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Hyper-heuristic algorithm for traffic flow-based VRP with simultaneous delivery and pickup 基于交通流的VRP同时送取的超启发式算法
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-28 DOI: 10.1093/jcde/qwad097
Wang Zheng, Liu Jinlong, Zhang Jingling
Abstract To address the realistic problem of seriously reducing distribution efficiency and increasing distribution cost caused by road traffic congestion, this paper constructs a time-dependent speed describing vehicle travel speed and road traffic flow by simulating the change of urban traffic flow, to establish a vehicle route problem model considering traffic flow with distribution cost and customer satisfaction as optimization objectives. To solve this problem, a hyper-heuristic algorithm based on Tabu search is designed in this paper, in which the underlying search operator is selected more efficiently by a high-level heuristic strategy. In addition, the correctness of the model and the effectiveness of the algorithm are verified by conducting simulation experiments on several benchmark sets. Experiment results are shown as the travel speed of the vehicle increases, the average customer satisfaction in lc1-type instances increases to 0.94. And the impact of urban traffic changes on logistics costs and customer satisfaction is further analyzed.
摘要针对道路交通拥堵导致配送效率严重降低、配送成本增加的现实问题,通过模拟城市交通流的变化,构建了描述车辆行驶速度和道路交通流的时变速度,建立了以配送成本和顾客满意度为优化目标的交通流车辆路线问题模型。为了解决这一问题,本文设计了一种基于禁忌搜索的超启发式算法,该算法通过高级启发式策略更有效地选择底层搜索算子。此外,在多个基准集上进行仿真实验,验证了模型的正确性和算法的有效性。实验结果表明,随着车速的增加,c1型实例的平均顾客满意度增加到0.94。并进一步分析了城市交通变化对物流成本和顾客满意度的影响。
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引用次数: 0
Improved Snow Ablation Optimizer with Heat Transfer and Condensation Strategy for Global Optimization Problem 面向全局优化问题的基于传热冷凝策略的改进雪消融优化器
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-26 DOI: 10.1093/jcde/qwad096
Heming Jia, Fangkai You, Di Wu, Honghua Rao, Hangqu Wu, Laith Abualigah
Abstract The Snow Ablation Optimizer (SAO) is a new metaheuristic algorithm proposed in April 2023. It simulates the phenomenon of snow sublimation and melting in nature and has a good optimization effect. The SAO proposes a new two-population mechanism. By introducing Brownian motion to simulate the random motion of gas molecules in space. However, as the temperature factor changes, most water molecules are converted into water vapor. Which breaks the balance between exploration and exploitation, and reduces the optimization ability of the algorithm in the later stage. Especially in the face of high-dimensional problems, it is easy to fall into local optimal. In order to improve the efficiency of the algorithm, this paper proposes an improved Snow Ablation Optimizer with Heat Transfer and Condensation Strategy(SAOHTC). Firstly, this article proposes a heat transfer strategy. Utilizes gas molecules to transfer heat from high to low temperatures and move their positions from low to high temperatures. Causing individuals with lower fitness in the population to move towards individuals with higher fitness, thereby improving the optimization efficiency of the original algorithm. Secondly, a condensation strategy is proposed. Which can transform water vapor into water by simulating condensation in nature, improve the deficiency of the original two-population mechanism. improve the convergence speed. Finally, to verify the performance of SAOHTC. In this paper, two benchmark experiments of IEEE CEC2014 and IEEE CEC2017 and five engineering problems are used to test the superior performance of SAOHTC.
雪消融优化器(SAO)是2023年4月提出的一种新的元启发式算法。模拟了自然界中雪的升华和融化现象,具有良好的优化效果。《准则》提出了新的双人口机制。通过引入布朗运动来模拟气体分子在空间中的随机运动。然而,随着温度因素的变化,大部分水分子转化为水蒸气。这就打破了探索与开发的平衡,降低了算法后期的优化能力。特别是面对高维问题时,很容易陷入局部最优。为了提高算法的效率,本文提出了一种基于传热冷凝策略的雪消融优化器(SAOHTC)。首先,本文提出了一种传热策略。利用气体分子将热量从高温传递到低温,并将其位置从低温移动到高温。使种群中适应度较低的个体向适应度较高的个体移动,从而提高原算法的优化效率。其次,提出了一种冷凝策略。它可以通过模拟自然界中的冷凝将水蒸气转化为水,改善了原有双种群机制的不足。提高收敛速度。最后,验证了SAOHTC的性能。本文通过IEEE CEC2014和IEEE CEC2017两个基准实验,以及五个工程问题,验证了SAOHTC的优越性能。
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引用次数: 0
Improve Coati Optimization Algorithm for Solving Constrained Engineering Optimization Problems 求解约束工程优化问题的改进Coati算法
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-26 DOI: 10.1093/jcde/qwad095
Heming Jia, Shengzhao Shi, Di Wu, Honghua Rao, Jinrui Zhang, Laith Abualigah
Abstract The coati optimization algorithm (COA) is a meta-heuristic optimization algorithm proposed in 2022. It creates mathematical models according to the habits and social behaviors of coatis: (1) In the group organization of the coatis, half of the coatis climb trees to chase their prey away, while the other half waits beneath to catch it; (2) Coatis avoidance predators behavior. Which gives the algorithm strong global exploration ability. However, over the course of our experiment, we uncovered opportunities for enhancing the algorithm's performance. When confronted with intricate optimization problems, certain limitations surfaced. Much like a long-nosed raccoon gradually narrowing its search range as it approaches the optimal solution, COA algorithm exhibited tendencies that could result in reduced convergence speed and the risk of becoming trapped in local optima. In this paper, we propose an improved coatis optimization algorithm (ICOA) to enhance the algorithm's efficiency. Through a sound-based search envelopment strategy, coatis can capture prey more quickly and accurately, allowing the algorithm to converge more rapidly. By employing a physical exertion strategy, coatis can have a greater variety of escape options when being chased, thereby enhancing the algorithm's exploratory capabilities and the ability to escape local optima. Finally, the lens opposition-based learning strategy is added to improve the algorithm's global performance. To validate the performance of the ICOA, we conducted tests using the IEEE CEC2014 and IEEE CEC2017 benchmark functions, as well as six engineering problems.
