Structural Optimization Problems Research Articles

Design cost minimization of a reinforced concrete column section using overnew swarm-based optimization algorithms

AbstractIt is very tiresome for a practiser to detect the best feasible sizing design of structural members including reinforced concrete columns that is a highly nonlinear and complicated structural engineering optimization problem. This is due to such a design is practically conducted via conventional trial-and-error computing methods in which resistance to external loads, cost efficiency, and aesthetic factors, etc. have to be considered. This study focuses on minimizing the design cost of primarily proposed reinforced concrete column design problem via three overnew swarm-based optimizers such as Coati Optimization Algorithm, Fox Optimizer and Pelican Optimization Algorithm (POA) that are firstly utilized for this purpose. In this regard, the type of steel rebar distribution, the characteristic strength of the concrete, the height and width of the column section, and the number and diameter of the rebars are treated as discrete design variables of the newly proposed complex reinforced concrete column design cost optimization problem. In solution, the design requirements specified in practice code provisions should also be met. Here, Turkish Building Earthquake Code 2018 specifications are considered as practice structural design constraints. Consequently, the algorithmic performances of three overnew swarm-based metaheuristic optimization algorithms are compared and evaluated in detail. Amongst them, the POA shows most fruitful algorithmic design solution performance.

Multiobjective optimization of bridge and viaduct design: Comparative study of metaheuristics and parameter calibration

This article focuses on multiobjective optimization in the design of bridges and viaducts. The problem is characterized as a multi-objective optimization, with the objective functions being the construction cost, the environmental impact (CO2 emissions) and the design service life. For optimization, three commonly used metaheuristics in structural optimization problems were tested: Multiple Objective Particle Swarm Optimization (MOPSO), Nondominated Sorting Genetic Algorithm II (NSGA-II) and Strength Pareto Evolutionary Algorithm 2 (SPEA2). The results showed that MOPSO outperformed the other methods, achieving the highest hypervolume and Pure Diversity values. Once the best performing metaheuristic was defined, the calibration of the MOPSO parameters was then developed to improve the quality of the solutions found, reduce the execution time and increase the robustness of the algorithm. Using the Taguchi method with an orthogonal matrix consisting of 54 experiments, five parameters were evaluated at three different levels, totaling 270 analyses. The results indicated that parameter calibration led to an increase in the average hypervolume compared to the results before calibration. Moreover, the coverage of two sets revealed the superior performance of the calibrated set, demonstrating better trade-offs among the objective functions.

Marathon runner algorithm: theory and application in mathematical, mechanical and structural optimization problems

Abstract This study proposes a novel human-inspired metaheuristic search algorithm called marathon runner algorithm. This method mimics competitive behaviors observed in real marathon runners through mathematical modeling. Unlike classical elitist algorithms that prioritize position of the best agent, the marathon runner algorithm introduces a novel concept called vision point. This point considers the quality of the entire population, not just the leader. By guiding the population towards vision point, the risk of getting trapped in local optima is reduced. A two-part evaluation was conducted to thoroughly assess the search capabilities of the marathon runner algorithm. First, it is tested against a set of unconstrained benchmark mathematical functions and the algorithm’s quantitative attributes, such as complexity, accuracy, stability, diversity, sensitivity, and convergence rate are analyzed. Subsequently, the algorithm was applied to mechanical and structural optimization problems with both continuous and discrete variables. This application demonstrated the effectiveness of the algorithm in solving practical engineering challenges with constraints. The outcomes are compared with those obtained by six other well-established techniques. The obtained results indicate that the marathon runner algorithm yields promising and competitive solutions for both mathematical, mechanical, and structural problems.

On the data-driven description of lattice materials mechanics

In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems.

