It is an irrefutable fact that the Differential Evolution (DE) algorithm is one of the most widely used stochastic algorithms for solving complex optimization problems. In recent decades, the DE algorithm has garnered significant interest from researchers due to its considerable potential. However, it is evident that the scientific community considers it necessary to modify and create variants of the original version to improve its performance. Within the DE algorithm, the mutation operator has been an essential component in improving performance and exploration/exploitation balance. The present manuscript proposes a novel approach to the mutation operator of the DE algorithm, grounded in the Mahalanobis distance. The Mahalanobis Distance Enhanced Differential Evolution (IMPDE) algorithm is an innovative methodology that aims to explore a new paradigm by measuring the distance of particles to the mean during each iteration. The enhancement of the algorithm is appraised by employing a series of CEC-2017 assessments and traditional optimization problems. Furthermore, a nonparametric Friedman test is conducted to refute the obtained results. This work represents a significant contribution to the ongoing efforts to enhance the optimization process of one of the most prevalent algorithms in recent times.

Optical Coherence Tomography (OCT) is an imaging technique that enables medical experts to obtain transverse scans of various small tissues, including relevant eye elements, such as the retina. The analysis of retinal OCT scans holds significant clinical relevance as it provides physicians with anatomical and pathological insights. However, speckle noise, inherent to OCT’s operational nature, negatively impacts image quality and hinders precise interpretation and diagnosis. In this regard, this paper presents the Metaheuristic-Driven Bayesian Speckle Denoising (MDBSD) framework: a fusion of a metaheuristic-based optimization using the Optimized Bayesian Non-local means with block selection (OBNLM) as the transformation function while introducing a specific fitness function for the evaluation of the potential solutions. Different classical metaheuristic algorithms are utilized and applied to a public retinal OCT dataset, followed by a numerical evaluation using contrast and denoising performance metrics to validate this framework. Regardless of the metaheuristic technique used for optimization, enhanced images present a notorious scan denoising while keeping retinal layers’ edges quite delimited, proving this framework’s efficiency. Additionally, future research directions are outlined for further advancement in this area.

Differential Evolution (DE) represents an advanced evolutionary algorithm due to its continuous innovation and advances around its operators and applications. In general, the mutation operator is designed to enhance the performance of Differential Evolution (DE) algorithms. The mutation operator is a vital component in enhancing the effectiveness of DE algorithms. The proposed mutation operator, the Lissajous Mutation (LM) is specifically designed to improve the balance between exploration and exploitation through the geometric origin of the Lissajous curves. This paper introduces an up-to-date version of Differential Evolution with Lissajous Mutation, Multi-crossover, and Dynamic selection (IDEL). This new DE variation presents changes in all the fundamental stages, well-known as Mutation, Crossover, and Selection. Through a series of meticulously designed experiments and rigorous comparisons with existing DE variants, the effectiveness of IDEL is demon-strated. IDEL showcases notable improvements in convergence speed, exploration-exploitation equilibrium, and solution quality across diverse benchmark scenarios. This paper contributes to the ongoing growth of DE and presents a novel way to enhance its overall performance.

In the context of evolutionary algorithms, having the ability to adapt to any search space within an optimization problem is an essential task. Appropriately adapting the population can lead to better solutions and more efficient use of function call resources. This article presents a renewed approach to population management inspired by modifying the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. The proposed strategy aims to improve the algorithm’s population adaptability to the search space and optimize function evaluations. Statistically evaluated experimental test outcomes demonstrate significantly better performance on high-dimensional problems in comparison to the original CMA-ES and seven other known evolutionary algorithms in the literature.

Particle Swarm Optimization (PSO) has efficiently solved several real-world applications and optimization problems. However, it has shortcomings, such as premature convergence and stagnation at local minima. Inertia weight is a parameter of this algorithm that controls the global and local exploration and exploitation capability by determining the influence of the previous velocity on its current motion. Therefore, this article proposes a PSO with a Diversity-aware Inertia and Velocity Control (PSOIVC) algorithm to improve the PSO performance. The PSOIVC employs a novel diversity-aware inertia weight and velocity control approach to tune the parameters to produce a trade-off between exploration and exploitation of the algorithm using the dimension-wise diversity. The PSOIVC algorithm is compared with eight algorithms, including variants of the PSO, on a set of 30 benchmark functions for a single objective real parameter in 30 and 50 dimensions. Based on the results, the proposal presents significant outcomes according to the average values obtained for both comparisons; because it performed similarly or better than the other algorithms in 23/30 and 16/30 for 30 and 50 dimensions, respectively.

Particle swarm optimization (PSO) is essential to evolutionary computation algorithms (ECA). The PSO has some drawbacks as premature convergence and stagnation at local minima. Inertia weight is a parameter that controls the global and local exploration and exploitation capability in the PSO by determining the influence of the previous velocity on its current motion. This article proposes using a stagnation counter that verifies the times the PSO is stuck in the same fitness value. In the proposed fuzzy controlled PSO with stagnation coefficient (FCPSO), a fuzzy controller is designed to tune the inertia weight based on the population's diversity and the search's stagnation. This modification allows the PSO to escape from suboptimal values enhancing its search capabilities. The FCPSO is tested over 28 benchmark functions in 50 dimensions. Besides, it has been compared with nine optimization algorithms from the state-of-the-art. The experiments and comparisons suggest that the FCPSO is an interesting tool for solving complex optimization problems.

Hyper-heuristics (HH) are strategies that have a high-level mechanism to combine, select or generate heuristics at a low level to find solutions based on the information received during the search process. Typically, an HH approach involves evaluating several algorithms and constructing a priori a structure containing the information required to select, combine or generate the appropriate heuristic to solve a given problem using a usually probabilistic selection method. This paper considers a constructive online learning HH with an agent population selection and control strategy for each heuristic with a reward-punishment approach based on a mean absolute deviation criterion and exploitation-exploration stages to optimize these phases in the optimization process. We compare our proposal, denominated Hyper-heuristic based on the mean absolute deviation metric and the exploration-exploitation stages for the population management (HH-MAD) using uni-modal, multi-modal, composite, and shifted benchmark functions among different optimization algorithms. The experimental results validated the central tendency measures and the non-parametric tests, showing that HH-MAD is competitive, outperforming the other approaches.