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Computation
Special Issues
Advanced Topology Optimization: Methods and Applications
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Advanced Topology Optimization: Methods and Applications

A special issue of Computation (ISSN 2079-3197).

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2849

Special Issue Editor

Dr. Yun-Fei Fu

E-Mail Website
Guest Editor
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada
Interests: topology optimization; structural optimization; composite materials; additive manufacturing

Special Issue Information

Dear Colleagues,

Structural topology optimization is a powerful computational design method that seeks the most efficient material distribution within a specified design domain to meet performance requirements. Some well-established algorithms are Solid Isotropic Material with Penalization (SIMP), Bi-directional Evolutionary Structural Optimization (BESO), the level-set method, Moving Morphable Components (MMCs), Floating Projection Topology Optimization (FPTO), and Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT). As a critical branch of lightweight design, topology optimization plays a prominent role across aerospace, automotive, civil, and defense industries. Advancements in both the theory and application of topology optimization are essential to drive innovation within the field. Despite extensive efforts by researchers to advance the theory and application of topology optimization, several challenges remain to be addressed.

This Special Issue aims to bring together researchers from diverse backgrounds to share their insights and findings. The Guest Editor welcomes all methodologies capable of addressing specific optimization challenges, with no preference for any particular algorithm. Topics for this Special Issue include, but are not limited to, algorithm and software development, design for manufacturing, lattice structure design, engineering and artistic applications, parallel computing, and AI-driven topology optimization.

The Guest Editor invites researchers working in these areas to contribute their latest work in the form of original research and review articles. Papers that present novel algorithms or applications, as well as those providing numerical validations of topologically optimized designs, are particularly encouraged.

Dr. Yun-Fei Fu
Guest Editor

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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Computation is an international peer-reviewed open access monthly 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 1800 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

  • topology optimization theory
  • light-weight design
  • design for manufacturing
  • lattice structure design
  • multi-physics problems
  • large-scale optimization problems
  • software development
  • novel furniture design
  • finite element analysis of topologically optimized designs
  • AI-based topology optimization

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Published Papers (4 papers)

