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Numerical and Evolutionary Optimization 2025

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A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (31 March 2026) | Viewed by 7494

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Prof. Dr. Daniel E. Hernández

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Departamento de Ingeniería Industrial, Tecnológico Nacional de México/Instituto Tecnológico de Tijuana, Calzada Tecnológico SN, Tomas Aquino, Tijuana 22414, México
Interests: data science; machine learning; evolutionary computation; HPC
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Dr. Marcela Quiroz-Castellanos

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Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa 91000, CP, Mexico
Interests: experimental algorithmics; metaheuristics; genetic algorithms; combinatorial optimization; machine learning; causal inference applications
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Dr. Leonardo Trujillo

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Departamento de Ingeniería en Electrónica y Eléctrica, Tecnológico Nacional de México/Instituto Tecnológico de Tijuana, Calzada Tecnológico SN, Tomas Aquino, Tijuana 22414, Mexico
Interests: evolutionary computation; machine learning; data science; computer vision
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Prof. Dr. Pierrick Legrand

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Bordeaux INP, IMS Laboratory, UMR CNRS 5218, ASTRAL Team, Centre Inria de l'Université de Bordeaux, 33400 Talence, France
Interests: signal enhancement; wavelets; fractals; fractal analysis; Hölderian regularity; Hölder exponents; estimation; regression; denoising; optimal rate of convergence; minimax; risk; interpolation; extrapolation; road/tyre friction; indenters; multi-scale; evolutionary algorithms; genetic programming; bloat control; stereovision; classification; matching; biomedical applications; EEG analysis; cochlear implants; virtual analogue modeling; amplifier; neural networks

Prof. Dr. Oliver Schütze

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Departamento de Computacion, Cinvestav, Mexico City 07360, Mexico
Interests: multi-objective optimization; evolutionary computation (genetic algorithms and evolution strategies); numerical analysis; engineering applications
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Special Issue Information

Dear Colleagues,

This Special Issue will mainly consist of selected papers presented at the 12th International Workshop on Numerical and Evolutionary Optimization (NEO 2025; see https://neo-workshop.com for detailed information). However, other works that fit within the scope of NEO are also welcome.

The aim of this Special Issue is to collect papers on the intersection of numerical and evolutionary optimization. We strongly encourage the development of fast and reliable hybrid methods that maximize the strengths and minimize the weaknesses of each underlying paradigm while also being applicable to a broader class of problems. Moreover, this Special Issue aims to foster an understanding and adequate treatment of real-world problems, particularly in emerging fields that affect us all, such as healthcare, smart cities, and big data, among many others.

Topics of interest include (but are not limited to) the following:

(A) Search and optimization:

Single- and multi-objective optimization;
Mathematical programming techniques;
Evolutionary algorithms;
Genetic programming;
Hybrid and memetic algorithms;
Set-oriented numerics;
Stochastic optimization;
Robust optimization.

(B) Real-world problems:

Optimization, machine learning, and metaheuristics applied to:

Energy production and consumption;
Health monitoring systems;
Computer vision and pattern recognition;
Energy optimization and prediction;
Modeling and control of real-world energy systems;
Smart cities.

Prof. Dr. Daniel E. Hernández
Dr. Marcela Quiroz-Castellanos
Dr. Leonardo Trujillo
Prof. Dr. Pierrick Legrand
Prof. Dr. Oliver Schütze
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

single- and multi-objective optimization
evolutionary algorithms
genetic programming
hybrid and memetic algorithms
set-oriented numerics

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Published Papers (9 papers)

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Research

28 pages, 3871 KB

Open AccessArticle

Simulated Annealing Applied to Alternative Assets in Mexican Stock Exchange

by Jose Luis Purata Aldaz, Juan Frausto Solís, Juan J. Gonzalez Barbosa, Guadalupe Castilla-Valdez and Juan Paulo Sánchez Hernández

Math. Comput. Appl. 2026, 31(3), 80; https://doi.org/10.3390/mca31030080 - 13 May 2026

