International Journal of Optimization in Civil Engineering

PREDICTING THE NATURAL FREQUENCIES OF TRUSS DOMES UNDER UNCERTAINTY USING DEEP FEEDFORWARD NEURAL NETWORKS

Pooya Zakian

This study employs Monte Carlo simulation together with a deep feedforward neural network to predict the natural frequencies of truss domes under uncertainty. Material and/or geometric properties of these structures are modeled as random variables, and their influence on the natural frequencies is examined. Monte Carlo simulation is applied to perform stochastic eigenvalue analyses of the finite element models. To reduce computational cost, a deep neural network is trained to predict natural frequencies in place of repeated eigenvalue solves, accelerating the overall simulation. Bayesian optimization is used to tune the network hyperparameters. Numerical examples show that the proposed approach substantially improves computational efficiency and predictive accuracy compared with direct Monte Carlo simulation for domes with random inputs.

OPTIMIZATION-BASED SIMPLIFICATION OF A HIGH-RISE BENCHMARK STEEL BUILDING FOR DYNAMIC ANALYSIS

M. Fahimi Farzam

Reducing the degrees of freedom of building models significantly reduces computational costs in time-consuming structural engineering problems, such as dynamic analysis, nonlinear analysis, or the optimal design of structural systems. In this study, the Finite Element (FE) model of a 20-story benchmark steel building with numerous degrees of freedom (DoF) is simplified to a 20-degree-of-freedom linear shear-type building. First, a preliminary linear shear-type model was derived by estimating the story stiffness so that the fundamental frequency matches that of the FE model. Then, an optimization problem is formulated and solved using a Genetic Algorithm (GA) combined with a weighted-sum method to achieve greater accuracy at higher frequencies in the preliminary model. Two objective functions were established and assessed for the optimization problem: one is the difference in frequencies between the FE model and the preliminary model with equal weighting, and the other is the first objective function improved with the modal participation percent weighting. The stiffness of each story in the preliminary model is selected as the design variable in both optimization problems. Finally, these optimized models are evaluated against the FE model using frequencies and dynamic time-history responses. The model derived from the weighted objective function demonstrates acceptable accuracy compared to its FE model in frequency and time-history analysis. It can be used for dynamic analysis and other structural and earthquake engineering purposes.

GEOMETRICAL AND MATERIAL OPTIMIZATION OF FUNCTIONALLY GRADED DOUBLY-CURVED SHELLS USING THE GREY WOLF OPTIMIZATION ALGORITHM

R. Kamgar

This study investigates the geometrical and material design aspects of functionally graded (FG) doubly-curved shells. The FG material system comprises a combination of metal and ceramic constituents, and the effective properties across the shell thickness are estimated using Voigt’s rule of mixtures. To analyze the structural behaviour, the finite element method is employed within the framework of third-order shear and normal deformation theories. The grey wolf optimization (GWO) algorithm is implemented to achieve design optimization. The objective function aims to minimize both the maximum displacement and the fundamental dimensionless natural frequency in each optimization process individually. The findings indicate that under highly constrained boundary conditions, the curvature parameters remain constant. Conversely, for less constrained conditions, the parameter R₂ assumes a value approximately ten times greater than R₁.

SEISMIC IMPROVEMENT OF LOW-RISE BUILDINGS USING OPTIMUM VARIABLE AND FIXED RADIUS FRICTION PENDULUM ISOLATOR

H. Heidarzadeh

Controlling vibrations in short-period structures subjected to seismic loading is crucial for improving the seismic performance of the structure. This paper investigates friction pendulum isolators with both constant and variable radius as a means to enhance the seismic behavior of structures. Friction pendulum isolators with a constant radius are susceptible to intensification phenomena in near-field earthquakes. Modifying the isolator radius leads to changes in its period and stiffness, thereby mitigating the amplification effect. The study first models and validates the friction pendulum isolator with a constant radius using ABAQUS software. Subsequently, the performance of these isolators, both with constant and variable radius, is examined under harmonic loading to improve structural behavior. The results show that variable radius pendulum friction isolators have been able to increase energy absorption by an average of 25%, 41%, and 14%, respectively, in response to near- and far-field earthquakes such as the Manjil, Loma Prieta, and Northridge earthquakes. This reduces the transfer of earthquake forces to the structure and maintains the integrity of the structure during an earthquake.

