桁架形状优化的自适应协方差矩阵进化策略方法

自适应协方差矩阵进化策略(CMA-ES)是在进化策略算法(ES)基础上发展起来的一种新的全局优化算法,对于处理复杂非线性多峰值优化问题具有很好的适用性.结合有限元方法,提出一种桁架形状优化的自适应协方差矩阵进化策略方法.采用空间25杆桁架和平面37杆桥形桁架两个桁架形状优化的经典算例对方法的可行性和先进性进行验证,其中,空间25杆桁架分为不考虑局部稳定约束和考虑局部稳定约束两种情况进行计算.研究结果表明,该方法是可行的,与基于遗传算法、粒子群优化算法等现代全局优化算法的桁架形状优化方法相比较,具有寻优效率高、收敛速度快、全局优化能力强的优点,在获得相同精度最优解的条件下,调用有限元分析的次数明显较少,从而有效地减少了计算耗时.     

基于自适应协方差矩阵进化策略的结构可靠度计算

自适应协方差矩阵进化策略(CMA-ES)算法是一种引导式随机优化算法,兼顾了深度搜索最优解和广度搜索解空间的能力。针对采用遗传算法(GA)、粒子群优化算法(PSO)等仿生优化算法求解复杂结构可靠度时往往遇到计算代价过高的问题,基于结构可靠度指标的几何涵义并结合验算点法,提出了结构可靠度计算的自适应协方差矩阵进化策略方法。研究结果表明,该方法是可行的,具有全局性好、收敛速度快的优点,与遗传算法、粒子群优化算法相比较,可大幅度地提高计算效率,为结构可靠度计算提供了一条新的途径。     

Optimisation of building form for solar energy utilisation using constrained evolutionary algorithms

In this paper we describe a new methodology for optimising building and urban geometric forms for the utilisation of solar irradiation, whether by passive or active means. For this we use a new evolutionary algorithm (a hybrid CMA-ES/HDE algorithm) to search the user-defined parameter space, within defined constraints. The fitness function, solar irradiation, is predicted using the backwards ray tracing program RADIANCE in conjunction with a cumulative sky model for fast computation.Application of this technique to three very different scenarios suggest that the new method consistently converges towards an optimal solution. Furthermore, with respect to configurations subjectively chosen to be intuitively well performing, annual irradiation is increased by up to 20%; sometimes yielding highly non-intuitive but architecturally interesting forms.     

四面体网格修匀算法研究

对有限元分析中网格优化的算法进行了研究。基于单元形状的度量准则,构造了与不可微目标函数等价的可微目标函数,建立了四面体网格修匀的优化模型。为了尽量避免陷入局部优化,采用了BFGS与混沌搜索相结合的求解算法,提高了获得全局最优解的概率。算例结果表明,该优化算法易于实现,稳定性好,效率较高,能够用于实际的网格优化。     

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。     

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.     

A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization

In solving optimization problems for building design and control, the cost function is often evaluated using a detailed building simulation program. These programs contain code features that cause the cost function to be discontinuous. Optimization algorithms that require smoothness can fail on such problems. Evaluating the cost function is often so time-consuming that stochastic optimization algorithms are run using only a few simulations, which decreases the probability of getting close to a minimum. To show how applicable direct search, stochastic, and gradient-based optimization algorithms are for solving such optimization problems, we compare the performance of these algorithms in minimizing cost functions with different smoothness. We also explain what causes the large discontinuities in the cost functions.     

高层建筑结构优化的若干建议

针对高层建筑结构优化中大型结构约束复杂,荷载组合多,截面与构件形式多样等特点,从优化变量、目标函数、约束条件等几个优化中最根本的问题出发,提出符合工程需要的建议,结合适当的优化准则编制成结构优化程序,对高层建筑结构优化设计有一定的借鉴作用。     