Viewed by 165

Abstract

Accurate price forecasting and portfolio optimization in emerging financial markets remain challenging due to the non-stationary dynamics, structural breaks, and heterogeneous behavior of traded instruments. This paper proposes the Time-series Adaptive Forecast Ensemble (TAFE), a method that combines single popular forecasting methods, such as ARIMA, by using an algorithm derived from both the simulated annealing (SA) and Threshold Accepting algorithms. The TAFE is applied to twenty-four weekly price series of Mexican exchange-traded funds (ETFs) and Real Estate Investment Trusts (FIBRAs) over the period 2020–2025. A top-K pre-selection strategy is used, mitigating the adverse cross-model interaction effect of some assets over others, in other words, reducing the propagation of errors from poorly performing base learners. In addition, the sample results show that the TAFE achieves the lowest mean SMAPE across the panel, with statistical superiority over the equal-weight benchmark and a Hybrid Model, confirmed by Diebold–Mariano and Harvey–Leybourne–Newbold tests. Out-of-sample evaluation over a 26-week horizon reveals a regime-shift-driven performance reversal consistent with the bias–variance tradeoff in adaptive combination schemes. Portfolio optimization using SA-generated forecasts yields with an expected return of 35.77%; thus, the model presents a slight overestimation of the return, with a variance of 2.4%. However, it has an acceptable level of risk. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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30 pages, 1617 KB

Open AccessArticle

ESIPO Methodology: An Ensemble Deep Learning and Metaheuristic Strategies for Stock Forecasting and Investment Portfolio Optimization

by Francisco Rivera Vargas, Juan Javier González Barbosa, Juan Frausto Solís, Mirna Ponce Flores, José Luis Purata Aldaz, Guadalupe Castilla-Valdez and Juan Paulo Sánchez Hernández

Math. Comput. Appl. 2026, 31(3), 75; https://doi.org/10.3390/mca31030075 - 4 May 2026

Viewed by 447

Abstract

An investment portfolio consists of a set of financial assets, such as stocks, fixed-income securities, mutual funds, and real estate, held to achieve diversification and to optimize returns. Accurate asset forecasting provides investors with valuable information to support decision-making. Although existing studies have proposed models for forecasting and portfolio optimization, most rely mainly on traditional techniques and metaheuristic approaches. This work introduces ESIPO (Ensemble Strategies for Investment Portfolio Optimization), a methodology that integrates deep learning and metaheuristic algorithms to perform asset forecasting and investment portfolio optimization. The dataset is obtained from the S&P 500 index, one of the main stock markets. To enhance forecasting accuracy, ESIPO combines five methods from the top-performing models of the international M4 competition: (a) ARIMA (AutoRegressive Integrated Moving Average) and ETS (the statistical exponential-smoothing state-space), which represent classical statistical approaches; (b) FFORMA (Feature-based FORecast Model Averaging) and JAGANATHAN, two ensemble-based methods; (c) CNN (Convolutional Neural Network), which is one of the most common deep learning models. ESIPO improves the forecast performance of the portfolio by applying the TAIPO (Threshold Accepting Investment Portfolio Optimization) metaheuristic to select the best assets and optimize portfolio composition. The results obtained 45% of improvement according to the Sharpe Ratio metric. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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29 pages, 6084 KB

Open AccessArticle

A Problem Landscape Visualisation Method for Multi-Objective Optimisation

by Zhiji Cui, Zimin Liang and Miqing Li

Math. Comput. Appl. 2026, 31(3), 67; https://doi.org/10.3390/mca31030067 - 27 Apr 2026

Viewed by 632

Abstract

Understanding the structure of multi-objective optimisation problems (MOPs) is essential for analysing search difficulty and supporting informed decision-making. In single-objective optimisation, fitness landscapes offer a spatial view of a problem, but extending such visualisations to MOPs is challenging due to the vector-valued nature of objectives. In this work, we introduce Pareto landscape, a fitness landscape visualisation technique for multi-objective optimisation on the basis of the Pareto dominance relation. We illustrate the main characteristics of a Pareto landscape, relate it to the classical fitness landscape, and examine its behaviour across benchmark suites, constrained problems, multimodal problems and real-world cases. We also show how it captures problem landscape structures relevant to optimisation difficulty. A comparison with gradient field heatmaps, PLOT, cost landscape, and constrained cost landscape further demonstrates that Pareto landscape offers complementary insight by highlighting structural patterns not visible with existing visualisation methods. Overall, the results indicate that the Pareto landscape provides a consistent way to observe problem structure across different classes of multi-objective optimisation problems. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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26 pages, 748 KB

Open AccessArticle

Diversity Management Techniques for the Upper-Bounded Hamiltonian p-Median Problem

by José Alejandro Cornejo-Acosta, Carlos Segura, Jesús García-Díaz and Julio César Pérez-Sansalvador

Math. Comput. Appl. 2026, 31(2), 64; https://doi.org/10.3390/mca31020064 - 18 Apr 2026

Viewed by 468

Abstract

The Hamiltonian p-median problem (HpMP) generalizes the classical traveling salesperson (TSP) and the Hamiltonian cycle problems. The HpMP aims to find a collection of p non-intersecting cycles that span all the vertices of a given edge-weighted graph [...] Read more.