OPTIMAL DESIGN OF RIBBED SLABS: A COMPARATIVE STUDY OF ACI 318 CODES

B. Ahmadi-Nedushan

This study presents a cost optimization approach for simply supported one-way ribbed slabs, with the primary objective of minimizing concrete and reinforcement costs. A Genetic Algorithm (GA), implemented in MATLAB, is utilized to address this optimization problem. The optimization model incorporates seven discrete design variables: rib dimensions (spacing, bottom/top width, and height), topping slab thickness, flexural reinforcement diameter, and concrete compressive strength. For validation, an initial optimization based on ACI 318-08 with six variables demonstrated a 3% cost reduction compared to established algorithms. To ensure practical relevance, subsequent optimizations incorporated actual market conditions utilizing the 2025 Iranian Building Construction Price List. Transitioning to ACI 318-19 resulted in a 10% increase in optimal cost relative to ACI 318-08, primarily due to stricter shear strength provisions. To mitigate this increase and enhance design efficiency, concrete compressive strength was introduced as a seventh design variable. This expanded optimization was evaluated across spans ranging from 5 to 8 meters, yielding a further 4.4% cost reduction for a 6-meter span. Conclusively, the results demonstrate that the strategic application of higher-strength concrete, informed by real-world market prices, significantly reduces the overall cost of one-way ribbed slab construction.

ENHANCED PRAIRIE DOG METAHEURISTIC OPTIMIZATION ALGORITHM FOR ENGINEERING OPTIMIZATION PROBLEMS

R. Sojoudizadeh

This paper presents an Enhanced Prairie Dog Optimization (IPDO) algorithm for solving complex engineering optimization problems. The proposed improvement integrates Lévy flight dynamics into the original PDO framework to enhance exploration-exploitation balance and accelerate convergence. The performance of IPDO is evaluated against seven established metaheuristics across four challenging civil engineering applications: (1) discrete sizing optimization of a 120-bar truss, (2) structural reliability analysis of a cantilever tube, (3) cost optimization of reinforced concrete beams, and (4) hyperparameter tuning of a Support Vector Machine (SVM) for shear strength prediction of steel fiber-reinforced concrete. Experimental results demonstrate that IPDO consistently achieves superior solution quality, robustness, and convergence speed. Notably, in SVM hyperparameter optimization, IPDO attained the lowest mean squared error (1.4881) with zero variance across runs, outperforming all competitors. The algorithm also proved highly effective in structural design and reliability problems, offering a reliable and efficient tool for real-world engineering optimization.

A CASCADE OPTIMIZATION APPROACH USING THE OPTISEARCH ALGORITHM IN CONCRETE FRAME WITH RELIABILITY CONSTRAINTS

A. Kaveh

This work investigates the optimization of concrete structures using metaheuristic algorithms-based reliability. One of the major challenges in the optimization of concrete structures is the extensive search domain, which may lead to convergence to local optima and incorrect results. In this study, instead of solely relying on optimization algorithms that are prone to local optima, a novel approach is proposed. Based on the Cascade Algorithm, this method discretized the search domain for section of beam and column dimensions and increased step by step. After each cross-section is created, it is assigned to the corresponding element. Subsequently, structural analysis is performed, and using reliability-based constraints and analysis, the least-cost section for each element is selected. Based on the obtained low-cost sections, the upper and lower bounds for each design variable are then narrowed. Finally, metaheuristic algorithms are applied to determine the optimal cross-sections with high precision. The results demonstrate that this approach significantly reduces the likelihood of falling into local optima and improves both the speed and accuracy of metaheuristic algorithms.

SEISMIC FRAGILITY AND RESILIENCE ASSESSMENT OF OPTIMALLY RETROFITTED RC FRAMES WITH NONLINEAR VISCOUS DAMPERS UNDER PARK–ANG DAMAGE CONSTRAINTS

M. Arjmand

The seismic resilience of existing reinforced concrete (RC) buildings can be improved by optimizing both energy dissipation and post-earthquake recovery. This study proposes a practical framework for upgrading RC moment-resisting frames using nonlinear fluid viscous dampers (NFVDs). Two typical frames, a four-story and an eight-story structure, were modeled and analyzed in OpenSees. Nonlinear time-history analyses with seven earthquake records were carried out to estimate the Park–Ang damage index, while incremental dynamic analyses (IDA) with 22 far-field records from FEMA P695 were used to evaluate fragility and collapse performance. The NFVDs were represented through a velocity-dependent Maxwell model, and the optimal damper parameters and locations were determined through a cost-based single-objective optimization scheme under predefined damage limits. The results show that the optimized damper configurations effectively reduced structural damage and improved post-event functionality recovery under seismic hazard levels corresponding to 10% and 2% probabilities of exceedance in 50 years. Overall, the proposed approach provides an efficient and economical solution for improving the seismic performance and resilience of existing RC frame buildings.