元启发式优化中参数选择的统一方法

在十几年前,元启发式优化算法引起了广泛的注意。这些算法中不同参数的调整是个耗时很长的过程,常需通过反复计算进行。故引入集中因子,评价这些算法的性能。集中因子可对参数的匹配性进行估计,并能增强算法自动调整参数的能力。分别采用遗传算法、蚁群优化算法,粒子群优化算法和大爆炸-大危机算法,对某钢支撑框架进行拓扑优化。数值结果表明,这些算法在解决优化问题时具有一些共同点。     

Shortening the search time in optimization of water distribution networks

Various optimization techniques have been implemented for minimizing the costs associated with water distribution networks (WDNs). In this regard, meta-heuristic algorithms have represented the highest efficiency. One of the weaknesses of these algorithms is their high computational costs, which make their implementation sometimes impracticable for optimization of large real life WDNs. In this article an optimization model based on the ant colony optimization algorithm is presented for least cost design of WDNs. In the proposed model, ants select pipe diameters so that the energy loss per unit length of pipes will be in a specific range. In this model, the number of objective function evaluations is small. Two sample networks have been optimized using the proposed model. Obtained results show that the model presented in this article has a very low search time, which makes its implementation possible for large real-life WDNs.     

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.     

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.     

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。     

A sequential exploration algorithm for the design optimization of horizontal road alignment

Most computer-aided optimization procedures for horizontal alignment optimization of roads require the use of information such as horizontal points of intersection (PIs) to determine an alignment. In these methods, to obtain parameters such as the radius of the curve corresponding to a specific PI, the previous and next PIs must be known. In this paper, a sequential exploration algorithm (SEA) is proposed, and the algorithm continuously explores the entire optimization space through certain steps. Only the parameters of the previous node are required to determine the current node's parameters during the exploration process, avoiding the tight coupling between PIs in traditional optimization algorithms. Furthermore, the proposed SEA does not require assumptions about the positions and numbers of the PIs, and it can design near-optimal road alignments that match geometric restrictions and automatically take transition curves into account. Another feature of the proposed algorithm is that it directly optimizes the geometric element parameters based on the actual milepost, and it is a fully collaborative optimization approach that does not require secondary optimization nesting during the optimization process. Analyses comparing the optimization effects of different algorithms are performed on a numerical case, that is, a problem of avoiding obstacles, and two actual cases from the literature, that is, a new road design problem and an existing road reconstruction problem. It is discovered that the proposed SEA results in an approximately 3% to 10% improvement in optimization effects when compared to two current cutting-edge optimization algorithms. This work offers a new perspective on road alignment optimization by merging discrete and continuous optimizations, with a discrete component handling optimization accuracy and a continuous component handling real optimization.     

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.     

基于v-SVR和MVPSO算法的边坡位移反分析方法及其应用

 针对传统粒子群算法存在搜索空间有限、容易陷入局部最优点的缺陷,通过引入迁徙算子和自适应变异算子,提出基于粒子迁徙和变异的粒子群优化(MVPSO)算法。基准测试函数结果表明,改进的MVPSO算法较传统的粒子群优化算法在收敛效率上有大幅度提高,在处理非线性、多峰值的复杂优化问题中能快速地搜索,得到全局最优解。应用改进的MVPSO算法搜索最佳的支持向量机(v-SVR)模型参数,建立岩体力学参数与岩体位移之间的非线性支持向量机模型,提高v-SVR的预测精度和推广泛化性。然后,利用v-SVR模型的外推预测替代耗时的FLAC正向计算,利用改进的MVPSO算法搜索岩体力学参数的最优组合,提出v-SVR和MVPSO相结合的边坡位移反分析方法(v-SVR-MVPSO算法),与传统的BP-GA算法和v-SVR-GA算法相比,该算法在反演精度和反演效率上均有较大幅度提高。最后,将本文发展的v-SVR-MVPSO算法应用到大岗山水电站右岸边坡岩体参数反演分析,并对边坡后续开挖位移和稳定性进行预测,取得较好的效果。     

Optimal design of double-layer barrel vaults using genetic and pattern search algorithms and optimized neural network as surrogate model

This paper presents a combined method based on optimized neural networks and optimization algorithms to solve structural optimization problems. The main idea is to utilize an optimized artificial neural network (OANN) as a surrogate model to reduce the number of computations for structural analysis. First, the OANN is trained appropriately. Subsequently, the main optimization problem is solved using the OANN and a population-based algorithm. The algorithms considered in this step are the arithmetic optimization algorithm (AOA) and genetic algorithm (GA). Finally, the abovementioned problem is solved using the optimal point obtained from the previous step and the pattern search (PS) algorithm. To evaluate the performance of the proposed method, two numerical examples are considered. In the first example, the performance of two algorithms, OANN + AOA + PS and OANN + GA + PS, is investigated. Using the GA reduces the elapsed time by approximately 50% compared with using the AOA. Results show that both the OANN + GA + PS and OANN + AOA + PS algorithms perform well in solving structural optimization problems and achieve the same optimal design. However, the OANN + GA + PS algorithm requires significantly fewer function evaluations to achieve the same accuracy as the OANN + AOA + PS algorithm.     

