteristics. Partial shading is an environmental phenomenon that prevents all or part of the light to be exposed to the PV cells. This phenomenon makes the cell's output power curve fluctuates and hence contains multiple peaks and has an essential impact on the entire output of the PV system. However, identifying the peak that has the global maximum output power is the main target of most of the conventional maximum power point tracking (MPPT) methods. In this context, the higher efficiency of the global MPPT technique becomes a must to operate the PV cells as close as possible to the global MPPT. Accordingly, the performance of the proposed mHBA is assessed based on the complex 2020 IEEE Congress on Evolutionary Computation (CEC′20) test suite. Then, it is applied to track the global MPPT of PV system-based triple-junction solar cells (TJSCs) under partial shading conditions, four shading scenarios have been considered. The results of the proposed mHBA are compared with common MHs including Gray wolf optimizer (GWO), Moth-flame optimizer (MFO), Whale optimization algorithm, Sine cosine algorithm (SCA), Salp swarm algorithm (SSA), Tunicate swarm algorithm (TSA), Sooty Tern Optimization Algorithm (STOA), and the original HBA. The findings of this research proved the effectiveness and robustness of the proposed mBHA for solving the global optimization problems of the MPPT as an engineering application.

Variants of bat algorithm for solving partitional clustering problems

Clustering is an exploratory data analysis technique that organize the data objects into clusters with optimal distance efficacy. In this work, a bat algorithm is considered to obtain optimal set of clusters. The bat algorithm is based on the echolocation feature of micro bats. Moreover, some improvements are proposed to overcome the shortcoming associated with bat algorithm like local optima, slow convergence, initial seed points and trade-off between local and global search mechanisms etc. An enhanced cooperative co-evolution method is proposed for addressing the initial seed points selection issue. The local optima issue is handled through neighbourhood search-based mechanism. The trade-off issue among local and global searches of bat algorithm is addressed through a modified elitist strategy. On the basis of aforementioned improvements, three variants (BA-C, BA-CN and BA-CNE) of bat algorithm is developed and efficacy of these variants is tested over twelve benchmark clustering datasets suing intra-cluster distance, accuracy and rand index parameters. Simulation results showed that BA-CNE variant achieves more effective clustering results as compared to BA-C, BA-CN and BA. The simulation results of BA-CNE are also compared with several existing clustering algorithms and two statistical tests are also applied to investigate the statistical difference among BA-CNE and other clustering algorithms. The simulation and statistical results confirmed that BA-CNE is an effective and robust algorithm for handling partitional clustering problems.

Kernel-Based Intuitionistic Fuzzy Clustering Image Segmentation Based on Grey Wolf Optimizer With Differential Mutation

Conventional fuzzy clustering algorithms present several disadvantages with respect to image segmentation, including a tendency to arrive at local optima and a relatively high sensitivity to noise and initial cluster centers. To address these issues, we herein propose a kernel-based intuitionistic fuzzy clustering approach combining an improved grey wolf optimizer with a kernel-based intuitionistic fuzzy C-means clustering (IGWO-KIFCM) algorithm capable of carrying out differential mutations for image segmentation. The proposed method extracts spatial information from images and then applies a kernel-based intuitionistic fuzzy clustering objective function to improve the robustness of the algorithm against noise. To cope with the initial sensitivity and local optima issues, we develop an improved grey wolf optimizer based on differential mutation for the global optimization of the cluster centers. A comparative optimization assessment using six classic functions reveals that the improved grey wolf optimizer algorithm outperforms both the grey wolf optimizer and mean grey wolf optimizer algorithms in terms of searching ability and does not easily run into local optima. Moreover, the IGWO-KIFCM algorithm surpasses several other algorithms with respect to clustering performance across multiple datasets, and achieves good results in segmenting images with various types of noises.

