A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> In this paper, the algorithmic concepts of the Cuckoo-search (CK), Particle swarm optimization (PSO), Differential evolution (DE) and Artificial bee colony (ABC) algorithms have been analyzed. The numerical optimization problem solving successes of the mentioned algorithms have also been compared statistically by testing over 50 different benchmark functions. Empirical results reveal that the problem solving success of the CK algorithm is very close to the DE algorithm. The run-time complexity and the required function-evaluation number for acquiring global minimizer by the DE algorithm is generally smaller than the comparison algorithms. The performances of the CK and PSO algorithms are statistically closer to the performance of the DE algorithm than the ABC algorithm. The CK and DE algorithms supply more robust and precise results than the PSO and ABC algorithms. <s> BIB001 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Microarray cancer gene expression datasets are high dimensional and thus complex for efficient computational analysis. In this study, we address the problem of simultaneous gene selection and robust classification of cancerous samples by presenting two hybrid algorithms, namely Discrete firefly based Support Vector Machines (DFA-SVM) and DFA-Random Forests (DFA-RF) with weighted gene ranking as heuristics. The performances of the algorithms are then tested using two cancer gene expression datasets retrieved from the Kent Ridge Biomedical Dataset Repository. Our results show that both DFA-SVM and DFA-RF can help in extracting more informative genes aiding to building high performance prediction models. <s> BIB002 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection (ACO-S) is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features (genes), they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter (q0) in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation. <s> BIB003 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> This article presents a newly proposed selection process for genetic algorithms on a class of unconstrained optimization problems. The k-means genetic algorithm selection process (KGA) is composed of four essential stages: clustering, membership phase, fitness scaling and selection. Inspired from the hypothesis that clustering the population helps to preserve a selection pressure throughout the evolution of the population, a membership probability index is assigned to each individual following the clustering phase. Fitness scaling converts the membership scores in a range suitable for the selection function which selects the parents of the next generation. Two versions of the KGA process are presented: using a fixed number of clusters K (KGAf) and via an optimal partitioning Kopt (KGAo) determined by two different internal validity indices. The performance of each method is tested on seven benchmark problems. <s> BIB004 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Kmeans is one of the most-efficient hard-clustering algorithms. It has been successfully applied to a number of problems. However, the efficiency of kmeans is dependent on its initialization of cluster centres. Different swarm intelligence techniques are applied for clustering problem. In this work, we have considered Ant Lion Optimization (ALO) which is a stochastic global optimization models. In this work Kmeans has been integrated with ALO for optimal clustering. The statistical measures of different performance metrics has been calculated and compared. The proposed method performs preferably better than Kmeans and PSO-Kmeans in terms of sum of intracluster distances and F-measure. <s> BIB005 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Abstract K-Means is a popular cluster analysis method which aims to partition a number of data points into K clusters. It has been successfully applied to a number of problems. However, the efficiency of K-Means depends on its initialization of cluster centers. Different swarm intelligence techniques are applied to clustering problem for enhancing the performance. In this work a hybrid clustering approach based on K-means and Ant Lion Optimization has been considered for optimal cluster analysis. Ant Lion Optimization (ALO) is a stochastic global optimization model. The performance of the proposed algorithm is compared against the performance of K-Means, KMeans-PSO, KMeans-FA, DBSCAN and Revised DBSCAN clustering methods based on different performance metrics. Experimentation is performed on eight datasets, for which the statistical analysis is carried out. The obtained results indicate that the hybrid of K-Means and Ant Lion Optimization method performs preferably better than the other three algorithms in terms of sum of intracluster distances and F-measure. <s> BIB006 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Abstract Abandoned areas with substances potentially harmful to the environment or human health have raised numerous concerns around the world. The objective of the present study is to analyze the possibility of building solar power plants capable of capturing solar energy in unproductive areas, both contaminated and uncontaminated. For this purpose, American data from the National Solar Radiation Database (NSRDB) were used, a collection of hourly solar radiation measurements and meteorological data, as well as data from the RE-Powering America's Land project, run by the United States Environmental Protection Agency (EPA). In the analysis, the information about “mapped area”, “distances to the transmission lines”, “solar direct normal irradiance on a utility scale” and “off-grid direct normal irradiance” were considered. To define the best locations, the data were initially pre-processed. A new hybrid fuzzy c-means (HFCM) algorithm was then applied, initialized, comparatively, by three metaheuristics: Differential Evolution (DE), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), for the data clustering. The number of clusters obtained was