---

Genetic algorithm is a robust meta-heuristic algorithm inspired by the theory of natural selection to solve various optimization problems. This study presents a method with the purpose of promoting the exploration and exploitation of genetic algorithm. Improvement in exploration ability is made by adjusting the initial population and adding a group of fixed stations. This modification increases the diversity among the solution population, which enables the algorithm to escape from local optimum and to converge to the global optimum even in fewer generations. On the other hand, to enhance the exploitation ability, increasing the number of selected parents is suggested and a corresponding crossover technique has been presented. In the proposed technique, the number of parents to generate offspring is variable during the process and it could be potentially more than two. The effectiveness of the modifications in the proposed method has been verified by examining several benchmark functions and engineering design problems.
 

---

The optimal design of structural systems represents a pivotal challenge, striking a balance between economic efficiency and safety. There has been a great challenge in balancing between the economic issues and safety factors of the structures over the past few decades; however, development of high-speed computing systems enables the experts to deal with higher computational efforts in designing structural systems. Recent advancements in computational methods have significantly improved our ability to address this challenge through sophisticated design schemes. The main purpose of this paper is to develop an intelligent design scheme for truss structures in which an optimization process is implemented into this scheme to help the process reach lower weights for the structures. For this purpose, the Artificial Rabbits Optimization (ARO) algorithm is utilized as one of the recently developed metaheuristic algorithms which mimics the foraging behaviour of the rabbits in nature. In order to reach better solutions, the improved version of this algorithm is proposed as I-ARO in which the well-known random initialization process is substituted by the Diagonal Linear Uniform (DLU) initialization procedure. For numerical investigations, 5 truss structures 10, 25, 52, 72, and 160 elements are considered in which stress and displacement constraints are determined by considering discrete design variables. By conducting 50 optimization runs for each truss structure, it can be concluded that the I-ARO algorithm is capable of reaching better solutions than the standard ARO algorithm which demonstrates the effects of DLU in enhancing this algorithm’s search behaviour.
 

---

The sine-cosine algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified sine-cosine algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of sine and cosine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic algorithms and its enhancement with respect to the standard sine-cosine algorithm.

---

Optimization has become increasingly significant and applicable in resolving numerous engineering challenges, particularly in the structural engineering field. As computer science has advanced, various population-based optimization algorithms have been developed to address these challenges. These methods are favored by most researchers because of the difficulty of calculations in classical optimization methods and achieving ideal solutions in a shorter time in metaheuristic technique methods. Recently, there has been a growing interest in optimizing truss structures. This interest stems from the widespread utilization of truss structures, which are known for their uncomplicated design and quick analysis process. In this paper, the weight of the truss, the cross-sectional area of the members as discrete variables, and the coordinates of the truss nodes as continuous variables are optimized using the HGPG algorithm, which is a combination of three metaheuristic algorithms, including the Gravity Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Gray Wolf Optimization (GWO). The presented formulation aims to improve the weaknesses of these methods while preserving their strengths. In this research, 15, 18, 25, and 47-member trusses were utilized to show the efficiency of the HGPG method, so the weight of these examples was optimized while their constraints such as stress limitations, displacement constraints, and Euler buckling were considered. The proposed HGPG algorithm operates in discrete and continuous modes to optimize the size and geometric configuration of truss structures, allowing for comprehensive structural optimization. The numerical results show the suitable performance of this process.

---

---

Tower cranes are essential for both vertical and horizontal movement of materials in construction and port operations. Optimizing their placement is crucial for reducing costs and enhancing overall efficiency. This study addresses the optimization of tower crane placement using the recently developed Mouth Brooding Fish (MBF) algorithm. The MBF algorithm is inspired by the life cycle of mouth-brooding fish, employing their behavioral patterns and the survival challenges of their offspring to find optimal solutions. The performance of the MBF algorithm is compared with the Genetic Algorithm (GA), Colliding Bodies Optimization (CBO), and Enhanced Colliding Bodies Optimization (ECBO). The results demonstrate that the MBF algorithm is effective and has potential advantages in tackling complex optimization problems.

