Special Issue: “Multi-objective Optimization and Applications”

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Special Issue “Multi-objective Optimization and Applications”

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section “Computational and Applied Mathematics.”

Deadline for manuscript submissions: 31 March 2025

Special Issue Editors

Prof. Dr. Víctor Yepes E-Mail Website Guest Editor

Institute of Concrete Science and Technology (ICITECH), Construction Engineering Department, Universitat Politècnica de València, 46022 València, Spain
Interests: multiobjective optimization; structures optimization; lifecycle assessment; social sustainability of infrastructures; reliability-based maintenance optimization; optimization and decision-making under uncertainty
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Moacir Kripka E-Mail Website Guest Editor

Civil and Environmental Engineering Graduate Program (PPGEng), University of Passo Fundo, Passo Fundo CEP 99052-900, Brazil
Interests: structural analysis; optimization; engineering optimization; linear programming; mathematical programming; heuristics; structural optimization; concrete; combinatorial optimization; structural engineering; multiobjective optimization; reinforced concrete; optimization methods; discrete optimization; optimization theory; optimization software
Special Issues, Collections and Topics in MDPI journals

Dr. José Antonio García E-Mail Website Guest Editor

Escuela de Ingeniería en Construcción, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2147, Valparaíso 2362804, Chile
Interests: optimization; deep learning; operations research; artificial intelligence applications to industrial problems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimization techniques have become frequent in recent decades due to the growing competitiveness brought about by globalization. With the development of new methods and the greater availability of computer resources, applications in the most diverse fields of knowledge have spread from academic banks to the day-to-day running of companies. However, a more realistic approach can be achieved if several objectives are integrated into the process. Thus, an exciting strategy cannot only meet cost requirements, for example, but it also concerns itself with durability, efficiency, reliability, and sustainability. Given that numerous objectives are involved, which are usually in conflict, new strategies are needed, while new and more complete applications are envisioned. In this sense, the Special Issue, “Multi-objective Optimization and Applications,” aims to provide a platform for disseminating knowledge related to multi-objective optimization. Research articles involving efficient and innovative optimization methods and new applications related to diverse areas of expertise are sought, promoting an exchange of new ideas and trends concerning the subject.

Prof. Dr. Víctor Yepes
Prof. Dr. Moacir Kripka
Dr. José Antonio García
Guest Editors

Manuscript Submission Information

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Keywords

multi-objective optimization
optimization methods
optimization applications
innovative methods and algorithms

Published Papers

This special issue is now open for submission.

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Mejora de la robustez en la optimización de estructuras modulares prefabricadas: Integración de NSGA-II, NSGA-III y RVEA para una infraestructura sostenible

Acaban de publicarnos un artículo en Mathematics, revista indexada en el primer decil del JCR. El documento explora el diseño de estructuras modulares prefabricadas sostenibles utilizando la optimización multiobjetivo (MOO) y la toma de decisión multicriterio (MCDM) con algoritmos avanzados como NSGA-II, NSGA-III y RVEA. El trabajo se enmarca dentro del proyecto de investigación HYDELIFE que dirijo como investigador principal en la Universitat Politècnica de València.

El artículo destaca la importancia de integrar la sostenibilidad del ciclo de vida en los proyectos de infraestructura de transporte para estimular la innovación y la colaboración entre las partes interesadas. Además, presenta una estrategia de diseño novedosa que se centra en la optimización del ciclo de vida de los marcos modulares prefabricados de hormigón armado (RCPMF). Por último, amplía la comprensión de la aplicabilidad de los algoritmos avanzados de MOO y las técnicas de MCDM para mejorar el desarrollo sostenible de la infraestructura.

Las conclusiones más importantes de este trabajo son las siguientes:

El estudio evalúa el rendimiento de optimización del ciclo de vida de los algoritmos NSGA-II, NSGA-III y RVEA dentro de una estructura prefabricada tipo marco de diseño coherente para una infraestructura de transporte sostenible.
El NSGA-III se identifica como el algoritmo con mejor rendimiento, lo que demuestra su potencial para facilitar enfoques de diseño sostenibles.
El problema del MCDM se evalúa rigurosamente y se abordan nueve soluciones no dominantes generadas por los algoritmos de optimización, lo que demuestra la eficiencia y la fiabilidad del marco integrado de MOO y MCDM.
Los resultados abogan por un enfoque transformador del desarrollo de infraestructuras, orientado hacia soluciones de ingeniería más avanzadas y sostenibles.

Abstract:

The advancement toward sustainable infrastructure presents complex multi-objective optimization (MOO) challenges. This paper expands the current understanding of design frameworks that balance cost, environmental impacts, social factors, and structural integrity. Integrating MOO with multi-criteria decision-making (MCDM), the study targets enhancements in life cycle sustainability for complex engineering projects using precast modular road frames. Three advanced evolutionary algorithms—NSGA-II, NSGA-III, and RVEA—are optimized and deployed to address sustainability objectives under performance constraints. The efficacy of these algorithms is gauged through a comparative analysis, and a robust MCDM approach is applied to nine non-dominated solutions, employing SAW, FUCA, TOPSIS, PROMETHEE, and VIKOR decision-making techniques. An entropy theory-based method ensures systematic, unbiased criteria weighting, augmenting the framework’s capacity to pinpoint designs, balancing life cycle sustainability. The results reveal that NSGA-III is the algorithm converging towards the most cost-effective solutions, surpassing NSGA-II and RVEA by 21.11% and 10.07%, respectively, while maintaining balanced environmental and social impacts. The RVEA achieves up to 15.94% greater environmental efficiency than its counterparts. The analysis of non-dominated solutions identifies the $A_{4}$ design, utilizing 35 MPa concrete and B500S steel, as the most sustainable alternative across 80% of decision-making algorithms. The ranking correlation coefficients above 0.94 demonstrate consistency among decision-making techniques, underscoring the robustness of the integrated MOO and MCDM framework. The results in this paper expand the understanding of the applicability of novel techniques for enhancing engineering practices and advocate for a comprehensive strategy that employs advanced MOO algorithms and MCDM to enhance sustainable infrastructure development.