G = (V, E, w)

while minimizing the sum of the costs of the cycles. This paper introduces a memetic algorithm (MA) with explicit diversity management for the upper-bounded HpMP (UB-HpMP), where upper-bounded means that each cycle in the solution cannot exceed a maximum number of vertices. This MA approaches the problem as a set-partitioning problem, where each cluster of the partition contains the vertices of each cycle. Moreover, it uses a novel crossover operator based on the Hungarian algorithm, exploits the Lin–Kernighan heuristic, a state-of-the-art algorithm for the TSP, and uses best-non-penalized (BNP) selection to explicitly manage the population’s diversity. The proposed MA is tested against state-of-the-art algorithms and classical techniques, including those with and without implicit diversity management, as well as an open-source heuristic solver. The computational experimentation results show that explicit diversity management has advantages over other techniques. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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25 pages, 2236 KB

Open AccessArticle

On the Unambiguous, Traceable and Dimensionally Homogeneous Calculation of Per-Unit Parameters for the Two-Mass Drive Train Model of a Set of Reference Wind Turbines

by Joel Rodríguez-Guillén, Rubén Salas-Cabrera, Bárbara María-Esther García-Morales, Miguel A. García-Morales and Juan Frausto-Solís

Math. Comput. Appl. 2026, 31(2), 51; https://doi.org/10.3390/mca31020051 - 1 Apr 2026

Viewed by 465

Abstract

The Bond Graph (BG) methodology, a multi-domain graphical description formalism, is used to study a horizontal-axis two-mass drive train of a wind turbine. The main contribution of this work is to address the lack of wind energy literature dealing with fully unambiguous, traceable, and dimensionally homogeneous per-unit quantities for two-mass drive train models. Data in real quantities for the drive train are collected from open-access datasheets and their corresponding design information files. Wind turbines that may serve as Reference Wind Turbines (RWTs), with traceable calculations, are carefully selected. A lumped-parameter order-reduction method is employed to convert data from higher-order models into data for a reduced-order two-mass model. The BG methodology is then used to formally derive the per-unit drive train model and its corresponding dimensionally homogeneous per-unit parameters for a set of six representative Reference Wind Turbines, covering a nominal power range from 0.75 MW to 5 MW. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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25 pages, 337 KB

Open AccessArticle

A Belief Model for BDI Agents Derived from Roles and Personality Traits

by Eduardo David Martínez-Hernández, Bárbara María-Esther García-Morales, María Lucila Morales-Rodríguez, Claudia Guadalupe Gómez-Santillán and Nelson Rangel-Valdez

Math. Comput. Appl. 2026, 31(2), 37; https://doi.org/10.3390/mca31020037 - 3 Mar 2026

Viewed by 670

Abstract

Recent advancements in AI have enabled autonomous agents to interact within complex environments, with deliberative BDI (Belief–Desire–Intention) agents standing out for their human-inspired reasoning capabilities. However, defining the initial beliefs that constitute an agent’s cognitive profile remains a significant challenge. This process often relies on manual approaches that limit scalability and validation. This study proposes the Personality–Role–Belief (P–R–B) Model for BDI agents, introducing a novel architecture for generating cognitive profiles applicable to domains such as social simulation and non-player characters (NPCs). The model translates Five-Factor Model (FFM) scores into specific social roles, assigning base beliefs to each. A key contribution is a weighting mechanism designed to resolve conflicts between beliefs when multiple roles coexist. Inspired by Cohen’s effect size conventions, this mechanism establishes an influence hierarchy that quantifies belief strength based on social roles. Consequently, this approach not only enables agents to exhibit coherent behavior consistent with their personality but also establishes a foundation for modeling ethical decision-making through role–trait alignment, thereby facilitating the creation of agents capable of navigating morally complex social contexts. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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43 pages, 1864 KB

Open AccessArticle

An Adaptive Grouping Genetic Algorithm with Controlled Gene Transmission Based on Fullness and Item Strategies (AGGA-CGT-FIS)

by Stephanie Amador-Larrea, Marcela Quiroz-Castellanos, Octavio Ramos-Figueroa and Alejandro Guerra-Hernández

Math. Comput. Appl. 2026, 31(2), 34; https://doi.org/10.3390/mca31020034 - 1 Mar 2026