Mapping structural topology optimization problems to quantum annealing

Mapping structural topology optimization problems to quantum annealing

Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application

The multi-dimensional optimization of mechanisms is a typical optimization problem encountered in mechanical design. Herein, the Hybrid strategy improved Beetle Antennae Search (HSBAS) algorithm is proposed to solve the multi-dimensional optimization problems encountered in structural design. To solve the problems of local optimization and low accuracy of the high-dimensional solution of the Beetle Antennae Search (BAS) algorithm, the algorithm adopts the adaptive step strategy, multi-directional exploration strategy, and Lens Opposition-Based Learning strategy, significantly reducing the probability of the algorithm falling into the local optimum and improving its global search capability. Comparative experiments of the improved algorithm are carried out by selecting eleven benchmark test functions. HSBAS can reach 1 × 10−22 accuracy from the optimal value when dealing with low-dimensional functions. It can also obtain 1 × 10−2 accuracy when dealing with high-dimensional functions, significantly improving the algorithm’s capability. According to Friedman’s ranking test result, HSBAS ranks first, which proves that HSBAS is superior to the other three algorithms. The HSBAS algorithm is further used to optimize the design of the altitude compensation module of the gravity compensation device for solar wings, controlling the fluctuation of bearing capacity within 0.25%, which shows that the algorithm can be used as an effective tool for engineering structural optimization problems.

Sizing and Shape Optimization of Discrete Truss Employing a Target-Oriented Krill Herd Algorithm

Abstract The krill herd (KH) algorithm is widely used for optimizing truss structures as no gradient information is necessary, and only a few parameters require adjustment. However, when the truss structure becomes discrete and complex, KH tends to fall into a local optimum. Therefore, a novel target-oriented KH (TOKH) algorithm is proposed in this study to optimize the design of discrete truss structures. Initially, a crossover operator is established between the “best krill” and “suboptimal krill” to generate a robust “cross krill” for global exploration. Additionally, an improved local mutation and crossover (ILMC) operator is introduced to fine-tune the “center of food” and candidate solutions for local exploitation. The proposed method and other optimization approaches are experimentally compared considering 15 benchmark functions. Then, the performance of the TOKH algorithm is evaluated based on four discrete truss structure optimization problems under multiple loading conditions. The obtained optimization results indicate that the proposed method presents competitive solutions in terms of accuracy, unlike other algorithms in the literature, and avoids falling into a local minimum.

Research of the optimization problem of structure hierarchical communication network with changing its parameters

The article is devoted to the study of the problem of optimizing the hierarchical structure of a multicommodity communication network with discrete flows when changing its important parameters, such as the capacity of network arcs in transport blocks and the size of the transport block for transportation of the discrete small-lot cargo or of the data transmission in a digital communication network. The network has three levels of hierarchy – a backbone, a zonal and an internal and four types of nodes - backbone nodes of the first, second and third types, forming the backbone and zonal levels of the network, and nodes of the fourth type, which subordinate to each backbone node and forming the internal levels of the network. Types of nodes differ from each other in terms of functionality. The main task of the study is to establish how the structure of the backbone network changes (the number and location of backbone nodes of the first, second, and third types), the flow processing and distribution scheme, and the technical and economic indicators of the network's functioning for different values of its parameters. The principles of organization of sorting and distribution of flows in a three-level network and its mathematical model are given. A mathematical model of the optimization problem of the backbone network structure and flow sorting and distribution scheme is formulated. Algorithms for solving the problem are based on the discrete analogue of the local descent method proposed by the authors earlier, when the neighborhoods of the metric space of possible solutions are chosen based on heuristic considerations, taking into account the specifics of the problem being solved. Computer modeling of the problem on a network containing 10 nodes at the specified change in the both parameters is carried out. The modeling was carried out on the example of the transport network of cargo transportation using a computer program that is part of the instrumental software of the Information and Analytical Decision Support System (IA DSS), which is being developed at the Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine. An experimental study of solution the problem showed that the structure of the network is weakly dependent on the change in the carrying capacity of the arcs and the size of the transport block. The proposed computer technology for solving problem when the network parameters are changed allows you to interactively modeling various options of a network, changing the topology, hierarchical structure, flows, parameters and constraints of the model and from the set of the obtained solutions to choose a best option, taking into account the selected a goal function and the accepted constraints; calculate preliminary technical and economic indicators of the network's functioning, estimate the cost of additional resources and plan the amount of investment required for the modernization and construction of its structural elements, which ultimately makes it possible to increase the efficiency functioning of the network by optimizing use of its resources and reducing the operating costs for the processing and transportation of flows.