---

Diagrids are of practical interest in high-rise buildings due to their architectural configuration and efficiency in withstanding lateral loads by exterior diagonal members. In the present work, diagrid models are screened based on a sizing optimization approach. Section index of each member group is treated as a discrete design variable in the optimization problem to be solved. The structural constraints are evaluated due to Load and Resistant Design Factor regulations under both gravitational and wind loadings. The research is threefold: first, falcon optimization algorithm is utilized as a meta-heuristic paradigm for such a large-scale and highly constrained discrete problem. Second, the effect of geometry variation in diagrids on minimal structural weight is studied for 18 diagrid models via three different heights (12, 20 and 30 stories) and three diagrid angles. Third, distinct cases of rigid and flexible bases are compared to study the effect of such boundary conditions on the results. The effect of soil flexibility beneath the foundation on the optimal design was found highly dependent on the diagrid geometry. The best weight and performance in most of the treated examples belong to the geometry that covers two stories by every grid line on the flexible-base.
 

---

Structural optimization plays a critical role in improving the efficiency, cost-effectiveness, and sustainability of engineering designs. This paper presents a comparative study of single-objective and multi-objective optimization in the structural design process. Single-objective problems focus on optimizing just one objective, such as minimizing weight or cost, while other important aspects are treated as constraints like deflections and strength requirements. Multi-objective optimization addresses multiple conflicting objectives, such as balancing cost, with displacement treated as a secondary objective and strength requirements defined as constraints within the given limits. Both optimization approaches are carried out using Chaos Game Optimization (CGO). While single-objective optimization produces a definitive optimal solution that can be used directly in the final design, multi-objective optimization results in a set of trade-off solutions (Pareto front), requiring a decision-making process based on design codes and practical criteria to select the most appropriate design. Through a real-world case study, this research will assess the performance of both optimization strategies, providing insights into their suitability for modern structural engineering challenges.

---

The multi-material size optimization of transmission tower trusses is carried out in the present study. Three real-size examples are designed, and statically analyzed, and the Black Hole Mechanics Optimization (BHMO) algorithm, a recently developed metaheuristic optimizer methodology, is employed. The BHMO algorithm's innovative search strategy, which draws inspiration from black hole quantum physics, along with a robust mathematical kernel based on the covariance matrix between variables and their associated costs, efficiently converges to global optimum solutions. Besides, three alloys of steel are taken into account in these examples for discrete size variables, each of which is defined in the problem by a weighted coefficient in terms of the elemental weight. The results also indicate that using multiple materials or alloys in addition to diverse cross-sectional sizes leads to the lowest possible cost and the most efficient solution.

---

In this study, the Improved Material Generation Algorithm (IMGA) is proposed to optimize the shape and size of structures. The original Material Generation Algorithm (MGA) introduced an optimization model inspired by the high-level and fundamental characteristics of material chemistry, particularly the configuration of compounds and chemical reactions for generating new materials. MGA uses a Gaussian normal distribution to produce new combinations. To enhance MGA for adapting truss structures, a new technique called Random Chaotic (RC) is proposed. RC increases the speed of convergence and helps escape local optima. To validate the proposed method, several truss structures, including a 37-bar truss bridge, a 52-bar dome, a 72-bar truss, a 120-bar dome, and a 200-bar planar structure, are optimized under natural frequency constraints. Optimizing the shape and size of structures under natural frequency constraints is a significant challenge due to its complexity. Choosing the frequency as a constraint prevents resonance in the structure, which can lead to large deformations and structural failure. Reducing the vibration amplitude of the structure decreases tension and deflection. Consequently, the weight of the structure can be minimized while keeping the frequencies within the permissible range. To demonstrate the superiority of IMGA, its results are compared with those of other state-of-the-art metaheuristic methods. The results show that IMGA significantly improves both exploitation and exploration.

---

Earthquakes are random phenomena and there has been no report of similar earthquakes occurring worldwide. Therefore, traditional methods of designing buildings based on past earthquakes with inappropriate discontinuity joints are sometimes ineffective for vital structures. This may lead to collision and destruction of adjacent structures during a severe earthquake. As in the Iranian Standard No. 2800-4, this distance should be at least five-thousandths of the building height from the base level to the adjacent ground boundary for buildings up to eight stories to prevent or reduce this damage. Also, for important or/with more than eight-story buildings, this value is determined using the maximum nonlinear lateral displacement of the structures by considering the effects of the P-delta. Also, if the properties of the adjacent building are not known, this distance should be considered at least equal to 70% of the maximum nonlinear lateral displacement of the structures. The main objective of this study is to investigate the adequacy of the discontinuity joint introduced in the Iranian Standard No. 2800-4 based on the critical excitation method. This method calculates critical earthquakes for three buildings (e.g., three-, seven- and eleven-story moment frames) by considering some constraints on the energy, peak ground acceleration, Fourier amplitude, and strong ground motion duration. The results indicate that the minimum gap between two adjacent buildings derived from the existing codes is lower than those calculated using the critical excitation method. Therefore, oscillation might occur if a structure is designed according to the seismic codes and subjected to a critical earthquake.