A Hybrid Particle Swarm—Gradient Algorithm for Global Structural Optimization

Abstract: The particle swarm optimization (PSO) method is an instance of a successful application of the philosophy of bounded rationality and decentralized decision making for solving global optimization problems. A number of advantages with respect to other evolutionary algorithms are attributed to PSO making it a prospective candidate for optimum structural design. The PSO‐based algorithm is robust and well suited to handle nonlinear, nonconvex design spaces with discontinuities, exhibiting fast convergence characteristics. Furthermore, hybrid algorithms can exploit the advantages of the PSO and gradient methods. This article presents in detail the basic concepts and implementation of an enhanced PSO algorithm combined with a gradient‐based quasi‐Newton sequential quadratic programming (SQP) method for handling structural optimization problems. The proposed PSO is shown to explore the design space thoroughly and to detect the neighborhood of the global optimum. Then the mathematical optimizer, starting from the best estimate of the PSO and using gradient information, accelerates convergence toward the global optimum. A nonlinear weight update rule for PSO and a simple, yet effective, constraint handling technique for structural optimization are also proposed. The performance, the functionality, and the effect of different setting parameters are studied. The effectiveness of the approach is illustrated in some benchmark structural optimization problems. The numerical results confirm the ability of the proposed methodology to find better optimal solutions for structural optimization problems than other optimization algorithms.     

Passive designs and strategies for low-cost housing using simulation-based optimization and different thermal comfort criteria

An optimum design of low-cost housing offers low-income urban inhabitants great opportunities to obtain a shelter at an affordable price and acceptable indoor thermal conditions. In this paper, the design and operation of a low-cost dwelling were numerically optimized using a simulation-based approach. Three multi-objective cost functions including construction cost, thermal comfort performance and 50-year operating cost were applied for naturally ventilated and air-conditioned buildings. Thermal environment inside the house was controlled and assessed by two thermal comfort models. Optimization problems which consist of 18 design parameters and 6 ventilation strategies were examined by two population-based probabilistic optimization algorithms (particle swarm optimization and hybrid algorithm). Optimum designs corresponding to each objective function, differences in optimal solutions, energy saving by the adaptive comfort approach and optimization effectiveness were outlined. The optimization method used in this paper shows a considerable potential of comfort improvement, energy saving and operating cost reduction.     

Building design optimization using a convergent pattern search algorithm with adaptive precision simulations

We propose a simulation–precision control algorithm that can be used with a family of derivative free optimization algorithms to solve optimization problems in which the cost function is defined through the solutions of a coupled system of differential algebraic equations (DAEs). Our optimization algorithms use coarse precision approximations to the solutions of the DAE system in the early iterations and progressively increase the precision as the optimization approaches a solution. Such schemes often yield a significant reduction in computation time.We assume that the cost function is smooth but that it can only be approximated numerically by approximating cost functions that are discontinuous in the design parameters. We show that this situation is typical for many building energy optimization problems. We present a new building energy and daylighting simulation program, which constructs approximations to the cost function that converge uniformly on bounded sets to a smooth function as precision is increased. We prove that for our simulation program, our optimization algorithms construct sequences of iterates with stationary accumulation points. We present numerical experiments in which we minimize the annual energy consumption of an office building for lighting, cooling and heating. In these examples, our precision control algorithm reduces the computation time up to a factor of four.     

Design of water distribution networks using particle swarm optimization

Application of particle swarm optimization (PSO) is demonstrated through design of a water distribution pipeline network. PSO is an evolutionary algorithm that utilizes the swarm intelligence to achieve the goal of optimizing a specified objective function. This algorithm uses the cognition of individuals and social behaviour in the optimization process. For the optimization of water distribution system, a simulation – optimization model, called PSONET is developed and used in which the optimization is by PSO. This formulation is applied to two benchmark optimization design problems. The results are compared with the results obtained by other optimization methods. The results show that the PSO is more efficient than other optimization methods as it requires fewer objective function evaluations.     

Finding optimal parameters of tuned mass dampers

In this paper, optimum design of tuned mass damper for seismically excited structures is discussed. In the design process, a benchmark multi‐degree of freedom system is considered, and the performance measure of the optimization criterion is selected as the H₂ and H_∞ norms of the transfer function of the combined tuned mass damper and building system. Differential evolution algorithm is then utilized to minimize these objective functions. The objective function choice on performance and the effectiveness of differential evolution optimization algorithm in comparison with other algorithms in the literature are investigated through numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