Augmented Space Integral Approach for Structural Reliability-Based Optimization

An efficient, fully decoupled approach is proposed to solve the structural reliability-based design optimization (RBDO) problem. The proposed approach utilizes augmented space integral and importance sampling (ASI-IS) to efficiently evaluate a functional relationship between the probability of failure and the design parameters, namely the so-called failure probability function. ASI-IS allows for the avoidance of both the intractable density fitting task associated with augmented space methods and the time-consuming repeated reliability evaluations associated with surrogate model approaches. The resulting functional relationship can be used to completely decouple the original RBDO problem into a deterministic one. Then, an iteration mechanism is constructed with gradually smaller design domains to enhance the efficiency of the optimization process. Furthermore, a sample reuse algorithm is proposed to improve the performance of the proposed approach by collecting the samples generated in previous iterations and reusing them in the current iteration in order to produce a better estimator of the failure probability function. Numerical and engineering examples, including a turbine blade and an aircraft inner flap, are given to demonstrate the efficiency and feasibility of the proposed approach.

PG-LBO: Enhancing High-Dimensional Bayesian Optimization with Pseudo-Label and Gaussian Process Guidance

Variational Autoencoder based Bayesian Optimization (VAE-BO) has demonstrated its excellent performance in addressing high-dimensional structured optimization problems. However, current mainstream methods overlook the potential of utilizing a pool of unlabeled data to construct the latent space, while only concentrating on designing sophisticated models to leverage the labeled data. Despite their effective usage of labeled data, these methods often require extra network structures, additional procedure, resulting in computational inefficiency. To address this issue, we propose a novel method to effectively utilize unlabeled data with the guidance of labeled data. Specifically, we tailor the pseudo-labeling technique from semi-supervised learning to explicitly reveal the relative magnitudes of optimization objective values hidden within the unlabeled data. Based on this technique, we assign appropriate training weights to unlabeled data to enhance the construction of a discriminative latent space. Furthermore, we treat the VAE encoder and the Gaussian Process (GP) in Bayesian optimization as a unified deep kernel learning process, allowing the direct utilization of labeled data, which we term as Gaussian Process guidance. This directly and effectively integrates the goal of improving GP accuracy into the VAE training, thereby guiding the construction of the latent space. The extensive experiments demonstrate that our proposed method outperforms existing VAE-BO algorithms in various optimization scenarios. Our code will be published at https://github.com/TaicaiChen/PG-LBO.

Optimal design of truss domes with frequency constraints using seven metaheuristic algorithms incorporating a comprehensive statistical assessment

In this article, seven recently developed metaheuristic algorithms are utilized for optimal design of dome-shaped trusses with natural frequency constraints. These algorithms are social network search, jellyfish search optimizer, equilibrium optimizer, teaching-learning-based optimization, grey wolf optimizer, colliding bodies optimization, and the improved grey wolf optimizer. This study focuses on the assessment and tuning of these algorithms to enhance both computational efficiency and solution quality. In particular, we introduce a hyperparameter tuning procedure that significantly improves the performance of the algorithms to make them more suitable for the solution of structural optimization problems. The performance of the selected algorithms is studied through five benchmark examples for design optimization of dome structures, from small-scale to large-scale cases, with frequency constraints. Many combination scenarios are studied for hyperparameter tuning of the algorithms in each design example in order to provide comprehensive statistical results determining the sufficient number of structural analyses as well as the number of particles to find an efficient condition of each algorithm. Indeed, this study also presents an insight into the efficient setting of hyperparameters for each algorithm, leading to a better solution with lower computational cost. Furthermore, the optimization results provide a comparison of the solutions obtained in the current and previous studies in order to demonstrate the suitability of the selected algorithms.

