Cyber‐physical approach to the optimization of semiactive structural control under multiple earthquake ground motions

This paper presents a cyber‐physical approach to optimize the semiactive control of a base‐isolated structure under a suite of earthquakes. The approach uses numerical search algorithms to guide the exploration of the design space and real‐time hybrid simulation (RTHS) to evaluate candidate designs, creating a framework for real‐time hybrid optimization (RHTO). By supplanting traditional numerical analysis (i.e., finite element methods) with RTHS, structural components that are difficult to model can be represented accurately while still capturing global structural performance. The efficiency of RTHO is improved for multiple design excitations with the creation of a multiinterval particle swarm optimization (MI‐PSO) algorithm. As a proof‐of‐concept, RTHO is applied to improve the seismic performance of a base‐isolated structure with supplemental control. The proposed RTHO framework with MI‐PSO is a versatile technique for multivariate optimization under multiple excitations. It is well suited for the accurate and rapid evaluation of structures with nonlinear experimental substructures, in particular, those that do not undergo permanent damage such as structural control devices. The RTHO framework integrates popular optimization algorithms with advanced experimental methods, creating an exciting new cyber‐physical approach to design.     

粒子群优化算法在桁架优化设计中的应用

粒子群优化（PSO）算法是近年来发展起来的一种基于群智能的随机优化算法,具有概念简单、易于实现、占用资源低等优点。为了解决有应力约束和位移约束的桁架的尺寸优化问题,将PSO算法应用于桁架结构的尺寸优化设计。首先介绍了原始的PSO算法的基本原理,然后引入压缩因子改进了PSO算法,并提出合理的参数设置值。对几个经典问题进行了求解,并与传统的优化算法和遗传算法进行了比较。数值结果表明,改进的PSO算法具有良好的收敛性和稳定性,可以有效地进行桁架结构的尺寸优化设计。     

Advanced energy‐based analyses of trusses employing hybrid metaheuristics

Total potential optimization using metaheuristic algorithm (TPO/MA) is an alternative method in structural analyses, and it is a black‐box application for nonlinear analyses. In the study, an advanced TPO/MA using hybridization of several metaheuristic algorithms is investigated to solve large‐scale structural analyses problems. The new generation algorithms considered in the study are flower pollination algorithm (FPA), teaching learning‐based optimization, and Jaya algorithm (JA). Also, the proposed methods are compared with methodologies using classic and previously used algorithms such as differential evaluation, particle swarm optimization, and harmony search. Numerical investigations were carried out for structures with four to 150 degrees of freedoms (design variables). It has been seen that in several runs, JA gets trapped into local solutions. For that reason, four different hybrid algorithms using fundamentals of JA and phases of other algorithms, namely, JA using Lévy flights, JA using Lévy flights and linear distribution, JA with consequent student phase, and JA with probabilistic student phase (JA1SP), are developed. It is observed that among the variants tried, JA1SP is seen to be more effective on approaching to the global optimum without getting trapped in a local solution.     

Constrained mean‐variance mapping optimization for truss optimization problems

Truss optimization is a complex structural problem that involves geometric and mechanical constraints. In the present study, constrained mean‐variance mapping optimization (MVMO) algorithms have been introduced for solving truss optimization problems. Single‐solution and population‐based variants of MVMO are coupled with an adaptive exterior penalty scheme to handle geometric and mechanical constraints. These tools are explained and tuned for weight minimization of trusses with 10 to 200 members and up to 1,200 nonlinear constraints. The results are compared with those obtained from the literature and classical genetic algorithm. The results show that a MVMO algorithm has a rapid rate of convergence and its final solution can obviously outperform those of other algorithms described in the literature. The observed results suggest that a constrained MVMO is an attractive tool for engineering‐based optimization, particularly for computationally expensive problems in which the rate of convergence and global convergence are important.     