Viewed by 756

Abstract

The one-dimensional Bin Packing Problem (1D-BPP) is a well-known NP-hard grouping problem characterized by high structural complexity and broad practical relevance. Among the metaheuristic approaches proposed for this problem, the Grouping Genetic Algorithm with Controlled Gene Transmission (GGA-CGT) has shown remarkable performance. In this work, an Adaptive Grouping Genetic Algorithm with Controlled Gene Transmission based on Fullness and Item Strategies (AGGA-CGT-FIS) is presented. This approach extends the original GGA-CGT by integrating domain-guided crossover mechanisms and adaptive parameter control schemes. The proposed algorithm incorporates a novel gene-level crossover operator, termed Fullness–Items Gene-Level Crossover 1 (FI-GLX-1). This operator exploits structural information from the solutions through Fullness- and Item-based ordering and transmission strategies. In addition, adaptive control schemes are introduced for key evolutionary parameters associated with crossover and mutation. These mechanisms allow the algorithm to dynamically adjust its behavior according to feedback extracted from the search process, resulting in a fully adaptive variant of the GGA-CGT. The effectiveness of AGGA-CGT-FIS is evaluated using two benchmark sets for the 1D-BPP: the classic and the BPP

v_{u}_c

instances. The proposed approach is compared against the baseline GGA-CGT using the original Gene-Level Crossover (GLX) operator. Experimental results show improvements in solution quality and convergence behavior, supported by statistical analyses that confirm the significance of the observed performance differences. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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28 pages, 572 KB

Open AccessArticle

New Adaptive Echolocation Radar Technique Incorporated into the Bat Algorithm Applied to Benchmark Functions (Radar-Bat)

by Miguel A. García-Morales, Rubén Salas-Cabrera, Bárbara María-Esther García-Morales, Juan Frausto-Solís and Joel Rodríguez-Guillén

Math. Comput. Appl. 2026, 31(1), 20; https://doi.org/10.3390/mca31010020 - 2 Feb 2026

Viewed by 660

Abstract

This article proposes a bat algorithm that incorporates novel techniques inspired by maritime radars, referred to as the Radar-Bat algorithm. This proposed method allows each virtual bat to identify the position of the best solution at a given distance within the search space. It incorporates an adaptive threshold to maintain a constant false alarm rate (CFAR), enabling the acceptance of solutions based on the best value found, thus improving the exploitation of the search space. Furthermore, a systematic directional sweep balances exploration and exploitation effectively. This algorithm is used to solve complex optimization problems, essentially those with multimodal functions, demonstrating that the proposed algorithm achieves better convergence and robustness compared to the basic bat algorithm, highlighting its potential as a novel contribution to the field of metaheuristics. To evaluate the performance of the proposed algorithm against the basic bat algorithm, the Wilcoxon and Friedman non-parametric tests are applied, with a significance level of 5%. Computational experiments show that the proposed algorithm outperforms the state-of-the-art algorithm. In terms of quality, the proposed algorithm shows clear superiority over the basic bat algorithm across most benchmark functions. Regarding efficiency, although Radar Bat incorporates additional mechanisms, the experimental results do not indicate a consistent disadvantage in execution time, with both algorithms exhibiting comparable performance depending on the problem and dimensionality. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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21 pages, 988 KB

Open AccessArticle

Study of Performance from Hierarchical Decision Modeling in IVAs Within a Greedy Context

by Francisco Federico Meza-Barrón, Nelson Rangel-Valdez, María Lucila Morales-Rodríguez, Claudia Guadalupe Gómez-Santillán, Juan Javier González-Barbosa, Guadalupe Castilla-Valdez, Nohra Violeta Gallardo-Rivas and Ana Guadalupe Vélez-Chong

Math. Comput. Appl. 2026, 31(1), 8; https://doi.org/10.3390/mca31010008 - 7 Jan 2026

Viewed by 1060

Abstract

This study examines decision-making in intelligent virtual agents (IVAs) and formalizes the distinction between tactical decisions (individual actions) and strategic decisions (composed of sequences of tactical actions) using a mathematical model based on set theory and the Bellman equation. Although the equation itself is not modified, the analysis reveals that the discount factor (γ) influences the type of decision: low values favor tactical decisions, while high values favor strategic ones. The model was implemented and validated in a proof-of-concept simulated environment, namely the Snake Coin Change Problem (SCCP), using a Deep Q-Network (DQN) architecture, showing significant differences between agents with different decision profiles. These findings suggest that adjusting γ can serve as a useful mechanism to regulate both tactical and strategic decision-making processes in IVAs, thus offering a conceptual basis that could facilitate the design of more intelligent and adaptive agents in domains such as video games, and potentially in robotics and artificial intelligence as future research directions. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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