SOS 2.0: an evolutionary approach for SOS algorithm

With the shortcomings on the solution given for most-recent optimization problems, decision-makers from different fields yearn the existence of tenacious breakthrough. In fact, they all shared the same obligation to optimize work efficiency, whether to minimize cost, consumption or to maximize the profit acquirement. Metaheuristic search is the more-advanced method proven to be useful for difficult optimization tasks. Moreover, development records also signalized rapid development of these algorithms, contributing several notable and powerful optimization algorithms. Among them, Symbiotic Organisms Search (SOS) received noticeable attention due to its simplicity and also its parameter-less nature. Nonetheless, several considerable issues are still challenging for further development. For instance, local optima and premature convergence issues found from any improper and inefficiency computational procedure on higher dimensional problems. Also, exploitation and exploration trade-off is another essential issue involving stability for optimal performance. In that case, this work proposed a new evolutionary approach named SOS 2.0. There are two distinct features associated with the evolution: Self-Parameter-Updating (SPU) technique and chaotic maps sequencing. Both features are integrated for a better balance of exploration and exploitation in which SPU focuses on exploration and chaotic map focuses on exploitation instead. This work also applied benchmarks function tests and engineering design optimization problem in advance for validation purpose of the performance. The experimental results showed that SOS 2.0 delivers not only better performance from its predecessor and also several recent SOS modifications which can be concluded as one successive approach for better SOS algorithm, but also enhances the computation efficiency and capability of searching optimal solution.

ACD3GPSO: automatic clustering-based algorithm for multi-robot task allocation using dynamic distributed double-guided particle swarm optimization

PurposeThe multi-robot task allocation (MRTA) problem is a challenging issue in the robotics area with plentiful practical applications. Expanding the number of tasks and robots increases the size of the state space significantly and influences the performance of the MRTA. As this process requires high computational time, this paper aims to describe a technique that minimizes the size of the explored state space, by partitioning the tasks into clusters. In this paper, the authors address the problem of MRTA by putting forward a new automatic clustering algorithm of the robots' tasks based on a dynamic-distributed double-guided particle swarm optimization, namely, ACD3GPSO.Design/methodology/approachThis approach is made out of two phases: phase I groups the tasks into clusters using the ACD3GPSO algorithm and phase II allocates the robots to the clusters. Four factors are introduced in ACD3GPSO for better results. First, ACD3GPSO uses the k-means algorithm as a means to improve the initial generation of particles. The second factor is the distribution using the multi-agent approach to reduce the run time. The third one is the diversification introduced by two local optimum detectors LODpBest and LODgBest. The last one is based on the concept of templates and guidance probability Pguid.FindingsComputational experiments were carried out to prove the effectiveness of this approach. It is compared against two state-of-the-art solutions of the MRTA and against two evolutionary methods under five different numerical simulations. The simulation results confirm that the proposed method is highly competitive in terms of the clustering time, clustering cost and MRTA time.Practical implicationsThe proposed algorithm is quite useful for real-world applications, especially the scenarios involving a high number of robots and tasks.Originality/valueIn this methodology, owing to the ACD3GPSO algorithm, task allocation's run time has diminished. Therefore, the proposed method can be considered as a vital alternative in the field of MRTA with growing numbers of both robots and tasks. In PSO, stagnation and local optima issues are avoided by adding assorted variety to the population, without losing its fast convergence.

PSO-based Dynamic Distributed Algorithm for Automatic Task Clustering in a Robotic Swarm

