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Modelling
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Optimization in Engineering: Models and Algorithms
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Optimization in Engineering: Models and Algorithms

A special issue of Modelling (ISSN 2673-3951).

Deadline for manuscript submissions: 31 December 2026 | Viewed by 3295

Editors

Dr. Pierluigi Fanelli

E-Mail Website
Guest Editor
Department of Economics, Engineering, Business and Society, University of Tuscia, 01100 Viterbo, Italy
Interests: structural analysis; finite element method; composite materials; lattice structure; welded structure; riveted and bolted structures; nuclear fusion; metamaterials
Special Issues, Collections and Topics in MDPI journals
Dr. Valerio Belardi

E-Mail Website
Guest Editor
Department of Enterprise Engineering, University of Rome Tor Vergata, Via del Politecnico, 1, 00133 Rome, Italy
Interests: finite element analysis; anisogrid lattice structures; structural engineering; solid mechanics; structural analysis; mechanics of materials; finite element modeling; mechanical behavior of materials; stress analysis; mechanics of composite materials
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As Guest Editors, we are pleased to announce a Special Issue of Modelling entitled "Optimization in Engineering: Models and Algorithms".

This Special Issue aims to present high-quality contributions on recent advances in optimization techniques and their applications across various branches of engineering. We welcome both original research articles and comprehensive review papers.

Optimization plays a crucial role in the design, analysis, and operation of modern engineering systems. The development of mathematical models and efficient algorithms enables engineers to make informed decisions, reduce costs, improve performance, and ensure sustainability. This Special Issue seeks to highlight the latest developments in modelling approaches, algorithmic strategies, and practical applications of optimization in engineering.

We are particularly interested in contributions that address, but are not limited to, the following topics:

  • Mathematical programming and numerical optimization methods;
  • Heuristic and metaheuristic algorithms (e.g., genetic algorithms, particle swarm, ant colony);
  • Multi-objective and multi-disciplinary optimization;
  • Surrogate models and reduced-order modelling for optimization;
  • Topology and shape optimization in structural and mechanical design;
  • Optimization under uncertainty and robust design;
  • Data-driven optimization and machine learning applications in engineering;
  • Real-time optimization and control of engineering systems;
  • Applications of optimization in energy systems, manufacturing, transportation, and robotics.

Submissions should be original, unpublished works that are not under consideration elsewhere. All manuscripts will undergo rigorous peer review by at least two experts in the field. Accepted papers will be published in this Special Issue of Modelling.

We look forward to receiving your contributions and thank you in advance for your interest and support.

Dr. Pierluigi Fanelli
Dr. Valerio Belardi
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-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Modelling 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 1200 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.

Publisher’s Notice

The Special Issue has been removed from Section Modelling in Engineering Structures on 6 November 2025. At the time of the move, there were no publications in this Special Issue.

Keywords

  • engineering optimization
  • mathematical modelling
  • metaheuristic algorithms
  • multi-objective optimization
  • structural optimization
  • machine learning in engineering
  • robust design
  • computational mechanics
  • surrogate modelling
  • design under uncertainty

