International Journal of Optimization in Civil Engineering

GENERATIVE ARTIFICIAL INTELLIGENCE IN STRUCTURAL OPTIMIZATION: OPPORTUNITIES, CHALLENGES, AND FUTURE DIRECTIONS

S. Talatahari

The emergence of Generative Artificial Intelligence (GenAI) presents new possibilities for transforming structural optimization processes in civil and structural engineering. Unlike traditional AI models focused on prediction or classification, GenAI models, such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), Diffusion Models, and Large Language Models (LLMs), enable the generation of novel structural designs by learning complex patterns within design-performance data. This paper provides a comprehensive review of how GenAI can support tasks such as design generation, inverse design, data augmentation for surrogate modeling, and multi-objective trade-off exploration. It also examines key challenges, including constraint integration, model interpretability, and data scarcity. By evaluating recent applications and proposing hybrid frameworks that blend generative modeling with domain knowledge and optimization strategies, this study outlines a research roadmap for the responsible and effective use of GenAI in structural optimization. The findings emphasize the need for interdisciplinary collaboration to translate GenAI’s creative potential into physically valid, structurally sound, and engineering-relevant solutions.

ON THE ROLE OF INPUT SIGNALS IN STRUCTURAL DESIGN BY SOUND ENERGY OPTIMIZER: A CASE STUDY

M. Shahrouzi

Sound Energy Optimizer (SEO) is a recent metaheuristic algorithm inspired by the propagation and reception of sound waves in physical environments. While conventional metaheuristics that rely on random number generators with certain distributions, SEO can utilize various real-world or simulated sound signals as the source of stochasticity to guide its search process. Concerning structural design by SEO, the effect of natural sound signals is compared with the artificial signals generated from uniform or normal distributions. In this regard, a 244-bar power transmission tower and a 1016-bar double-layer grid are simultaneously optimized with continuous geometry as well as discrete sizing variables to evaluate the impact of input signals on convergence behavior, solution quality and robustness of the algorithm. A sensitivity analysis is conducted to calibrate key control parameters of SEO. The results declare that the nature of the input sound signal can significantly affect the algorithm’s exploration-exploitation balance. In this study, the "Knocking sound" signal yields the best performance, while the synthetic random signals revealed less stable optimization trajectories.

OPTIMAL ANALYSIS OF SKELETAL STRUCTURES VIA FORCE METHOD: A REVIEW

A. Kaveh

In this paper, a review is provided for the optimal analysis of structures using the graph theoretic force method. An analysis is defined as “optimal” if the corresponding structural matrices (flexibility or stiffness) are sparse, well-structured, and well-conditioned. An expansion process together with the union-intersection theorem is utilized for generating subgraphs, forming a special cycle basis, corresponding to highly localized self equilibration systems. Admissibility checks are used in place of the more common independence checks to speed up the formation of the basis. An efficient solution requires organizing the non-zero entries into various well-defined patterns. Algorithms are provided to form matrices having banded matrices and small profiles. Though the paper considers mainly skeletal structures, the presented concepts are easily extensible to other finite element models. References for such generalizations have been provided. A brief review of swift analysis methods that skirt the harder problem of matrix conditioning is also provided. The iterative nature of optimal structural design via metaheuristic algorithms rewards any speedup in the analysis process. This review recommends utilizing the force method instead of the alternative displacement method to achieve said speedup. The work concludes with a discussion of future challenges in the field of optimal analysis.

SEISMIC PERFORMANCE-BASED TOPOLOGY OPTIMIZATION AND COLLAPSE ANALYSIS OF STEEL SHEAR WALL SYSTEMS

K. Farzad

The use of steel shear wall systems has increased significantly in recent years as an effective solution for resisting lateral loads in buildings. This study focuses on the seismic collapse safety assessment of steel frames with optimal positions of steel shear walls obtained through various metaheuristic optimization algorithms and concepts of performance-based design methodology. Due to potential irregularities and discontinuities in the lateral load-resisting system and the limitations of code-based linear analysis, nonlinear pushover analyses with multiple lateral load patterns are employed to estimate key structural responses during the optimization process. The seismic collapse performance of the optimized frames is further evaluated using the FEMA P-695 methodology, which involves nonlinear dynamic analysis to assess collapse capacity. The primary objective is to examine the influence of steel plate shear wall placement on the structural weight optimization of steel frames. To this end, two case studies, a 10-story and a 15-story steel frame equipped with steel shear walls, are presented. The results demonstrate the critical role of shear wall location in achieving optimal structural designs.