Comparative seismic design optimization of spatial steel dome structures through three recent metaheuristic algorithms

Steel dome structures, with their striking structural forms, take a place among the impressive and aesthetic load bearing systems featuring large internal spaces without internal columns. In this paper, the seismic design optimization of spatial steel dome structures is achieved through three recent metaheuristic algorithms that are water strider (WS), grey wolf (GW), and brain storm optimization (BSO). The structural elements of the domes are treated as design variables collected in member groups. The structural stress and stability limitations are enforced by ASD-AISC provisions. Also, the displacement restrictions are considered in design procedure. The metaheuristic algorithms are encoded in MATLAB interacting with SAP2000 for gathering structural reactions through open application programming interface (OAPI). The optimum spatial steel dome designs achieved by proposed WS, GW, and BSO algorithms are compared with respect to solution accuracy, convergence rates, and reliability, utilizing three real-size design examples for considering both the previously reported optimum design results obtained by classical metaheuristic algorithms and a gradient descent-based hyperband optimization (HBO) algorithm.     

Design optimization of tall steel buildings by a modified particle swarm algorithm

Optimal design of tall buildings, as large‐scale structures, is a rather difficult task. To efficiently achieve this task, the computational performance of the employed standard meta‐heuristic algorithms needs to be improved. One of the most popular meta‐heuristics is particle swarm optimization (PSO) algorithm. The main aim of the present study is to propose a modified PSO (MPSO) algorithm for optimization of tall steel buildings. In order to achieve this purpose, PSO is sequentially utilized in a multi‐stage scheme where in each stage an initial swarm is generated on the basis of the information derived from the results of previous stages. Two large‐scale examples are presented to investigate the efficiency of the proposed MPSO. The numerical results demonstrate the computational advantages of the MPSO algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural reliability assessment based on particles swarm optimization

The PSO algorithm is very efficient to solve global optimization problems with continuous variables. Its use in the structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. Several examples of the literature studied in this paper show that the results yielded by PSO are quasi-exact with respect to those yielded by MC and response surface methods. The low computing time of this zero order algorithm is also a great advantage to solve optimization problem. Therefore, this algorithm can be considered as an additional efficient algorithm to those existing in the literature based on gradient method.     

Reliability‐based optimum seismic design of RC frames by a metamodel and metaheuristics

The present study is devoted to reliability‐based optimum seismic design (RBOSD) of reinforced concrete (RC) moment frames within the context of performance‐based design. A chaotic enhanced colliding bodies optimization (CECBO) metaheuristic algorithm is proposed to achieve the optimization task. In the framework of CECBO, chaotic maps are employed to achieve randomness that results in better convergence rate in comparison with its standard version. For reliability assessment of structures during the optimization process, the Monte Carlo simulation method is employed. In order to reduce the prohibitive computational burden of the MCS in the optimization setting, a metamodel is proposed to accurately evaluate the required deterministic and probabilistic structural seismic nonlinear responses. Efficiency of the proposed methodology for implementation of RBOSD process for RC frames is illustrated by presenting two numerical examples.     

Design optimization of truss structures with continuous and discrete variables by hybrid of biogeography‐based optimization and differential evolution methods

This paper presents a hybrid BBO‐DE algorithm by hybridizing biogeography‐based optimization (BBO) and differential evolution (DE) methods for optimum design of truss structures with continuous and discrete variables. In BBO‐DE, the migration operator of BBO method serves as a local exploiter mechanism during the search process. Besides, DE has a role of the global exploration by performing multiple search directions in the search space to preserve more diversity in the population. By embedding of DE algorithm in BBO method as a mutation mechanism, the balance between the exploration and exploitation abilities is further improved. The comparative results with some of the most recently developed methods demonstrate the fast convergence properties of the proposed algorithm and confirm its effectiveness to solve optimum design problems of truss structures with continuous and discrete variables.     

基于生长空间限定与并行搜索的模拟植物生长算法的空间结构优化方法

为弥补传统设计理念和优化方法的不足,促进空间结构的发展与创新,结合前沿优化理论,依据模拟植物生长算法(PGSA)的基本原理,提出基于生长空间限定与并行搜索的模拟植物生长算法(GSL&PS-PGSA),并与空间结构优化相结合,建立了基于GSL&PS-PGSA的空间结构优化方法。给出了相应的结构优化流程,并采用MATLAB及ANSYS二次开发语言APDL编制了优化程序。通过单层球面网壳截面优化和弦支穹顶预应力优化的典型空间结构算例分析,结果表明：所提出的GSL&PS-PGSA为算法提供了有效的终止机制,且具有高效的计算效率及全局搜索能力;与遗传算法(GA)、粒子群算法(PSO)、ANSYS自带优化方法以及其他改进PGSA算法等相比,GSL&PS-PGSA的优化效果更为显著且具有明显优势;所建立的基于GSL&PS-PGSA的空间结构优化方法,可适用于各类传统和新型空间结构体系的优化问题。     