---

The optimization process of space structures considering the nonlinear material behavior requires significant computational efforts due to the large number of design variables and the complexities of nonlinear structural analysis. Accordingly, the Force Analogy Method (FAM) serves as an efficient tool to reduce computational workload and enhance optimization speed. In this study, the weight optimization of space structures in the inelastic region under seismic loading is carried out using the Shuffled Shepherd Optimization Algorithm (SSOA), with the nonlinear structural analysis based on the FAM. To do this, the FAM formulation for axially loaded members of space structures under seismic forces is presented. Subsequently, weight optimization is performed on two double-layer space structures: a flat double-layer structure with 200 members and a barrel vault structure with 729 members under the Kobe earthquake record. Based on the results, the optimized design using the inelastic behavior showed that the FAM provided accurate results when compared to the precise nonlinear structural analysis. The optimized design based on the FAM is considered acceptable, and the computational time for the optimization process has been significantly reduced.
 

---

Structural optimization plays a crucial role in engineering design, aiming to minimize weight and cost while satisfying performance constraints. This research presents a novel Self-Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm that automatically adjusts algorithm parameters to improve optimization performance. The algorithm is applied to two challenging examples from the International Student Competition in Structural Optimization (ISCSO) benchmark suite: the 314-member truss structure (ISCSO_2018) and the 345-member truss structure (ISCSO_2021). Results demonstrate that SA-EVPS achieves significantly better solutions compared to previous studies using the Exponential Big Bang-Big Crunch (EBB-BC) algorithm. For ISCSO_2018, SA-EVPS achieved a minimum weight of 16543.57 kg compared to 17934.3 kg for the best EBB-BC variant—a 7.75% improvement. Similarly, for ISCSO_2021, SA-EVPS achieved 4292.71 kg versus 4399.0 kg for the best EBB-BC variant—a 2.42% improvement. The proposed algorithm also demonstrates superior convergence behavior and solution consistency, with coefficients of variation of 3.13% and 1.21% for the two benchmark problems, compared to 12.5% and 2.4% for the best EBB-BC variant. These results highlight the effectiveness of the SA-EVPS algorithm for solving complex structural optimization problems and demonstrate its potential for engineering applications.

---

This paper introduces a novel two-phase metamodel-driven methodology for the simultaneous topology and size optimization of truss structures. The approach addresses critical limitations in computational efficiency and solution quality. The framework integrates the Flexible Stochastic Gradient Optimizer (FSGO) with adaptive sampling and machine learning to minimize the number of structural analyses (NSAs), while achieving lighter, high-performance designs. In Phase One, FSGO employs a dual global-local search strategy governed by Extensive Constraints (EC), a dynamic constraint relaxation mechanism to balance exploration of unconventional topologies and exploitation of optimal member sizes. By creating adaptive margins around design constraints, EC enables broader exploration of the design space while ensuring feasibility. Phase Two focuses on precision size optimization, leveraging pruned metamodels trained on critical regions of the design space to refine cross-sectional areas for the finalized topology. Comparative evaluations on benchmark planar and spatial trusses demonstrate the method’s superiority: it reduces NSAs by 22–79% compared to state-of-the-art approaches and achieves 0.04–0.7% lighter designs while eliminating up to 31% of redundant members. Results validate the framework as a paradigm shift in truss optimization, merging computational efficiency with structural innovation.

---

The tuned mass damper inerter systems have recently received considerable attention in the field of structural control. The present work offers a practical configuration of such a device, called double tuned mass damper inerter (DTMDI) that connects the inerter into the damper masses rather than be attached to the main structure. Soil-structure interaction is also taken into account for the soft and dense soils as well as for the fixed based condition. The H∞  norm of the transfer functions for the roof response is minimized as the objective function. The parameters of DTMDI are optimized using opposition-switching search as an efficient parameter-less algorithm in comparison with lightning attachment procedure optimization, sine cosine algorithm and particle swarm optimization. The system performance is evaluated in the frequency domain, as well as in the time domain under various earthquakes including far-field records, near-field records with forward directivity and with fling-step. The results show superiority of opposition-switching search for optimal design of the proposed DTMDI so that it can significantly reduce both the roof displacement and acceleration response for all the SSI conditions.

