GSA is badly suffering from slow convergence rate and poor local search ability, when solving complex optimization problems. To solve this problem, a new hybrid population-based algorithm is proposed with the combination of dynamic multi swarm particle swarm optimization and gravitational search algorithm (GSADMSPSO). The proposed algorithm has divided the main population of masses into smaller sub-swarms and also stabilizing them by presenting new neighborhood strategy. Then, by adopting the global search ability of proposed algorithm, each agent (particle) improves the position and velocity. The main idea is to integrate the ability of GSA with the DMSPSO to enhance the performance of exploration and exploitation of a proposed algorithm. In order to evaluate the competences of the proposed algorithm, benchmark functions are employed. The experimental results have been confirmed a better performance of GSADMSPSO as compared to the other gravitational and PSO variants in terms of fitness rate.

The K-nearest neighbour classifier is very effective and simple non-parametric technique in pattern classification; however, it only considers the distance closeness, but not the geometricalplacement of the k neighbors. Also, its classification performance is highly influenced by the neighborhood size k and existing outliers. In this paper, we propose a new local mean based k-harmonic nearest centroid neighbor (LMKHNCN) classifier in orderto consider both distance-based proximity, as well as spatial distribution of k neighbors. In our method, firstly the k nearest centroid neighbors in each class are found which are used to find k different local mean vectors, and then employed to compute their harmonic mean distance to the query sample. Lastly, the query sample is assigned to the class with minimum harmonic mean distance. The experimental results based on twenty-six real-world datasets shows that the proposed LMKHNCN classifier achieves lower error rates, particularly in small sample-size situations, and that it is less sensitive to parameter k when compared to therelated four KNN-based classifiers.

Neighborhood preserving embedding (NPE) is a classical and very promising supervised dimensional reduction (DR) technique based on a linear graph, which preserves the local neighborhood relations of the data points. However, NPE uses the K nearest neighbor (KNN) criteria for constructing an adjacent graph which makes it more sensitive to neighborhood size. In this article, we propose a novel DR method called weighted neighborhood preserving ensemble embedding (WNPEE). Unlike NPE, the proposed WNPEE constructs an ensemble of adjacent graphs with the number of nearest neighbors varying. With this graph ensemble building, WNPEE can obtain the low-dimensional projections with optimal embedded graph pursuing in a joint optimization manner. WNPEE can be applied in many machine learning fields, such as object recognition, data classification, signal processing, text categorization, and various deep learning tasks. Extensive experiments on Olivetti Research Laboratory (ORL), Georgia Tech, Carnegie Mellon University-Pose and Illumination Images (CMU PIE) and Yale, four face databases demonstrate that WNPEE achieves a competitive and better recognition rate than NPE and other comparative DR methods. Additionally, the proposed WNPEE achieves much lower sensitivity to the neighborhood size parameter as compared to the traditional NPE method while preserving more of the local manifold structure of the high-dimensional data.

Gene selection and cancer classification are inherently multi-objective tasks that require balancing competing objectives, such as maximizing classification accuracy while minimizing irrelevant or redundant genes. Existing methods often optimize a single objective or treat gene selection and classification independently, limiting their overall effectiveness. This study proposes a unified framework, MORPSO_ECD+ELM, which formulates gene selection and classification as a multimodal multi-objective optimization problem (MMOP) to optimize both objectives simultaneously. The framework introduces two key innovations: (1) an enhanced crowding distance (ECD) metric to improve diversity preservation and (2) an advanced multi-objective particle swarm optimization variant (MORPSO_ECD) that incorporates ECD and ring topography to effectively explore the MMOP solution space. Integrated with the Extreme Learning Machine (ELM), this framework achieves robust and efficient cancer classification. Extensive experimental validations demonstrate that the proposed approach achieves high classification accuracy while identifying biologically meaningful gene subsets, providing a powerful solution to bridge the gap between gene selection and cancer classification.

The analysis of high-dimensional microarray gene expression data presents critical challenges, including excessive dimensionality, increased computational burden, and sensitivity to random initialization. Traditional optimization algorithms often produce inconsistent and suboptimal results, while failing to preserve local data structures limiting both predictive accuracy and biological interpretability. To address these limitations, this study proposes an adaptive neighborhood-preserving multi-objective particle swarm optimization (ANPMOPSO) framework for gene selection. ANPMOPSO introduces four key innovations: (1) a weighted neighborhood-preserving ensemble embedding (WNPEE) technique for dimensionality reduction that retains local structure; (2) Sobol sequence (SS) initialization to enhance population diversity and convergence stability; (3) a differential evolution (DE)-based adaptive velocity update to dynamically balance exploration and exploitation; and (4) a novel ranking strategy that combines Pareto dominance with neighborhood preservation quality to prioritize biologically meaningful gene subsets. Experimental evaluations on six benchmark microarray datasets and eleven multi-modal test functions (MMFs) demonstrate that ANPMOPSO consistently outperforms state-of-the-art methods. For example, it achieves 100% classification accuracy on Leukemia and Small-Round-Blue-Cell Tumor (SRBCT) using only 3–5 genes, improving accuracy by 5–15% over competitors while reducing gene subsets by 40–60%. Additionally, on MMFs, ANPMOPSO attains superior hypervolume values (e.g., 1.0617 ± 0.2225 on MMF1, approximately 10–20% higher than competitors), confirming its robustness in balancing convergence and diversity. Although the method incurs higher training time due to its structural and adaptive components, it achieves a strong trade-off between computational cost and biological relevance, making it a promising tool for high-dimensional gene selection in bioinformatics.