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Research

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17 pages, 1543 KiB  
Article
Simultaneous Multi-Objective and Topology Optimization: Effect of Mesh Refinement and Number of Iterations on Computational Cost
by Daniel Miler, Matija Hoić, Rudolf Tomić, Andrej Jokić and Robert Mašović
Computation 2025, 13(7), 168; https://doi.org/10.3390/computation13070168 - 11 Jul 2025
Viewed by 210
Abstract
In this study, a multi-objective optimization procedure with embedded topology optimization was presented. The procedure simultaneously optimizes the spatial arrangement and topology of bodies in a multi-body system. The multi-objective algorithm determines the locations of supports, joints, active loads, reactions, and load magnitudes, [...] Read more.
In this study, a multi-objective optimization procedure with embedded topology optimization was presented. The procedure simultaneously optimizes the spatial arrangement and topology of bodies in a multi-body system. The multi-objective algorithm determines the locations of supports, joints, active loads, reactions, and load magnitudes, which serve as inputs for the topology optimization of each body. The multi-objective algorithm dynamically adjusts domain size, support locations, and load magnitudes during optimization. Due to repeated topology optimization calls within the genetic algorithm, the computational cost is significant. To address this, two reduction strategies are proposed: (I) using a coarser mesh and (II) reducing the number of iterations during the initial generations. As optimization progresses, Strategy I gradually refines the mesh, while Strategy II increases the maximum allowable iteration count. The effectiveness of both strategies is evaluated against a baseline (Reference) without reductions. By the 25th generation, all approaches achieve similar hypervolume values (Reference: 2.181; I: 2.112; II: 2.133). The computation time is substantially reduced (Reference: 42,226 s; I: 16,814 s; II: 21,674 s), demonstrating that both strategies effectively accelerate optimization without compromising solution quality. Full article
(This article belongs to the Special Issue Advanced Topology Optimization: Methods and Applications)
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18 pages, 2168 KiB  
Article
A New Approach to Topology Optimization with Genetic Algorithm and Parameterization Level Set Function
by Igor Pehnec, Damir Sedlar, Ivo Marinic-Kragic and Damir Vučina
Computation 2025, 13(7), 153; https://doi.org/10.3390/computation13070153 - 26 Jun 2025
Viewed by 371
Abstract
In this paper, a new approach to topology optimization using the parameterized level set function and genetic algorithm optimization methods is presented. The impact of a number of parameters describing the level set function in the representation of the model was examined. Using [...] Read more.
In this paper, a new approach to topology optimization using the parameterized level set function and genetic algorithm optimization methods is presented. The impact of a number of parameters describing the level set function in the representation of the model was examined. Using the B-spline interpolation function, the number of variables describing the level set function was decreased, enabling the application of evolutionary methods (genetic algorithms) in the topology optimization process. The traditional level set method is performed by using the Hamilton–Jacobi transport equation, which implies the use of gradient optimization methods that are prone to becoming stuck in local minima. Furthermore, the resulting optimal shapes are strongly dependent on the initial solution. The proposed topology optimization procedure, written in MATLAB R2013b, utilizes a genetic algorithm for global optimization, enabling it to locate the global optimum efficiently. To assess the acceleration and convergence capabilities of the proposed topology optimization method, a new genetic algorithm penalty operator was tested. This operator addresses the slow convergence issue typically encountered when the genetic algorithm optimization procedure nears a solution. By penalizing similar individuals within a population, the method aims to enhance convergence speed and overall performance. In complex examples (3D), the method can also function as a generator of good initial solutions for faster topology optimization methods (e.g., level set) that rely on such initial solutions. Both the proposed method and the traditional methods have their own advantages and limitations. The main advantage is that the proposed method is a global search method. This makes it robust against entrapment in local minima and independent of the initial solution. It is important to note that this evolutionary approach does not necessarily perform better in terms of convergence speed compared to gradient-based or other local optimization methods. However, once the global optimum has been found using the genetic algorithm, convergence can be accelerated using a faster local method such as gradient-based optimization. The application and usefulness of the method were tested on typical 2D cantilever beams and Michell beams. Full article
(This article belongs to the Special Issue Advanced Topology Optimization: Methods and Applications)
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14 pages, 5255 KiB  
Article
A Framework of the Meshless Method for Topology Optimization Using the Smooth-Edged Material Distribution for Optimizing Topology Method
by Jingbo Huang, Kai Long, Yutang Chen, Rongrong Geng, Ayesha Saeed, Hui Zhang and Tao Tao
Computation 2025, 13(1), 6; https://doi.org/10.3390/computation13010006 - 29 Dec 2024
Cited by 2 | Viewed by 927
Abstract
Density variables based on nodal or Gaussian points are naturally incorporated in meshless topology optimization approaches, pursuing distinct topological layouts with solid and void solutions. However, engineering applications have been hampered by the fact that the authentic structure boundary cannot be identified without [...] Read more.
Density variables based on nodal or Gaussian points are naturally incorporated in meshless topology optimization approaches, pursuing distinct topological layouts with solid and void solutions. However, engineering applications have been hampered by the fact that the authentic structure boundary cannot be identified without manual intervention. To alleviate this issue, the Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) method is developed within the context of meshless approximation. In meshless analysis, the non-overlap cell variables instead of nodal or Gaussian-based variables are adopted to characterize the existence or absence of sub-regions. This work proposes a non-penalized SEMDOT where an interpolation-based heuristic sensitivity expression is utilized. The 2D and 3D compliance minimization problems serve to validate the efficiency and applicability of the proposed non-penalized SEMDOT approach based on the framework of the meshless method. The numerical results demonstrated that the proposed approach is capable of generating final designs with continuous and smooth edges or surfaces. Full article
(This article belongs to the Special Issue Advanced Topology Optimization: Methods and Applications)
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Review

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19 pages, 4217 KiB  
Review
Optimization of Rock-Cutting Tools: Improvements in Structural Design and Process Efficiency
by Yuecao Cao, Qiang Zhang, Shucheng Zhang, Ying Tian, Xiangwei Dong, Xiaojun Song and Dongxiang Wang
Computation 2025, 13(7), 152; https://doi.org/10.3390/computation13070152 - 23 Jun 2025
Viewed by 466
Abstract
Rock-breaking cutters are critical components in tunneling, mining, and drilling operations, where efficiency, durability, and energy consumption are paramount. Traditional cutter designs and empirical process optimization methods often fail to address the dynamic interaction between heterogeneous rock masses and tool structures, leading to [...] Read more.
Rock-breaking cutters are critical components in tunneling, mining, and drilling operations, where efficiency, durability, and energy consumption are paramount. Traditional cutter designs and empirical process optimization methods often fail to address the dynamic interaction between heterogeneous rock masses and tool structures, leading to premature wear, high specific energy, and suboptimal performance. Topology optimization, as an advanced computational design method, offers transformative potential for lightweight, high-strength cutter structures and adaptive cutting process control. This review systematically examines recent advancements in topology-optimized cutter design and its integration with rock-cutting mechanics. The structural innovations in cutter geometry and materials are analyzed, emphasizing solutions for stress distribution, wear/fatigue resistance, and dynamic load adaptation. The numerical methods for modeling rock–tool interactions are introduced, including discrete element method (DEM) simulations, smoothed particle hydrodynamics (SPH) methods, and machine learning (ML)-enhanced predictive models. The cutting process optimization strategies that leverage topology optimization to balance objectives such as energy efficiency, chip formation control, and tool lifespan are evaluated. Full article
(This article belongs to the Special Issue Advanced Topology Optimization: Methods and Applications)
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