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.

Maintaining population diversity in evolutionary computation poses a significant challenge throughout the optimization process. A balanced exploration-exploitation dynamic is crucial for achieving optimal results, and a diverse population proportion plays a key role in achieving this balance. Over the years, various methods have been proposed to evaluate diversity. However, relying on a single value to gauge population diversity has its limitations. This paper explores the shortcomings of existing population diversity metrics through extensive experimentation with different population configurations. The findings reveal that some metrics may be misleading, as a lower diversity value does not necessarily imply poor performance in solving optimization problems. In response to these challenges, this paper introduces a new and improved diversity metric, building upon the Dimension-Wise Diversity notion. The proposed metric corrects the shortcomings associated with its predecessors, leading to a more accurate interpretation of diversity values.

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.

Population size is an important variable in evolutionary algorithms (EA). Its proper configuration improves the performance of the search process not only in terms of the fitness function but also for the resources required. This article introduced a population management mechanism that includes different operators. Such operators are designed and applied based on the diversity of the population. In general terms, the operators address problems in EA regarding stagnation and the inefficient use of the function evaluations. As a case of study, the proposed method is applied in the Differential Evolution (DE) to provide it the ability to change its population size according to its needs. The experimental results and comparisons demonstrate greatly improved performance when compared to the unmodified DE, some of its most successful variants, and other much more complex algorithms from the state-of-the-art.

The balance between exploration and exploitation is an important feature in Evolutionary Algorithms (EA). The use of different operators permits to explore the search space and exploit the most prominent regions. This article introduces a dynamic operator selection method that considers different criteria at the same time. The proposed approach uses a dynamic decision matrix (DyDM) to identify which operators must be used at each iteration based on how the algorithm behaves. The DyDM considers specific information as the diversity of the algorithm to avoid stagnation, the actual iteration to work accordingly, and the fitness to direct the search. The proposed approach is called Dynamic Decision Matrix Optimizer (DyDMO) and it has been compared with different well-known algorithms tested on the CEC 2017 benchmark functions. The comparative analysis and non-parametric statistical tests validate how DyDMO im-proves the quality of the solutions and is more stable than its comnetitors.