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

22 pages, 1233 KB  
Article
Enhancing Construction Simulation Optimization Performance Through Variance Reduction Techniques
by Mohammed Mawlana and Amin Hammad
Modelling 2026, 7(4), 137; https://doi.org/10.3390/modelling7040137 - 5 Jul 2026
Viewed by 364
Abstract
Simulation optimization has been used to analyze construction operations and support planning decisions under uncertainty. It enables the identification of effective planning strategies throughout a project’s lifecycle. However, the use of stochastic simulation to evaluate alternative strategies results in higher computational demands and [...] Read more.
Simulation optimization has been used to analyze construction operations and support planning decisions under uncertainty. It enables the identification of effective planning strategies throughout a project’s lifecycle. However, the use of stochastic simulation to evaluate alternative strategies results in higher computational demands and the generation of inferior solutions within the resulting optimal solutions. This study examines the feasibility of overcoming these issues by implementing variance reduction techniques into a discrete-event simulation optimization framework. Three variance reduction techniques are evaluated in a case study: Common Random Numbers, Antithetic Variates, and a combined application of both. While these techniques are well established in simulation, their impact on the optimization performance of construction problems has not been fully explored. The results show that VRT not only reduces the computational effort required to evaluate planning strategies but also provides better planning strategies. Among the evaluated techniques, the combined approach demonstrates the best improvements. Overall, the study highlights that variance reduction techniques can make simulation optimization frameworks more practical and reliable for complex construction projects. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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35 pages, 9700 KB  
Article
A Globally Adaptive Ant Colony System with Stagnation Recovery and Candidate-List Search for Traveling Salesman Problems
by Shang Wang, Yajuan Zhang and Linjie Li
Modelling 2026, 7(4), 130; https://doi.org/10.3390/modelling7040130 - 30 Jun 2026
Viewed by 446
Abstract
The Traveling Salesman Problem (TSP) is a fundamental NP-hard combinatorial optimization problem with broad applications in logistics, scheduling, and satellite mission planning. While Ant Colony Optimization (ACO) offers distributed search and positive feedback, conventional variants suffer from premature convergence and quadratic construction costs [...] Read more.
The Traveling Salesman Problem (TSP) is a fundamental NP-hard combinatorial optimization problem with broad applications in logistics, scheduling, and satellite mission planning. While Ant Colony Optimization (ACO) offers distributed search and positive feedback, conventional variants suffer from premature convergence and quadratic construction costs that limit scalability. We propose the Globally Adaptive Ant Colony System (GACS), which integrates three synergistic mechanisms: (1) K-nearest neighbor candidate-list pruning that reduces per-step construction complexity from O(n) to O(K); (2) a globally adaptive pheromone weighting scheme that dynamically calibrates reinforcement intensity as the search matures; and (3) an adaptive stagnation recovery mechanism that applies pheromone smoothing to escape local optima. Numerical experiments demonstrate that GACS consistently outperforms four traditional ACO baselines under an equivalent time budget. On a large benchmark set from TSPLIB, GACS achieves highly competitive results against various state-of-the-art metaheuristics, with non-parametric statistical tests confirming its significant superiority in both solution quality and convergence rank. Ablation and sensitivity analyses verify that all three mechanisms are individually indispensable and that the framework is robust to parameter perturbation. Specifically, the evaporation rate and stagnation threshold are identified as the most critical parameters affecting performance, while the smoothing and adaptive range parameters exhibit low sensitivity. These results establish GACS as a lightweight, scalable, and adaptable framework for the TSP. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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30 pages, 12985 KB  
Article
Crashworthiness Assessment Using Lumped Parameter Models for Reduced-Order Modelling in Railway Crashworthiness Analysis
by Rogério F. F. Lopes, Christian J. Silva, Rodrigo R. Menéres, Pedro J. S. C. P. Sousa, Pedro M. G. P. Moreira, João S. Silva and Rodrigo S. Andrade
Modelling 2026, 7(3), 120; https://doi.org/10.3390/modelling7030120 - 18 Jun 2026
Viewed by 341
Abstract
The design of a railway coach must meet strict certification requirements, especially in crashworthiness analysis under the European standard EN 15227. Performing this analysis with full-scale FEM models is highly demanding in terms of time, computational power and engineering resources, even with large [...] Read more.
The design of a railway coach must meet strict certification requirements, especially in crashworthiness analysis under the European standard EN 15227. Performing this analysis with full-scale FEM models is highly demanding in terms of time, computational power and engineering resources, even with large server clusters. To improve efficiency, it is useful to simplify regions of the structure that are less influenced by external loads. In this approach, less critical parts are replaced with flexible one-dimensional elements, reducing the number of degrees of freedom while preserving the vehicle’s main dynamic behaviour. By concentrating on a specific mid-span section, the model becomes more robust and easier to manage. Calibrated elements are introduced to accurately reproduce the mass and stiffness of the removed structural components. The methodology also integrates mass and stiffness elements to capture structural response over a broader frequency range. An iterative non-gradient calibration procedure is then applied to adjust the equivalent stiffness and mass distribution so that the simplified model reproduces the response of the full-scale reference model. The results show that this strategy is effective, achieving a 77.6% reduction in simulation time while maintaining reliable accuracy. However, the process is still labour-intensive, and its performance may decline under large deformation conditions. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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22 pages, 847 KB  