A new improved Newton metaheuristic algorithm for solving mathematical and structural optimization problems

A new improved Newton metaheuristic algorithm for solving mathematical and structural optimization problems

Development of a non-uniform cellular automata framework for sizing, topology and layout optimization of truss structures

This article presents a bi-level non-uniform cellular automata (CA) algorithm for the solution of sizing, topology and layout optimization of truss structures. The non-uniform CA was successfully used in a previous study to solve the weight optimization problem of truss structures for topology and sizing (El Bouzouiki, Sedaghati, and Stiharu 2021. Computers & Structures 242: 106394). In this article, an extended version of the non-uniform CA algorithm is proposed, based on the fully stressed design approach and the distribution of strain energy within the structure, to find the optimal position of the cell’s (joint’s) coordinates. The proposed non-uniform CA algorithm can solve the minimum weight optimization problem of truss structures subjected to both stress and displacement constraints. Several benchmark problems are presented to demonstrate the efficiency and accuracy of the proposed methodology.

Parameter and Topology Optimization of Structures in the Frequency Domain under Nevanlinna–Pick Interpolation Constraints

The design optimization of structures can be conducted in either the time domain or the frequency domain. The frequency domain approach is advantageous compared to its time domain counterpart, especially if the degree of freedom is large, the objectives and/or constraints are formulated in the frequency domain, or the structure is subject to random loading. In this paper, an attempt is undertaken to obtain feasible optimal solutions by implementing the Nevanlinna–Pick (NP) interpolation theory across multi-objective structural optimization problems in the frequency domain. The NP equations introduce a trade-off that originates from the interpolation theory for complex variables. According to the NP theory, a complex function cannot have an independent amplitude from its derivative at a certain frequency. Consequently, the frequency response of a physical system cannot be shaped arbitrarily at discrete frequencies. Our objectives within this paper include calculating the weight, natural frequency, fatigue life, frequency domain response, and its derivative. To illustrate our claims, sample parameter and topology optimization problems were formulated and solved, both with and without the NP constraints. It was found that the inclusion of NP constraints induced a considerable improvement in the optimal solutions, while also causing the convergence to the optimal solution to become smoother.

A Formulation of Structural Design Optimization Problems for Quantum Annealing

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems.

Research on Multi-Objective Optimization on Explosion-Suppression Structure-Nonmetallic Spherical Spacers

Intense burning phenomena (fire disasters) need to be prevented in the combustible gas utilization and transportation processes to ensure industrial safety. Nonmetallic spherical spacers (NSSs) have been investigated and applied in lots of explosive atmospheres to prevent explosion execution in a confined space. In this work, a novel fuzzy-based analytic hierarchy process (FAHP) is developed to take into account the uncertainty in decision-making and effectively solve the problem of factor weight allocation in multi-objective optimization. Optimal Latin Hypercube Design (Opt LHD), Chebyshev Orthogonal Polynomials (COP), and Adaptive Simulated Annealing (ASA) were combined. A multi-objective optimization method is proposed for the structural parameter optimization problem on NSSs in order to achieve conflicting multiple-objective optimization of low displacement rate and minimal deformation. That is to say, the small volume (low displacement rate) and high explosion-suppression performance (minimal deformation) of NSSs were optimized simultaneously. The results show that, compared with the original NSS model’s deformation (2.85 mm) and displacement rate (3.63%), the optimized NSSs with weight allocation had optimized the deformation by 12.98% and displacement rate by 6.1%. Compared with the optimized design model of NSSs without weight allocation with a deformation of 2.75 mm and a displacement rate of 3.48%, the deformation has been optimized by 9.82%, and the displacement rate has been optimized by 2.0%. It was verified that the proposed method is effective. At the same time, it was verified that the suppression effect of NSSs can be enhanced by changing the shape of the NSS spacer reasonably by experimental verification.

