Numerical and Evolutionary Optimization 2024

This Special Issue was inspired by the 11th International Workshop on Numerical and Evolutionary Optimization (NEO 2024), held from 3 to 6 September 2024 in Mexico City, Mexico, and hosted by Cinvestav. Solving real-world scientific and engineering problems has always been a challenge, and the complexity of these tasks has increased in recent years as more sources of data and information have been continuously developed. Thus, the design and analysis of powerful search and optimization techniques is of great importance. Two well-established fields that focus on this task are (i) traditional numerical optimization techniques and (ii) bio-inspired metaheuristic methods. Both of these general approaches have unique strengths and weaknesses, allowing researchers to solve some challenging problems while failing to solve others. The goal of the NEO workshop series is to gather experts from both fields to discuss, compare, and merge these complementary perspectives. Collaborative work allows researchers to maximize the strengths and minimize the weaknesses of both paradigms. NEO also intends to help researchers in these fields to understand and tackle real-world problems like pattern recognition, routing, energy, lines of production, prediction, and modeling, among others.

This Special Issue consists of 17 research papers that we will summarize below. The papers are presented chronologically in terms of their publication in Mathematical and Computational Applications (MCA).

In [1], Alvarado-Méndez et al. propose an alternative methodology for simultaneous parameter and actuator disturbance estimation for a general class of nonlinear systems. To this end, the authors develop an $H\infty$-adaptive nonlinear observer of a class of Lipschitz nonlinear systems with disturbances. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer is analyzed in the presence of disturbances using Lyapunov stability theory and using an $H\infty$ performance criterion. Numerical simulations are carried out to demonstrate the applicability of this observer on a semi-active car suspension.

In [2], Barradas-Palmeros et al. present a multi-objective feature selection framework that significantly reduces computational costs by integrating fixed and incremental sampling-fraction strategies with memory into a permutation-based Differential Evolution algorithm. Based on the DE-FS^PM approach, and adopting the GDE3 selection mechanism, the proposal avoids redundant fitness evaluations and reduces both running time and function evaluations during the search. The experimental results demonstrate the effectiveness of this method in single-objective optimization and suggest that cost-reduction strategies are only partially sustained for multi-objective feature selection.

In [3], Serrano-Cruz et al. develop a mathematical model of the human cardiovascular system to simulate both normal and pathological conditions within the systemic circulation. Their novel approach reformulates the cardiovascular system into quadratic normal form through coordinate transformation. The latter allows for robust state estimation via sliding mode observers despite linear unobservability, which is particularly valuable for fault detection in scenarios where traditional observability conditions fail. The simulation results demonstrate strong agreement with established data, validating the model’s accuracy in representing cardiovascular dynamics.

In [4], Cavita-Huerta et al. present an interesting new approach for classifying physical activities that exclusively uses accelerometry data processed through artificial neural networks (ANNs). The methodology involves data acquisition, preprocessing, feature extraction, and the application of deep learning algorithms to accurately identify activity patterns. A major innovation in this study is the incorporation of a new feature derived from the radius of curvature. The findings demonstrate the potential of this model to improve the precision and reliability of physical activity recognition in wearable health-monitoring systems.

In [5], González-Cárdenas et al. present a trajectory-tracking controller for an inverted pendulum system on a self-balancing differential drive platform. The system modeling is described by considering approximations of the swing angles. A discrete convex representation of the system is obtained via the nonlinear sector technique, considering the nonlinearities associated with the nonholonomic constraint. A discrete parallel distributed compensation controller is designed through an alternative method due to the presence of uncontrollable points that hinder finding a solution for the entire polytope. Finally, the results of simulations and an experiment using a prototype illustrate the effectiveness of the proposal.

In [6], Molina-Pérez and Rojas-López address the problem of enhancing image quality. Since two common goals in this context (improving the contrast and maintaining fine details) conflict with each other, the authors propose a multi-objective optimization approach that combines sigmoid transformation and unsharp masking–highboost filtering with the NSGA-II algorithm. A posterior preference articulation method identifies three representative outcomes from the obtained Pareto front: one maximizing contrast, one maximizing detail, and a balanced “knee point” solution. The method is tested on diverse image types, including medical and natural scenes, showing significant improvements over the original images in both contrast and detail.

In [7], García-Morales et al. propose two new metaheuristics to solve the Internet Shopping Optimization Problem with Sensitive Prices. The first approach is a memetic algorithm that integrates an evolutionary search with an improved local search and adaptive parameter adjustment, while the second one is an enhanced Particle Swarm Optimization algorithm incorporating a diversification technique and adaptive control parameters. Both methods are tested against the Branch and Bound (B&B) algorithm on nine problem instances of varying sizes, showing that the proposed algorithms perform similarly and outperform B&B.