Article
Estimation of the Voltage Stability Margin in Power Systems Under Transmission Line Contingencies Using a Convex Formulation and a Heuristic Approach
by Jenny Vanessa Rojas-Báez, María Fernanda Laverde-Rojas and Oscar Danilo Montoya
Modelling 2026, 7(3), 106; https://doi.org/10.3390/modelling7030106 - 30 May 2026
Viewed by 437
Abstract
Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage [...] Read more.
Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage stability margin under N−1 transmission line contingencies through three solution methodologies: a nonlinear programming formulation solved via an interior-point algorithm (IPOPT) with a multi-start strategy, a recursive heuristic approach based on successive Newton–Raphson power flow solutions with progressive load scaling, and a convex second-order cone programming relaxation. The proposed methods are validated on the IEEE 9-, 14-, 30-, and 57-bus test systems, thereby covering networks of varying topological complexity and redundancy. A comparative analysis evaluates the accuracy of each approach against a nonlinear programming reference, as well as their computational efficiency under a comprehensive set of contingency scenarios. The results indicate that the heuristic method achieves higher precision, while the convex formulation offers a substantially faster solution, with both approaches demonstrating robustness in cases where the nonlinear programming method fails to converge. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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21 pages, 12506 KB  
Article
A Weak Magnetic Anomaly Signal Enhancement Method Based on an Adaptive Variable-Structure Stochastic Resonance System
by Hexing Zheng, Jinguo Liu, Haitao Gu, Fang Shi and Kexin Zhang
Modelling 2026, 7(3), 104; https://doi.org/10.3390/modelling7030104 - 26 May 2026
Cited by 1 | Viewed by 380
Abstract
Magnetic anomaly detection (MAD) is a passive technique for detecting ferromagnetic targets, but weak magnetic anomaly signals are often submerged in background noise. Existing stochastic resonance (SR)-based MAD methods mainly focus on target detection and generally provide limited capability for waveform and amplitude [...] Read more.
Magnetic anomaly detection (MAD) is a passive technique for detecting ferromagnetic targets, but weak magnetic anomaly signals are often submerged in background noise. Existing stochastic resonance (SR)-based MAD methods mainly focus on target detection and generally provide limited capability for waveform and amplitude reconstruction. To address this problem, this paper proposes a weak magnetic anomaly signal enhancement method based on an adaptive variable-structure stochastic resonance (AVSSR) system. A potential function capable of switching among monostable, bistable, and multistable structures is designed to improve the adaptability of SR processing under different noise conditions. The noisy vector magnetic signals are processed by the AVSSR system, and the normalized sliding-window standard deviation is combined with a scaling factor to reconstruct the magnetic anomaly signal’s waveform and amplitude. The system parameters are optimized using the differential evolution algorithm. Simulation results show that the proposed method can effectively reconstruct magnetic anomaly signals under Gaussian white noise and colored 1/fα noise, even at an input SNR of −15 dB. Comparisons with the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method and an adaptive multistable SR method demonstrate better waveform preservation and more stable amplitude reconstruction. Experimental results using measured Bt signals further verify its practical applicability. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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18 pages, 3134 KB  
Article
Research on the Multi-Objective Optimization of a Pulsating Assembly Line of Aircraft Components Based on a Hierarchical Hybrid Algorithm
by Haiwei Li, Xi Zhang, Fansen Kong, Guoqiu Song and Lie Cao
Modelling 2026, 7(3), 85; https://doi.org/10.3390/modelling7030085 - 29 Apr 2026
Viewed by 455
Abstract
To improve the assembly efficiency and productivity of complex aircraft components, the optimization of an assembly line was investigated in this study. A hierarchical hybrid multi-objective optimization algorithm (HHMOA) was proposed using an improved non-dominated sorting genetic algorithm II and an enhanced longest [...] Read more.
To improve the assembly efficiency and productivity of complex aircraft components, the optimization of an assembly line was investigated in this study. A hierarchical hybrid multi-objective optimization algorithm (HHMOA) was proposed using an improved non-dominated sorting genetic algorithm II and an enhanced longest processing time algorithm. The algorithm incorporates a two-layer framework for global–local optimization; an information entropy-based problem formulation with three objectives, including line balance rate, load balance index and assembly complexity smoothness index; and a hybrid initialization strategy for high-quality initial solutions. Based on the assembly line datasets of different scales, the algorithm performance was verified by comparing the hypervolume and the calculation efficiency using HHMOA and three benchmark algorithms, and the sensitivity analyses verified the algorithm robustness. For an actual aircraft component assembly line, the optimizations carried out with the given process time, number of workstations and precedence relationships indicate that the balance rate of the optimized line increased 72%, and the load balance index and the assembly complexity smoothing index were reduced by 80.3% and 92% respectively, which proved the reliability of the hybrid algorithm in optimizing the aircraft component assembly line. Finally, the optimization analyses with various workstation numbers and assembly process times suggest that reducing the workstations and adopting robotic automated processing can improve the aircraft component assembly line. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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