Optimal tuning of fuzzy parameters for structural motion control using multiverse optimizer

In recent years, there is an increasing interest in optimization of structural control algorithms. Fuzzy logic controller is one of the most common and versatile control algorithms that is generally formulated based on the human knowledge and expert. Human knowledge and experience do not yield optimal control responses for a given structure, and tuning of the fuzzy parameters is necessary. This paper focuses on the optimization of a fuzzy controller applied to a seismically excited nonlinear building. In the majority of cases, this problem is formulated based on the linear behavior of the structure; however, in this paper, objective functions and the evaluation criteria are considered with respect to the nonlinear responses of the structures. Multiverse optimizer is a novel nature‐inspired optimization algorithm that is based on the three concepts of cosmology as white hole, black hole, and wormhole. This algorithm has fast convergence rate and can be utilized in continuous and discrete optimization problems. In this paper, the multiverse optimizer is considered as the optimization algorithm for optimization of the fuzzy controller. The performance of the selected algorithm is compared with eight different optimization algorithms. The results prove that the selected algorithm is able to provide very competitive results.     

基于微粒群算法的污水管网优化设计

针对遗传算法存在的问题，提出一种利用微粒群算法（PSO）优化污水管网的模型，并阐述了应用微粒群算法进行污水管网优化设计的原理、特点。在南京市某地区的污水系统设计中采用了该算法，取得了良好的社会效益和经济效益。     

Particle swarm optimization of tuned mass dampers

Tuned mass dampers (TMD) have been widely used to attenuate undesirable vibrations in engineering. Most optimization problems of TMD are solved by either numerical iteration technique or conventional mathematical methods that require substantial gradient information. The selection of the starting values is very important to ensure convergence. In this paper, we use a novel evolutionary algorithm of particle swarm optimization (PSO) for optimization of the required parameters of a TMD. Optimum parameters of the TMD system attached to a viscously damped single degree-of-freedom main system are obtained by minimizing some response quantities, for examples, the mean square displacement responses and displacement amplitude of the main system under various combinations of different kinds of excitations. The excitations considered include external force and base acceleration modeled as Gaussian white-noise random processes. Harmonic base acceleration with frequency invariant amplitude is also considered. The PSO can be used to find the optimum mass ratio, damper damping and tuning frequency of the TMD system and can be easily programmed for practical engineering applications. Explicit expressions of the optimum TMD parameters are given for engineering designers.     

Fluid transients and pipeline optimization using GA and PSO: the diameter connection

This paper describes the optimal selection of pipe diameters in a network considering steady state and transient analysis in water distribution systems. Two evolutionary approaches, namely genetic algorithms (GA) and particle swarm optimization (PSO), are used as optimization methods to obtain pipe diameters. Both optimization programs, inspired by natural evolution and adaptation, show excellent performance for solving moderately complex real-world problems which are highly nonlinear and demanding. The case study shows that the integration of GA or PSO with a transient analysis technique can improve the search for effective and economical hydraulic protection strategies. This study also shows that not only is the selection of pipe diameters crucially sensitive for the surge protection strategies but also that more global systematic approaches should be involved in water distribution system design, preferably at an early stage in the design process.     

Optimum design of post‐tensioned axially symmetric cylindrical walls using novel hybrid metaheuristic methods

An efficient methodology for various structural design problems is needed to optimize the total cost for structures. Although some methods seem to be efficient for applications, due to using special algorithm parameters, computational cost, and some other reasons, there is still much to be done in order to develop an effective method for general design applications. This paper describes the influence of the selected procedure on the design of cost‐optimized, post‐tensioned axially symmetric cylindrical reinforced concrete walls. In this study, the optimum design of axially symmetric cylindrical walls using several metaheuristic algorithms is investigated. The new generation algorithms used in the study are flower pollination algorithm, teaching–learning‐based optimization, and Jaya algorithm (JA). These algorithms are also compared with one of the previously developed algorithm called harmony search. The numerical examples were done for walls with 4‐ to 10‐m height and for 1, 5, 10, 15, 20, and 25 post‐tensioned load cases, respectively. Several independent runs are conducted, and in some of these runs, JA may trap to a local solution. To overcome this situation, hybrid algorithms such as JA using Lévy flights, JA using Lévy flights with probabilistic student phase (JALS), JA using Lévy Flights with consequent student phase (JALS2), and JA with probabilistic student phase are developed. It is seen that in many respects, the JALS2 and JALS are the most effective within the proposed hybrid approaches.     