validated by three metrics: Calinski-Harabasz Criterion, Davies-Bouldin Criterion and Silhouette Coefficient, with all three unanimously indicating two clusters as the ideal number: one cluster for locations with greater potential for allocating facilities to capture solar energy, and another for locations with a lower potential. With the new approach, an increase of 23.3% in the training velocity of the HFCM algorithm was identified, which required fewer iterations to achieve the same value of the objective function. Else, a round of experiments was conducted with six different datasets (instances from literature) and the results showed that the proposed method can achieve better results (faster convergence and smaller solution cost) than the classic FCM. Visually, the predominance of the allocation of facilities was perceived in states with a greater average incidence of solar radiation. Therefore, this was the predominant factor in the convergence of the algorithm, which is in accordance with expectations for solar energy. Finally, the social, economic and environmental gains were considered with the revitalization of unproductive land with the possibility of implementing solar power plants in these areas. <s> BIB007 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Approximative methods are widely used in the resolution of complex computational problems, since they are able to present significant results regarding the quality of the solution in a satisfactory time in general. This paper addresses the problem of automatic grouping, admittedly NP-difficult. In the context of this problem, non-exact methods, whose complexity is polynomial, are desirable. To solve the problem, the work presents a metaheuristic based on collective intelligence, inspired by the behavior of the ants. The silhouette index was used to measure the quality of the generated clusters. The results obtained by the proposed algorithm were compared with the literature and indicated that the algorithm is able to find clusters that represent well the original distribution of the data. Key words: Ants colony, clustering, metaheuristics. <s> BIB008 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Cluster analysis is a data mining technique that has been widely used to exploit useful information in a great amount of data. Because of their evaluation mechanism based on an intracluster distance (ICD) function, traditional single-objective clustering algorithms are not appropriate for not-well-separated data. Specifically, they may easily result in the drop of the optimal solution accuracy on their late stages of search when dealing with the latter. To overcome the problem, in this paper a novel index reflecting the similarity of data within a cluster is presented and called intracluster cohesion (ICC). However, if a multiobjective method is used to cluster with ICD and ICC as the specified objectives, its clustering accuracy may depend on one's experience. Motivated by these, we propose an accelerated two-stage particle swarm optimization (ATPSO) in which K-means is utilized to accelerate particles' convergence during the population initialization. Its clustering process consists of two stages. First, the main objective of minimizing ICD is to execute preliminary clustering; second, ICC is optimized to promote the clustering accuracy. Extensive experiments with the help of 17 open-source clustering sets in various geometric distributions are conducted. The results show that ATPSO outperforms PSO, K-means PSO (KPSO), chaotic PSO (CPSO), and accelerated CPSO in terms of accuracy, and its efficiency is approximate to that of KPSO. Its convergence trend indicates that the adoption of the proposed ICC contributes to the clustering accuracy. Remarkably, compared with the Pareto-based multiobjective PSO, ATPSO can detect clusters more accurately and quickly through the proposed two-stage search. <s> BIB009 </s> A Review of Computational Methods for Clustering Genes with Similar Biological Functions <s> Strategy 1: Population-Based Optimization <s> Support vector machine (SVM) parameters such as penalty parameter and kernel parameters have a great influence on the complexity and accuracy of SVM model. In this paper, quantum-behaved particle swarm optimization (QPSO) has been employed to optimize the parameters of SVM, so that the classification error can be reduced. To evaluate the proposed model (QPSO-SVM), the experiment adopted seven standard classification datasets which are obtained from UCI machine learning data repository. For verification, the results of the QPSO-SVM algorithm are compared with the standard PSO, and genetic algorithm (GA) which is one of the well-known optimization algorithms. Moreover, the results of QPSO are compared with the grid search, which is a conventional method of searching parameter values. The experimental results demonstrated that the proposed model is capable to find the optimal values of the SVM parameters. The results also showed lower classification error rates compared with standard PSO and GA algorithms. <s> BIB010
Population-based optimization is performed in terms of exploration and exploitation BIB001 BIB004 . Exploration is the technique able to reach the best solution within the search space, while exploitation expresses the ability of the technique to reach a global optimum solution. Metaheuristic search can apply in this optimization for global optimal solutions using informative parameters. However, the optimization still has difficultly avoiding the problems of local minima and early convergence BIB005 BIB006 BIB002 . Several examples of population-based optimization are reviewed, which are ant colony optimization (ACO), ant lion optimization (ALO), firefly algorithm (FA), and particle swarm optimization (PSO) BIB005 BIB006  BIB007 BIB008 BIB009 BIB003  BIB010 . In the literature related to PSO, most previous studies used PSO because it does not have any complex evolution BIB009 . Fister et al.  found that FA is suitable for multi-modal optimization and fast convergence.