Diversity Metrics in Combinatorial Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 2363

Special Issue Editors


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Escuela de Construcción Civil, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile
Interests: metaheuristics; combinatorial optimization; swarm intelligence; hybrid algorithms; reinforcement learning; machine learning; civil engineering; infrastructure optimization; UAV

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Escuela de Negocios Internacionales, Universidad de Valparaíso, Alcalde Prieto Nieto 452, Viña del Mar, Chile
Interests: metaheuristics; combinatorial optimization; swarm intelligence; hybrid algorithms; reinforcement learning; machine learning; discretization methods; set covering problem; applied artificial intelligence; soft computing

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Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso, Chile
Interests: applied artificial intelligence; predictive and prescriptive analytics; hospital operations optimization; surgical scheduling; resource allocation; renewable energy forecasting; AI for healthcare management; smart infrastructure; data integration platforms

Special Issue Information

Dear Colleagues,

Combinatorial optimization problems remain at the core of modern optimization, where balancing exploration and exploitation determines the efficiency and robustness of solutions. In this context, diversity metrics have become essential tools for understanding and enhancing the behavior of metaheuristic algorithms, helping prevent premature convergence and promote more adaptive and efficient search processes.

This Special Issue invites researchers to contribute theoretical, methodological, or applied studies that explore the role of diversity in combinatorial optimization. Contributions may include new diversity measures, hybrid strategies, integration with reinforcement learning, as well as applications in engineering, planning, or complex systems.

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

  • Diversity metrics in metaheuristic algorithms;
  • Diversity in combinatorial optimization;
  • Reinforcement learning integrated with metaheuristics;
  • Adaptive parameter control driven by diversity;
  • Population-based and swarm-intelligence diversity;
  • Hybridization of heuristic and exact methods;
  • Exploration-exploitation balance and theoretical analysis;
  • Applications in civil engineering, transportation, energy, and intelligent systems.

We warmly invite the research community to share advances that foster more diverse, robust, and sustainable optimization approaches.

Dr. José Lemus-Romani
Prof. Dr. Gino Astorga
Dr. Marcelo Becerra
Guest Editors

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Keywords

  • diversity metrics
  • combinatorial optimization
  • metaheuristics
  • swarm intelligence
  • evolutionary algorithms
  • population diversity
  • exploration–exploitation balance
  • adaptive search
  • reinforcement learning
  • hybrid algorithms
  • diversity control
  • adaptive parameter tuning
  • diversity-based selection
  • algorithmic diversity
  • diversity-guided optimization
  • stochastic search
  • diversity indicators
  • fitness landscape analysis
  • diversity quantification
  • diversity in reinforcement learning
  • combinatorial landscapes
  • search space exploration
  • diversity-driven convergence
  • algorithm robustness
  • engineering optimization
  • intelligent systems

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Published Papers (2 papers)

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23 pages, 616 KB  
Article
Robust Metaheuristic Optimization for Algorithmic Trading: A Comparative Study of Optimization Techniques
by Kaled Hernández-Romo, José Lemus-Romani, Emanuel Vega, Marcelo Becerra-Rozas and Andrés Romo
Mathematics 2026, 14(1), 69; https://doi.org/10.3390/math14010069 - 24 Dec 2025
Cited by 2 | Viewed by 1543
Abstract
Algorithmic trading heavily relies on the optimization of rule-based strategies to maximize profitability and ensure robustness under volatile market conditions. Traditional optimization methods often face limitations when dealing with the nonlinear, high-dimensional, and dynamic nature of financial search spaces. This study introduces a [...] Read more.
Algorithmic trading heavily relies on the optimization of rule-based strategies to maximize profitability and ensure robustness under volatile market conditions. Traditional optimization methods often face limitations when dealing with the nonlinear, high-dimensional, and dynamic nature of financial search spaces. This study introduces a Metaheuristic-based framework for financial strategy optimization that focuses on the modeling and resolution of the problem through population-based search algorithms. The framework evaluates four Metaheuristic optimization techniques within a unified design, enabling a consistent and fair comparison of their performance in optimizing trading rules. To ensure realistic and time-consistent evaluation, the experimental setup incorporates a Rolling Windows Validation approach, allowing the assessment of model performance across successive market periods. Beyond improving convergence behavior, Diversity is employed as a metric to assess the quality and exploration capability of the search process, providing deeper insight into algorithmic performance. Experimental results, obtained from real market data, demonstrate substantial improvements in profitability consistency and risk-adjusted performance compared to conventional optimization approaches. The findings confirm that Metaheuristic optimization offers a robust and flexible alternative for the design and refinement of algorithmic trading systems in complex and dynamic financial environments. Interestingly, Differential Evolution exhibited persistently high Diversity, suggesting the presence of multiple distant yet competitive optima in the financial search space, where functional convergence coexists with geometric dispersion. Full article
(This article belongs to the Special Issue Diversity Metrics in Combinatorial Problems)
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37 pages, 3341 KB  
Systematic Review
Quality–Diversity and Illumination Algorithms in Discrete Combinatorial Domains: Diversity Metrics and Implications for Resilient Mining Operations
by Luis Rojas, Emanuel Vega, Lorena Jorquera and José Garcia
Mathematics 2026, 14(7), 1091; https://doi.org/10.3390/math14071091 - 24 Mar 2026
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Abstract
Quality–Diversity (QD) optimization has emerged as a distinctive paradigm in evolutionary computation, shifting the focus from identifying a single global optimum to illuminating a high-dimensional repertoire of elite solutions that jointly maximize performance and behavioral diversity. While algorithms like MAP-Elites have enabled transformative [...] Read more.
Quality–Diversity (QD) optimization has emerged as a distinctive paradigm in evolutionary computation, shifting the focus from identifying a single global optimum to illuminating a high-dimensional repertoire of elite solutions that jointly maximize performance and behavioral diversity. While algorithms like MAP-Elites have enabled transformative results in robotics and procedural content generation, their generalization to discrete combinatorial domains remains insufficiently consolidated in the literature. To address this gap, a systematic literature review was conducted strictly following PRISMA 2020 guidelines. The synthesis reveals rapid exponential growth in QD research, accompanied by significant algorithmic diversification toward gradient-informed variations and hardware-accelerated implementations. Despite this maturation, discrete combinatorial applications remain comparatively underrepresented, with only a small fraction (12.5%) of the analyzed corpus explicitly addressing discrete problems using domain-specific representations and heuristics. Based on these empirical findings, a conceptual framework is proposed. This framework positions QD as a vital mechanism for operational resilience in stochastic industrial contexts—specifically mining operations, including predictive maintenance, mineral processing optimization, and blast design—demonstrating its strategic value for complex decision-making. Full article
(This article belongs to the Special Issue Diversity Metrics in Combinatorial Problems)
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