基于微粒群算法的工程项目质量、费用和工期综合优化

进度、费用和质量称为工程项目的三大控制目标,三者之间相互依存、相互影响。工程项目控制的理想状态是同时实现合理的工期、较低的费用和较高的质量。微粒群算法(PSO)是新近出现的一种仿生算法,具有简单容易实现,而且随机搜索的优点,使得搜索不易陷于局部最优。将该算法引入工程项目优化领域,研究工程项目的质量、费用和工期的综合优化问题。系统介绍微粒群算法原理、流程以及算法的改进发展,研究工程项目质量、费用和工期的优化,并建立质量、费用和工期的多目标综合优化模型,介绍应用微粒群算法编码解决工程项目多目标优化的方法步骤。最后,通过一个应用实例,计算表明微粒群算法可以准确快速地解决工程项目多目标优化问题。     

BuildOpt—a new building energy simulation program that is built on smooth models

Building energy simulation programs compute numerical approximations to physical phenomena that can be modeled by a system of differential algebraic equations (DAE). For a large class of building energy analysis problems, one can prove that the DAE system has unique solution that is once continuously differentiable in the building design parameters. Consequently, if building simulation programs are built on models that satisfy the smoothness assumptions required to prove existence of a unique smooth solution, and if their numerical solvers allow controlling the approximation error, one can use such programs with generalized pattern search optimization algorithms that adaptively control the precision of the solutions of the DAE system. Those optimization algorithms construct sequences of iterates with stationary accumulation points and have been shown to yield a significant reduction in computation time compared to algorithms that use fixed precision cost function evaluations.In this paper, we state the required smoothness assumptions and present the theorems that state existence of a unique smooth solution of the DAE system. We present BuildOpt, a detailed thermal and daylighting building energy simulation program. We discuss examples that explain the smoothing techniques used in BuildOpt. We present numerical experiments that compare the computation time for an annual simulation with the smoothing techniques applied to different parts of the models. The experiments show that high precision approximate solutions can only be computed if smooth models are used. This is significant because today's building simulation programs do not use such smoothing techniques and their solvers frequently fail to obtain a numerical solution if the solver tolerances are tight. We also present how BuildOpt's approximate solutions converge to a smooth function as the precision parameter of the numerical solver is tightened.     

Optimization of shape and functional structure of buildings as well as heat source utilisation example

The purpose of this article is to present the method of solving the optimization problem of the internal partitions of the building, the shape of the building, as well as heat sources.

The optimization of the internal partitions of the building is based on particular selection from the given list, and determination of the thickness of thermal insulation.

Solving the problem of the shape has been solved first in order to determine approximately the building height, proportions of building sides and orientation of the building with respect to the north–south axis, as well as to check which of the inequality constraints are active in this case. Following this, after obtaining the results, it was checked whether replacing the rectangular plan of the building by a rectangle and two trapezoids is advantageous.

The optimum choice of heat source types for heating for domestic use and the determination of share in covering the demand for heat in the time interval under consideration has been formulated and solved using continuous and discrete decision variables.

Part-problems of the optimization are solved by analytical–numerical method. They consist of determining some decision variables using analytical methods and the remaining using numerical methods applying CAMOS computer system, original algorithms and programs. In optimization of heat sources, original numerical methods were used for the determination of the compromise set in case of discontinuous objective functions.     

Optimal placement of metallic dampers for seismic upgrading of multistory buildings based on a cost‐effectiveness criterion using genetic algorithm

In this paper, an optimal placement methodology for metallic dampers is proposed to upgrade the seismic performance of multistory buildings. Most previous studies on optimal damper placement (ODP) problems have been focused on minimizing the seismic responses, whereas the present study aims to utilize the minimum total cost of dampers to achieve a prescribed level of seismic response. To this end, the optimization objective is constructed based on a cost‐effectiveness criterion, and the optimization constraint is defined based on a desired level of seismic response. An improved integer‐coded genetic algorithm is presented for solving the ODP problem. A 16‐story shear building is illustrated to verify the proposed optimal placement methodology. It is shown that the proposed methodology can be used to achieve the predetermined performance level while minimizing the retrofitting cost. Moreover, different algorithms, objective functions, and levels of accuracy on the optimization are also compared. Finally, a two‐step optimization approach is proposed for achieving better placement schemes with less computational efforts.     

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.     

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.