In [8], Pérez-Pérez et al. study the problem of detecting faults and leaks in water pipelines. These systems are notoriously difficult to inspect, with leaks and faults leading to the production of large amounts of waste and inefficiency. Given the scarcity of fresh water in many places around the world, the development of efficient methods to detect faults in water pipelines is of immense importance. The authors present another hybrid approach that combines neuro-fuzzy systems with Kalman filters to achieve very high precision and a low false positive rate under a variety of fault conditions.

In [9], Guadarrama-Estrada et al. present a new approach to design a generalized dynamic observer (GDO) in order to detect and isolate attack patterns that compromise the functionality of cyber–physical systems. The considered attack patterns include denial-of-service (DoS), false data injection (FDI), and random data injection (RDI) attacks. To model an attacker’s behavior and enhance the effectiveness of the attack patterns, Markovian logic is employed. A three-tank interconnected system, modeled under the discrete Takagi–Sugeno representation, is used as a case study to validate the proposed approach.

In [10], Contreras Ortiz et al. evaluate vision transformers for an industrial inspection problem, detecting defects in industrial welding. The study considers different versions of the problem, showing that vision transformers outperform convolutional networks and are nearly 30% more effective in a multiclass classification task. The study shows how transformer models can be applied to real-world quality control and inspection tasks.

In [11], Amador-Larrea et al. introduce adaptive mutation strategies for a grouping genetic algorithm, GGA-CGT, applied to the One-Dimensional Bin Packing Problem (1D-BPP). These strategies dynamically control the level of change that will be introduced to each solution by using feedback on population diversity, enabling better exploration. A performance comparison of this algorithm to the base algorithm on selected benchmark problems indicates an increase in the detection of optimal solutions and a severe reduction in the average proportion of individuals with equal fitness (from over 50% to less than 1%), enhancing diversity and avoiding local optima. The adaptive strategies are particularly effective in problem instances with larger item weights. These findings demonstrate the potential of adaptive mechanisms to improve genetic algorithms, offering a robust strategy for tackling complex optimization problems.

In [12], Purata-Aldaz et al. propose MASIP, a heuristic-based approach designed to construct and optimize investment portfolios using principles from the Markowitz and Sharpe models. The methodology performs three key tasks: selecting candidate stocks for an initial portfolio, forecasting asset values over short- and medium-term horizons, and optimizing the portfolio using the Sharpe ratio. The methodology incorporates a dynamic rebalancing process to enhance portfolio performance over time. A comparison on the S&P 500 data shows that MASIP is highly competitive compared to traditional methods for this problem class.

In [13], Marquez-Zepeda et al. present a novel method to monitor and predict air quality, using machine learning tools and Internet of Things (IoT) technologies. The approach is useful for indoor settings, such as offices or classrooms. These technologies can allow for the development of “smart” buildings and “cities”, which proactively respond to environmental issues that can affect human health and behavior.

In [14], Sánchez Márquez et al. propose two evolutionary strategies based on the generalized Mallows model for the numerical treatment of the Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP). The proposed approaches are compared with algorithms previously used to address the studied problem. Statistical tests of the experimental results show that one of these methods, ES-GMMc, achieves reductions in execution time, especially in instances of large problems, where the shortest computing times are obtained in 23 of 30 instances, without affecting the quality of the solutions.

In [15], Gamboa et al. address a medical problem using a nonlinear third-order mathematical model described by ODEs. In particular, they study the dynamics of insulin and of $\beta$-cells, and the concentration of glucose, using a Thau observer, and conduct an analysis to study the models’ dynamic bounds. The study represents a crucial initial step towards the potential development of new treatments for diabetes using a digital twin approach, as the method can describe how insulin levels develop over time at various glucose concentrations.

In [16], Goñi et al. study the effective design of content distribution networks over cloud computing platforms. A bio-inspired evolutionary multi-objective optimization approach is applied as a viable alternative to solve realistic problems where exact optimization methods are not applicable. Ad hoc representation and search operators are applied to optimize relevant metrics from the perspective of both system administrators and users. The numerical results indicate that the obtained solutions can provide different options for content distribution network design, enabling fast configuration that fulfills specific quality-of-service demands.

Finally, in [17], Frausto Solís et al. present TAE Predict, a methodology for multivariate time series forecasting of climate variables in the context of climate change. The method incorporates feature selection with an ensemble approach for prediction. The ensemble combines several machine learning models using metaheuristic optimization, and the work analyzes meteorological data from several cities in Mexico. The results are encouraging, showing how metaheuristic optimization and machine learning methods can be effectively hybridized to solve real-world problems.

We thank the NEO 2024 participants and the authors who submitted studies to this Special Issue. We hope that it can serve as a contemporary reference for the use and applications of numerical and evolutionary optimization.