The Multi-Robot Task Allocation (MRTA) problem has recently become a key research topic. Task allocation is the problem of mapping tasks to robots, such that the most appropriate robot is selected to perform the most fitting task, leading to all tasks being optimally accomplished. Expanding the number of tasks and robots may cause the collaboration among the robots to become tougher. Since this process requires high computational time, this paper describes a technique that reduces the size of the explored state space, by partitioning the tasks into clusters. In real-world problems, the absence of information regarding the number of clusters is ordinarily occurring. Hence, a dynamic clustering is auspicious for partitioning the tasks to an appropriate number of clusters. In this paper, we address the problem of MRTA by putting forward a new simple, automatic and efficient clustering algorithm of the robots’ tasks based on a dynamic distributed particle swarm optimization, namely, ACD2PSO. Our approach is made out of two stages: stage I groups the tasks into clusters using the dynamic distributed particle swarm optimization (D2PSO) algorithm and stage II allocates the robots to the clusters. The assignment of robots to the clusters is represented as multiple traveling salesman problems (MTSP). Computational experiments were carried out to prove the effectiveness of our approach in term of clustering time, cost, and the MRTA time, compared to the distributed particle swarm optimization (dPSO) and genetic algorithm (GA). Thanks to the D2PSO algorithm, stagnation and local optima issues are avoided by adding assorted variety to the population, without losing the fast convergence of PSO.

Probabilistic Common Spatial Patterns for Multichannel EEG Analysis

Common spatial patterns (CSP) is a well-known spatial filtering algorithm for multichannel electroencephalogram (EEG) analysis. In this paper, we cast the CSP algorithm in a probabilistic modeling setting. Specifically, probabilistic CSP (P-CSP) is proposed as a generic EEG spatio-temporal modeling framework that subsumes the CSP and regularized CSP algorithms. The proposed framework enables us to resolve the overfitting issue of CSP in a principled manner. We derive statistical inference algorithms that can alleviate the issue of local optima. In particular, an efficient algorithm based on eigendecomposition is developed for maximum a posteriori (MAP) estimation in the case of isotropic noise. For more general cases, a variational algorithm is developed for group-wise sparse Bayesian learning for the P-CSP model and for automatically determining the model size. The two proposed algorithms are validated on a simulated data set. Their practical efficacy is also demonstrated by successful applications to single-trial classifications of three motor imagery EEG data sets and by the spatio-temporal pattern analysis of one EEG data set recorded in a Stroop color naming task.

A New Method on Data Clustering Based on Hybrid K-Harmonic Means and Imperialist Competitive Algorithm

Data clustering is one of the commonest data mining techniques. The K-means algorithm is one of the most wellknown clustering algorithms thatare increasingly popular due to the simplicity of implementation and speed of operation. However, its performancecouldbe affected by some issues concerningsensitivity to the initialization and getting stuck in local optima. The K-harmonic means clustering method manages the issue of sensitivity to initialization but the local optimaissue still compromises the algorithm. Particle Swarm Optimization algorithm is a stochastic global optimization technique which is a good solution to the above-mentioned problems. In the present article, the PSOKHM, a hybrid algorithm which draws upon the advantages of both of the algorithms, strives not only to overcome the issue of local optima in KHM but also the slow convergence speed of PSO. In this article, the proposed GSOKHM method, which is a combination of PSO and the evolutionary genetic algorithmwithin PSOKHM,has been positedto enhancethe PSO operation. To carry out this experiment, four real datasets have been employed whose results indicate thatGSOKHMoutperforms PSOKHM.

Topology optimization of piezoelectric energy harvesting devices considering static and harmonic dynamic loads

A topology optimization (TO) procedure is developed to design optimal layouts for piezoelectric energy harvesting devices (EHDs) by considering the effect of static and harmonic dynamic mechanical loads. To determine the optimal material distributions of a piezoelectric material considering the harmonic dynamic coupling effects between the electric energy and a structure for efficient EHDs, harmonic dynamic responses and the complex sensitivity analyses for various objectives related to the energy efficiency are calculated and derived. For the relaxation method of the density design variable for TO, material properties such as the anisotropic linear elasticity coefficients, piezoelectric coefficients, and permittivity coefficients are independently interpolated through the solid isotropic material with penalization (SIMP) approach with three penalization values. Through several numerical tests for various configurations of piezoelectric materials, it is found that depending on the choice of penalization value, complex behaviors of energies are possible and these in turn lead to a serious local optima issue in TO. Through several three-dimensional design problems, the validity and usefulness of the developed optimization procedure for efficient EHDs are demonstrated.