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.

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.

The proper use of evolutionary operators is crucial to find optimal solutions in a search space. Moreover, the diversity of the population affects the performance of Evolutionary Algorithms (EAs). This article introduces an EA called BWEAD which balances the influence of the operators. The proposal also performs a statistical analysis of the population when the diversity is low and decides which solutions might be replaced. Then BWEAD is able to explore the search space and exploit the prominent regions. The BWEAD has been tested over the CEC2014 set of benchmark functions. The experiments provide competitive results showing an improvement of 30% in 30-dimensional and 50-dimensional functions in comparison with state-of-the-art algorithms, overcoming some addressed instances and providing evidence of its capabilities on complex optimization problems.