地下水渗流模型参数识别的模拟退火算法

反问题的求解常常需要转化为非线性优化问题，其目标函数定义为观测数据与模型数据之间的残差平方和。地下水模型参数识别最常用的优化方法都是基于梯度搜索，其缺陷在于对模型参数初始估计比较敏感和局部极小问题。与传统的基于梯度搜索的优化方法相比，模拟退火算法具有良好的全局收敛特性。把含水层参数识别反问题转化为组合优化问题，提出模拟退火算法识别二维、非稳态地下水流动模型的渗透系数和储水系数的策略。反问题的不适定性由解的不唯一性和不稳定性来表征，模拟退火算法具有解决这一问题的能力。通过与梯度搜索算法相对比，数值模拟计算结果显示所提出反演方法的有效性和适用性。     

Optimization of Mediterranean building design using genetic algorithms

While it is possible to check the energy performance of a given building by means of several available methods, the inverse problem of determining the optimum configuration given a desired performance is more difficult to solve. In the Mediterranean region this problem is more complex due to the following two reasons: the air-conditioning load is as important as the heating load, and the energy needs depend on a high number of architectural parameters which have different, even contradictory, effects on summer and winter loads. In this paper we present an optimization algorithm that couples pseudo-random optimization techniques, the genetic algorithms (GA), with a simplified tool for building thermal evaluation (CHEOPS) for the purpose of minimizing the energy consumption of Mediterranean buildings. Since increasing the energy performance usually requires the use of special devices resulting in a high construction cost, we also propose to use GA for the purpose of economical optimization.     

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.     

基于数值逆吊法的树状结构智能设计算法

由于美观的造型以及高效的结构效率,树状结构越来越多地应用于大型建筑以及地标性建筑中.树状结构研究的关键除找形问题外,更为关键的问题是最优拓扑的确定,即寻找能够高效承受外部荷载的各分枝之间的连接关系.在前期基于数值逆吊法研究成果的基础上,提出了树状结构的拓扑优化数值算法,该算法根据构件的效能选取移除分枝,最终达到每一级的...     

Optimization of energy consumption in buildings with hydronic heating systems considering thermal comfort by use of computer-based tools

The paper deals with an optimization of parameters, which influence the energy and investment cost as well as the thermal comfort. The parameters considered in this study are: the insulation thickness of the building envelope, the supply-water temperature and the heat exchange area of the radiators. A combination of the building energy simulation software EnergyPlus ¹ and the generic optimization program GenOpt (see footnote 1) has been used for this purpose. The paper presents the application of a one-objective optimization algorithm solving the problems with two objectives, because the optimization algorithm is one-objective and the problem has two objectives, which are minimal total costs and satisfied thermal comfort. The total costs represent the sum of energy consumption and the investment costs. The thermal comfort is represented by Predicted Percentage of Dissatisfied (PPD) in this study. The optimization is used to determine the values of parameters that give the lowest sum of investment and energy cost, under the condition that the thermal comfort is satisfied. In addition, the optimization processes show the mutual influence of parameters on both the total cost and the thermal comfort.     

Calibration of the descent local search algorithm parameters using orthogonal arrays

Solving optimization problems using heuristic algorithms requires the selection of its parameters. Traditionally, these parameters are selected by a trial and error process that cannot guarantee the quality of the results obtained because not all the potential combinations of parameters are checked. To fill this gap, this paper proposes the application of Taguchi's orthogonal arrays to calibrate the parameters of a heuristic optimization algorithm (the descent local search algorithm). This process is based on the study of the combinations of discrete values of the heuristic tool parameters and it enables optimization of the heuristic tool performance with a reduced computational effort. To check its efficiency, this methodology is applied to a technical challenge never studied before: the optimization of the tensioning process of cable‐stayed bridges. The statistical improvement of the heuristic tool performance is studied by the optimization of the tensioning process of a real cable‐stayed bridge. Results show that the proposed calibration technique provided robust values of the objective function (with lower minimum and mean values, and lower standard deviation) with reduced computational cost.     