Keywords:

Multi-objective optimization; multi-criteria decision-making; NSGA-II; NSGA-III; RVEA; SAW; FUCA; TOPSIS; PROMETHEE; VIKOR

Reference:

RUIZ-VÉLEZ, A.; GARCÍA, J.; ALCALÁ, J.; YEPES, V. (2024). Enhancing Robustness in Precast Modular Frame Optimization: Integrating NSGA-II, NSGA-III, and RVEA for Sustainable Infrastructure. Mathematics, 12(10):1478. DOI:10.3390/math12101478

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Toma de decisiones sobre infraestructuras viarias sostenibles: NSGA-II con operadores de reparación para optimización multiobjetivo

Acaban de publicarnos un artículo en Mathematics, revista indexada en el primer decil del JCR. El trabajo trata sobre la toma de decisiones en infraestructuras viales sostenibles. Para ello se utiliza una variante personalizada de la técnica NSGA-II con operadores de reparación para una optimización multiobjetivo. El trabajo se enmarca dentro del proyecto de investigación HYDELIFE que dirijo como investigador principal en la Universitat Politècnica de València.

El documento propone un enfoque novedoso que combina la optimización multiobjetivo (MOO) con técnicas de toma de decisiones basadas en criterios múltiples (MCDM) para el diseño y la selección de estructuras modulares prefabricadas de hormigón armado (RCPMF) en infraestructuras viales, con un enfoque en la sostenibilidad. El estudio evalúa la eficacia de tres operadores de reparación a la hora de optimizar los objetivos económicos, ambientales y sociales, y utiliza algoritmos personalizados y un análisis del ciclo de vida (LCA) para una evaluación precisa. Los resultados muestran que el operador de reparaciones basado en estadísticas ofrece soluciones con un menor impacto en todas las dimensiones y demuestra una variabilidad mínima, lo que lo convierte en el más adecuado para cumplir con los requisitos de diseño del RCPMF.

Las contribuciones más importantes de este trabajo son las siguientes:

El documento presenta un enfoque novedoso que combina la optimización multiobjetivo (MOO) con técnicas de toma de decisiones basadas en criterios múltiples (MCDM) para el diseño y la selección de estructuras modulares prefabricadas de hormigón armado (RCPMF) en infraestructuras viales, con un enfoque en la sostenibilidad.
El estudio evalúa la eficacia de tres operadores de reparación (basados en estadísticas, aleatorios y de proximidad) a la hora de optimizar los objetivos económicos, ambientales y sociales.
El artículo presenta una versión personalizada del algoritmo NSGA-II (NSGA-II) de clasificación no dominada, complementada con un análisis detallado del ciclo de vida (LCA), para facilitar la evaluación precisa de las funciones objetivas.
El artículo demuestra el uso de dos técnicas de MCDM, a saber, la ponderación aditiva simple (SAW) y (FUCA), para puntuar y clasificar las soluciones MOO.
La investigación proporciona una estrategia clara y metódica para integrar el MOO y el MCDM, formando un marco coherente para la implementación práctica en contextos de ingeniería complejos.
El estudio destaca la importancia de tener en cuenta los principios de sostenibilidad desde la fase de diseño y de emplear las técnicas de MOO para encontrar soluciones equilibradas y óptimas en la ingeniería civil.

Abstract:

Integrating sustainability principles into the structural design and decision-making processes for transportation infrastructure, particularly concerning reinforced concrete precast modular frames (RCPMF), is recognized as crucial for ensuring environmentally responsible, economically feasible, and socially beneficial outcomes. In this study, this challenge is addressed, with the significance of sustainable development in modern engineering practices being underscored. A novel approach, which combines multi-objective optimization (MOO) with multi-criteria decision-making (MCDM) techniques, is proposed, tailored specifically for the design and selection of RCPMF. The effectiveness of three repair operators—statistical-based, random, and proximity based—in optimizing economic, environmental, and social objectives is evaluated. Precise evaluation of objective functions is facilitated by a customized Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, complemented by a detailed life cycle analysis (LCA). The utilization of simple additive weighting (SAW) and fair un choix adéquat (FUCA) methods for the scoring and ranking of the MOO solutions has revealed that notable excellence in meeting the RCPMF design requirements is exhibited by the statistical-based repair operator, which offers solutions with lower impacts across all dimensions and demonstrates minimal variability. MCDM techniques produced similar rankings, with slight score variations and a significant correlation of 0.9816, showcasing their consistent evaluation capacity despite distinct operational methodologies.

Keywords:

Multi-objective optimization; multi-criteria decision-making; modular structure; life cycle sustainability; NSGA-II; simple additive weighting; fair un choix adéquat.

Reference:

RUIZ-VÉLEZ, A.; GARCÍA, J.; ALCALÁ, J.; YEPES, V. (2024). Sustainable Road Infrastructure Decision-Making: Custom NSGA-II with Repair Operators for Multi-objective Optimization. Mathematics, 12(5):730. DOI:10.3390/math12050730

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