Automatic Column Grouping of 3D Steel Frames via Multi-Objective Structural Optimization

Formulations of structural optimization problems are proposed in this paper to automatically find the best grouping of columns in 3D steel buildings. In these formulations, the conflicting objective functions, minimized simultaneously, are the weight of the structure and the number of different groups of columns. In other words, the smaller the number of different groups of columns, the greater the weight of the structure, and the greater the number of groups, the smaller the structure’s weight. The design variables are the bracing system configuration, column cross-section orientation, and assigned W-shaped profile indices for columns, beams, and braces. The design constraints are the allowable displacements, strength, and geometric considerations. After solving the multi-objective optimization problem, the result is a Pareto front, presenting non-dominated solutions. Three evolutionary algorithms based on differential evolution are adopted in this paper to solve three computational experiments. Even if preliminary groupings of columns are adopted, considering architectural aspects such as the symmetry of the structure, it is possible to discover other interesting structural configurations that will be available to the decision maker, who will be able to make their choices based on the impacts on manufacturing, cutting, transporting, checking and welding.

The design and optimization of heterogeneous catalysts using computational methods

Computational design of catalytic materials is a high dimensional structure optimization problem that is limited by the bottleneck of expensive quantum computation tools. An illustration of interaction of different factors involved in the design and optimization of a catalyst.

A topology optimization method for problems with design-dependent loads based on non-uniform rational basis spline entities

In this paper, topology optimization (TO) problems of structures subjected to design-dependent loads are formulated in the context of a special density-based TO approach wherein a Non Uniform Rational Basis Spline (NURBS) hyper-surface is used to represent the topological descriptor. Unlike classical density-based TO approaches, the NURBS-density-based method allows representing the pseudo-density field through a purely geometric computer-aided design compatible entity. In this context, the problem is formulated in the most general case of inhomogeneous Neumann-Dirichlet boundary conditions. Moreover, a thorough study of the penalty function of the design-dependent loads is carried out to investigate its effect on the optimized topologies and overcome the singularity effect related to the zones characterized by low values of the pseudo-density field. Finally, a wide campaign of sensitivity analyses is conducted to investigate the influence of the integer parameters of the NURBS entity, of the combination of design-depedent loads and inhomogeneous Neumann-Dirichlet boundary conditions, and of the concentrated load on the optimized topology. The effectiveness of the approach is tested on 2D and 3D benchmark problems.

INTEGRATING ENHANCED OPTIMIZATION WITH FINITE ELEMENT ANALYSIS FOR DESIGNING STEEL STRUCTURE WEIGHT UNDER MULTIPLE CONSTRAINTS

Real-world optimization problems are ubiquitous across scientific domains, and many engineering challenges can be reimagined as optimization problems with relative ease. Consequently, researchers have focused on developing optimizers to tackle these challenges. The Snake Optimizer (SO) is an effective tool for solving complex optimization problems, drawing inspiration from snake patterns. However, the original SO requires the specification of six specific parameters to operate efficiently. In response to this, enhanced snake optimizers, namely ESO1 and ESO2, were developed in this study. In contrast to the original SO, ESO1 and ESO2 rely on a single set of parameters determined through sensitivity analysis when solving mathematical functions. This streamlined approach simplifies the application of ESOs for users dealing with optimization problems. ESO1 employs a logistic map to initialize populations, while ESO2 further refines ESO1 by integrating a Lévy flight to simulate snake movements during food searches. These enhanced optimizers were compared against the standard SO and 12 other established optimization methods to assess their performance. ESO1 significantly outperforms other algorithms in 15, 16, 13, 15, 21, 16, 24, 16, 19, 18, 13, 15, and 22 out of 24 mathematical functions. Similarly, ESO2 outperforms them in 16, 17, 18, 22, 23, 23, 24, 20, 19, 20, 17, 22, and 23 functions. Moreover, ESO1 and ESO2 were applied to solve complex structural optimization problems, where they outperformed existing methods. Notably, ESO2 generated solutions that were, on average, 1.16%, 0.70%, 2.34%, 3.68%, and 6.71% lighter than those produced by SO, and 0.79%, 0.54%, 1.28%, 1.70%, and 1.60% lighter than those of ESO1 for respective problems. This study pioneers the mathematical evaluation of ESOs and their integration with the finite element method for structural weight design optimization, establishing ESO2 as an effective tool for solving engineering problems.