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.     

基于双生长点并行生长机制的模拟植物生长算法及其结构优化

针对模拟植物生长算法(PGSA)系列算法中存在的搜索路径相对单一、搜索覆盖面不够广等问题,结合复杂结构优化问题中设计变量多、存在多个局部最优解、算法难以自动终止等特点,基于PGSA的基本原理和植物的实际生长规律,提出一种新的算法机制——双生长点并行生长机制,并与基于生长空间限定与并行搜索(GSL&PS-PGSA)算法相融合。通过典型数学及空间桁架结构算例进行了验证,结果表明：双生长点并行生长机制增加了寻优搜索路径,拓宽了搜索覆盖面,降低了陷入局部最优解的概率,并为算法提供更为有效的终止机制,从而具有更加显著的优化效率及全局搜索能力;与序列两级算法、蚁群算法等常用优化方法相比,融入双生长点并行生长机制的GSL&PS-PGSA进一步提升了算法的优化求解能力,在结构优化问题中表现出良好的适应性及有效性。     

Plant growth simulation algorithm based on double growth point parallel growth mechanism and its structural optimization

针对模拟植物生长算法(PGSA)系列算法中存在的搜索路径相对单一、搜索覆盖面不够广等问题，结合复杂结构优化问题中设计变量多、存在多个局部最优解、算法难以自动终止等特点，基于PGSA的基本原理和植物的实际生长规律，提出一种新的算法机制——双生长点并行生长机制，并与基于生长空间限定与并行搜索(GSL&PS-PGSA)算法相融合。通过典型数学及空间桁架结构算例进行了验证，结果表明：双生长点并行生长机制增加了寻优搜索路径，拓宽了搜索覆盖面，降低了陷入局部最优解的概率，并为算法提供更为有效的终止机制，从而具有更加显著的优化效率及全局搜索能力；与序列两级算法、蚁群算法等常用优化方法相比，融入双生长点并行生长机制的GSL&PS-PGSA进一步提升了算法的优化求解能力，在结构优化问题中表现出良好的适应性及有效性。     

Back analysis of geomechanical parameters in underground works using an Evolution Strategy algorithm

The purpose of this work is to evaluate the performance of an optimization algorithm from the field of evolutionary computation, namely an Evolution Strategy, in back analysis of geomechanical parameters in underground structures. This analysis was carried out through a parametric study of a synthetic case of a tunnel construction. Different combinations of parameters and measurements were carried out to test the performance of the algorithm. In order to have a comparison base for its performance also three classical optimization algorithms based on the gradient of the error function and a Genetic Algorithm were used. It was concluded that the Evolution Strategy algorithm presents interesting capabilities in terms of robustness and efficiency allowing the mitigation of some of the limitations of the classical algorithms.Moreover a back analysis study of geomechanical parameters using real monitoring data and a 3D numerical model of a hydraulic underground structure being built in the North of Portugal was performed using the Evolution Strategy algorithm, in order to reduce the uncertainties about the parameters evaluated by in situ and laboratory tests. It was verified that the low quantity of monitoring data available hinders the possibility to identify the parameters of interest. The existence of information of only one additional extensometer perpendicular to the existing one would allow this identification to succeed.     

Improving prediction of soil liquefaction using hybrid optimization algorithms and a fuzzy support vector machine

The phenomenon of soil liquefaction is one of the most complex and interesting fields in geotechnical earthquakes that has drawn the attention of many researchers in recent years. The present study used hybrid particle swarm optimization and genetic algorithms with a fuzzy support vector machine (FSVM) as the classifier for the soil liquefaction prediction problem. Fuzzy logic is used to decrease the outlier sensitivity of the system by inferring the importance of each sample in the training phase to increase the ability of the classifier’s generalization. Using the appropriate combination of optimization algorithms, we can find the best parameters for the classifier during the training phase without the need for trial and error by the user due to the high accuracy of the classifier. The proposed approach was tested on 109 CPT-based field data from five major earthquakes between 1964 and 1983 recorded in Japan, China, the USA and Romania. Good results have been demonstrated for the proposed algorithm. Classification accuracy is 100% for the combination of the optimization algorithms with the FSVM classifier. The results show that the best kernel used in the training of the FSVM classifier is a radial basis function (RBF). According to the experimental results, the proposed algorithm can improve classification accuracy and that it is a feasible method for predicting soil liquefaction using the optimal parameters of the classifier with no user interface.