---

This paper utilized the multi-objective cuckoo search (mocs) optimization algorithm to compute the optimum parameters of three-dimensional frame structures controlled by the triple friction pendulum bearing (TFPB) systems. For this purpose, firstly, the maximum capacity of the unisolated structure (uncontrolled structures) is evaluated for six main earthquakes using an incremental dynamic analysis (IDA). Then, the structure is controlled using the TFPB systems and excited using the maximum acceleration calculated from the previous step to calculate the optimal parameters of the TFPB system (i.e., the coefficients of friction and effective radius of curvature) subjected to some constraints in such a way that the maximum local drift ratio and also the Park-Ang damage index ratio minimized. Finally, to evaluate the behavior of the controlled structure, it is excited by main shock-aftershock earthquakes under sequence IDA. The results showed an average seismic improvement of 30% and 40% for the controlled structures according to the Park-Ang damage and drift indices, respectively.

---

In this research, different types of weirs have been numerically investigated to determine the optimal design based on two hydraulic and structural criteria. FLOW 3D and ABAQUS software were utilized for the hydraulic and structural analysis, respectively. The accuracy of the numerical models was verified with the available experimental and numerical results. In the hydraulic investigation, 18 models of different types of weirs including rectangular (6 models), square, triangular (3 models), circular, ogee (3 models), and labyrinth (4 models) weirs were examined. In the structural study of weirs, there are 13 models, including rectangular, square, triangular (3 models), circular, ogee (3 models), and labyrinth (4 models) weirs were analyzed. The results of hydraulic analyzes showed that the dimensions of the rectangular weir significantly affect the output velocity. In triangular weirs, the highest energy dissipation will occur with an apex angle of 45°, and with the increase of the apex angle in the ogee weir, more turbulence is observed in the downstream flow. In labyrinth weirs, by changing the shape of the weir from triangular to rectangular, the output velocity and also turbulence of the flow will be much less. According to the findings of the structural analyses, the increase of the apex angle in triangular weirs, the weir will be more critical, but the situation will be more suitable in ogee weirs. Additionally, the rectangular labyrinth weir performs the best structurally among the labyrinth weirs.

---

Metaheuristic algorithms mostly consist of some parameters influencing their performance when faced with various optimization problems. Therefore, this paper applies Multi-Stage Parameter Adjustment (MSPA), which employs Extreme Latin Hypercube Sampling (XLHS), Primary Optimizer, and Artificial Neural Networks (ANNs) to a recently developed algorithm called the African Vulture Optimization Algorithm (AVOA) and a well-known one named Particle Swarm Optimization (PSO) for tuning their parameters. The performance of PSO is tested against two engineering and AVOA for two structural optimization problems, and their corresponding results are compared to those of their default versions. The results showed that the employment of MSPA improved the performance of both metaheuristic algorithms in all the considered optimization problems.

---

This study presents a novel approach for optimizing critical failure surfaces (CFS) in homogeneous soil slopes by incorporating seepage and seismic effects through the Self-Adaptive Enhanced Vibrating Particle System (SA_EVPS) algorithm. The Finite Element Method (FEM) is employed to model fluid flow through porous media, while Bishop's simplified method calculates the Factor of Safety (FOS). Two benchmark problems validate the proposed approach, with results compared against traditional and meta-heuristic methods. The SA_EVPS algorithm demonstrates superior convergence and accuracy due to its self-adaptive parameter optimization mechanism. Visualizations from Abaqus simulations and comprehensive statistical analyses highlight the algorithm's effectiveness in geotechnical engineering applications. The results show that SA_EVPS consistently achieves lower FOS values with smaller standard deviations compared to existing methods, indicating more accurate identification of critical failure surfaces.

---

This study aims to deal with multi-material topology optimization problems by using the Methods of Moving Asymptotes (MMA) method. The optimization problem is to minimize the strain energy while a certain amount of material is used. Several types of structures, including plane, plate and shell structures, are considered and optimal materials distribution is investigated. To parametrize the topology optimization problem, the Solid Isotropic Material with Penalization (SIMP) method is utilized. Analytical sensitivity analysis is performed to obtain the derivatives of the objective function and volume constraints with respect to the design variables. Two types of material with different modulus of elasticities are considered and, therefore, each element has two design variables. The first design variable represents the presence or absence of material in an element, while the second design variable determines the type of material assigned to the element. In order to analyze the structures required during the optimization process, the ABAQUS software is employed. To integrate the topology optimization procedure with ABAQUS model, a Python script is developed. The obtained results demonstrate the performance of the proposed method in generating reasonable and effective topologies.