PARAMETER-FREE STRUCTURAL OPTIMIZATION OF DOME TRUSSES: DEVELOPMENT AND APPLICATION OF THE SA_EVPS ALGORITHM WITH STATISTICAL LEARNING MECHANISMS

P. Hosseini

This study presents the application of the Self-Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm for large-scale dome truss optimization under frequency constraints. SA-EVPS incorporates self-adaptive parameter control, memory-based learning mechanisms, and statistical regeneration strategies to overcome limitations of traditional metaheuristic algorithms in structural optimization. The algorithm's performance is evaluated on three benchmark dome structures: (1) a 600-bar single-layer dome with 25 design variable groups, (2) an 1180-bar single-layer dome with 59 design variable groups, and (3) a 1410-bar double-layer dome with 47 design variable groups, all subject to natural frequency constraints. Comparative analysis against five state-of-the-art algorithms—Dynamic Particle Swarm Optimization (DPSO), Colliding Bodies Optimization (CBO), Enhanced Colliding Bodies Optimization (ECBO), Vibrating Particles System (VPS), and Enhanced Vibrating Particles System (EVPS)—demonstrates SA-EVPS's superior convergence characteristics and solution quality. Results show that SA-EVPS consistently achieves the lowest structural weights with remarkable stability across all test cases. The algorithm's self-adaptive mechanisms eliminate manual parameter tuning while the statistical regeneration mechanism prevents premature convergence in large-scale optimization problems. This research establishes SA-EVPS as a robust and efficient metaheuristic for frequency-constrained structural optimization of complex dome structures.

OPTIMAL SEISMIC RETROFIT OF STEEL MOMENT-RESISTING MOMENT USING BRACING-FRICTION DAMPER SYSTEMS

M. Khatibinia

Bracing-friction damper system (BFDS), one of passive control devices, consists of a Pall friction damper added in-line with a diagonal, which is utilized for the seismic retrofit of building structures. The BFDS can dissipate the input energy of earthquakes and mitigate a considerable amount of the hysteretic energy of structures. This study presents the optimal seismic retrofit of inelastic steel moment-resisting frames (SMRFs) through the optimum design of the BFDSs installed in each story of SMRFs. For this purpose, minimizing the maximum damage index of stories averaged over seven scaled earthquake excitations is selected as the objective function so that the story damage is uniformly distributed along the height of SMRFs. The damage index is calculated based on the Park-Ang damage model which is expressed based on a linear combination of deformation, moment, and absorbed hysteretic energy of structural elements imposed by an earthquake excitation. The results indicate that the optimized BFDSs-equipped SMRFs exhibits the better distribution of story damage than that of uncontrolled SMRFs. Finally, the seismic assessment of SMRFs is done by the fragility analysis. The results of the seismic fragility assessment demonstrate that the optimized BFDSs improve the seismic performance of retrofitted SMRFs compared to that of uncontrolled SMRFs at different damage states.

OPTIMAL DESIGN OF UNPROTECTED STEEL MOMENT FRAMES UNDER FIRE CONDITION

S. R. Hoseini Vaez

This study addresses the critical necessity for optimized structural design under fire conditions, where conventional methods often prove inadequate. The research focuses on the optimal design of two three and nine story steel moment-resisting frames, without fireproofing protection. The optimization objectives were to minimize the structural weight while satisfying constraints under critical fire scenarios. The key design constraints included inter-story drift and the demand-to-capacity ratio of structural members. The study employed the Enhanced Vibrating Particles System (EVPS) and the Accelerated Water Evaporation Optimization (AWEO) algorithms. A significant aspect of the investigation involved analyzing various severe fire scenarios to identify which parts of the structures are most vulnerable during a fire event. The results demonstrate the effectiveness of the proposed optimization framework in achieving a lightweight yet resilient structural design that meets regulations under extreme thermal loading.

OPTIMAL DESIGN OF LARGE-SCALE DOME STRUCTURES WITH MULTIPLE FREQUENCY CONSTRAINTS USING PLASMA GENERATION OPTIMIZATION

A. Kaveh

This paper presents the application of the Plasma Generation Optimization (PGO) algorithm to the optimal design of large-scale dome trusses subjected to multiple frequency constraints. Such problems are notoriously challenging due to their highly non-linear and non-convex nature, characterized by numerous local optima. PGO is a physics-inspired metaheuristic that simulates the processes of excitation, de-excitation, and ionization in plasma generation, balancing global exploration and local refinement through its unique search mechanisms. The performance of PGO is evaluated on three well-established dome truss benchmarks: a 52-bar, a 120-bar, and a 600-bar structure, encompassing both sizing and sizing-shape optimization. A comprehensive statistical analysis based on multiple independent runs demonstrates the algorithm's effectiveness and robustness. The results show that PGO achieves the best-reported minimum weight for the 120-bar and 600-bar domes, while obtaining a highly competitive, near-optimal design for the 52-bar dome. Furthermore, PGO consistently produced low average weights across all problems, confirming its reliability. The convergence histories further validate the algorithm's efficiency in locating feasible, high-quality designs. The findings conclusively establish PGO as a powerful and reliable optimizer for handling complex structural optimization problems with dynamic constraints.