Optimal seismic design of steel structures by an efficient soft computing based algorithm

The main aim of this study is to propose advanced soft computing techniques for the optimal seismic design of real steel structures subjected to natural ground motion records. For the solution of the optimization problem an efficient combination of the particle swarm optimization (PSO) and adaptive virtual sub-population (AVSP) algorithms is proposed. Also an efficient combination of the adaptive neuro-fuzzy inference system (ANFIS), wavelet transforms (WT) and radial basis function (RBF) neural networks, termed as fuzzy wavelet radial basis function (FWRBF), is proposed to accurately predict the structural responses. The numerical results demonstrate the computational advantages of the proposed methodology.     

Reliability-based design optimization with discrete design variables and non-smooth performance functions: AB-PSO algorithm

The purpose of reliability-based design optimization (RBDO) is to find a balanced design that is not only economical but also reliable in the presence of uncertainty. Practical applications of RBDO involve discrete design variables, which are selected from commercially available lists, and non-smooth (non-differentiable) performance functions. In these cases, the problem becomes an NP-complete combinatorial optimization problem, which is intractable for discrete optimization methods. Moreover, the non-smooth performance functions would hinder the use of gradient-based optimizers as gradient information is of questionable accuracy. A framework is presented in this paper whereby subset simulation is integrated with a new particle swarm optimization (PSO) algorithm to solve the discrete and non-smooth RBDO problem. Subset simulation overcomes the inefficiency of direct Monte Carlo simulation (MCS) in estimating small failure probabilities, while being robust against the presence of non-smooth performance functions. The proposed PSO algorithm extends standard PSO to include two new features: auto-tuning and boundary-approaching. The former feature allows the proposed algorithm to automatically fine tune its control parameters without tedious trial-and-error procedures. The latter feature substantially increases the computational efficiency by encouraging movement toward the boundary of the safe region. The proposed auto-tuning boundary-approaching PSO algorithm (AB-PSO) is used to find the optimal design of a ten-bar truss, whose component sizes are selected from commercial standards, while reliability constraints are imposed by the current design code. In multiple trials, the AB-PSO algorithm is able to deliver competitive solutions with consistency. The superiority of the AB-PSO algorithm over standard PSO and GA (genetic algorithm) is statistically supported by non-parametric Mann-Whitney U tests with the p-value less than 0.01.     

A unified approach to parameter selection in meta-heuristic algorithms for layout optimization

Meta-heuristic optimization algorithms have attracted many researchers in the last decade. Adjustment of different parameters of these algorithms is usually a time consuming task which is mostly done by a trial and error approach. In this study an index, namely convergence factor (CF), is introduced that can show the performance of these algorithms. CF of an algorithm provides an estimate of the suitability of the parameters being set and can also enforce the algorithm to adjust its parameters automatically according to a pre-defined CF.In this study GA, ACO, PSO and BB-BC algorithms are used for layout (topology plus sizing) optimization of steel braced frames. Numerical examples show these algorithms have some similarities in common that should be taken into account in solving optimization problems.     

New improved metaheuristic approaches for optimum design of posttensioned axially symmetric cylindrical reinforced concrete walls

Two novel hybrid approaches are presented for optimum design of axially symmetric cylindrical walls subjected to posttensioning loads using metaheuristic algorithms such as harmony search (HS), flower pollination algorithm (FPA), and teaching learning based optimization (TLBO). The objective function of the optimization problem is to minimize the total cost of the wall subjected to constraints on the basis of sectional capacities (bending moment, shear force, and axial tension), ACI 318 (building code requirements for structural concrete) requirements and design variables such as wall thickness, compressive strength of concrete, location and intensities of posttensioning cables, size, and spacing of reinforcement. In the optimum design, the performance of the iterative population based metaheuristic algorithms, HS, FPA, and TLBO are compared and tested by taking wall thickness as discrete and continuous variable. In order to improve the efficiency on finding global optimum results, hybrid forms of the HS combined with FPA and TLBO are effective for the optimization problem.