coati优化算法(COA)是2022年提出的一种元启发式优化算法。它根据浣熊的习性和社会行为建立数学模型:(1)在浣熊的群体组织中,一半的浣熊爬上树去追赶猎物,另一半在树下等待猎物;(2)浣熊躲避捕食者行为。这使得算法具有较强的全局搜索能力。然而,在我们的实验过程中,我们发现了增强算法性能的机会。当面对复杂的优化问题时,一定的局限性浮出水面。就像长鼻浣熊在接近最优解时逐渐缩小搜索范围一样,COA算法可能会导致收敛速度降低,并有陷入局部最优的风险。为了提高算法的效率,本文提出了一种改进的coatis优化算法(ICOA)。通过基于声音的搜索包络策略,浣熊可以更快更准确地捕获猎物,从而使算法更快地收敛。通过使用体力消耗策略,浣熊在被追逐时可以有更多的逃脱选择,从而增强算法的探索能力和逃离局部最优的能力。最后,加入基于镜头对立的学习策略,提高算法的全局性能。为了验证ICOA的性能,我们使用IEEE CEC2014和IEEE CEC2017基准函数以及六个工程问题进行了测试。
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引用次数: 0
Utilizing Bee Foraging Behavior in Mutational Salp Swarm for Feature Selection: A Study on Return Intentions of Overseas Chinese after COVID-19 利用突变Salp群体的蜜蜂觅食行为进行特征选择——COVID-19后海外华人回归意愿研究
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-19 DOI: 10.1093/jcde/qwad092
Jie Xing, Qinqin Zhao, Huiling Cheny, Yili Zhang, Feng Zhou, Hanli Zhao
Abstract We present a Bee Foraging Behavior Driven Mutational Salp Swarm Algorithm (BMSSA) based on an improved bee foraging strategy and an unscented mutation strategy. The improved bee foraging strategy is leveraged in the follower location update phase to break the fixed range search of SSA, while the unscented mutation strategy on the optimal solution is employed to enhance the quality of the optimal solution. Extensive experimental results on public CEC 2014 benchmark functions validate that the proposed BMSSA performs better than nine well-known metaheuristic methods and seven state-of-the-art algorithms. The Binary BMSSA algorithm is further proposed for feature selection by using BMSSA as the selection strategy and support vector machine as the classifier. Experimental comparisons on twelve UCI datasets demonstrate the superiority of binary BMSSA. Finally, we collected a dataset on the return-intentions of overseas Chinese after COVID-19 through an anonymous online questionnaire and performed a case study by setting up a binary BMSSA-based feature selection optimization model. . The case study shows that the development prospects, the family and job in the place of residence, seeking opportunities in China, and the possible time to return to China are critical factors influencing the willingness to return to China after COVID-19.
摘要提出了一种基于改进蜜蜂觅食策略和无气味突变策略的蜜蜂觅食行为驱动突变Salp群算法(BMSSA)。在跟踪者位置更新阶段利用改进的蜜蜂觅食策略打破了SSA的固定范围搜索,而在最优解上采用无气味突变策略提高了最优解的质量。在公共CEC 2014基准函数上的大量实验结果验证了所提出的BMSSA优于9种知名的元启发式方法和7种最先进的算法。采用BMSSA作为特征选择策略,支持向量机作为分类器,进一步提出了二元BMSSA算法进行特征选择。在12个UCI数据集上的实验比较表明了二元BMSSA的优越性。最后,我们通过匿名在线问卷收集了海外华人在新冠肺炎疫情后的回归意愿数据集,并通过建立基于二元bmssa的特征选择优化模型进行了案例研究。案例研究表明,发展前景、居住地的家庭和工作、在中国寻找机会以及可能回国的时间是影响新冠肺炎后回国意愿的关键因素。
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引用次数: 0
Sand Cat Arithmetic Optimization Algorithm for Global Optimization Engineering Design Problems 全局优化工程设计问题的沙猫算法优化
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-17 DOI: 10.1093/jcde/qwad094
Shuilin Chen, Jianguo Zheng
Abstract Sand cat swarm optimization (SCSO) is a recently introduced popular swarm intelligence metaheuristic algorithm, which has two significant limitations – low convergence accuracy and the tendency to get stuck in local optima. To alleviate these issues, this paper proposes an improved SCSO based on the arithmetic optimization algorithm (AOA), the refracted opposition-based learning and crisscross strategy, called the sand cat arithmetic optimization algorithm (SC-AOA), which introduced AOA to balance the exploration and exploitation and reduce the possibility of falling into the local optimum, used crisscross strategy to enhance convergence accuracy. The effectiveness of SC-AOA is benchmarked on 10 benchmark functions, CEC 2014, CEC 2017, CEC 2022, and eight engineering problems. The results show that the SC-AOA has a competitive performance.
摘要沙猫群优化算法(SCSO)是近年来兴起的一种流行的群智能元启发式算法,存在收敛精度低和容易陷入局部最优的两大局限性。为了解决这些问题,本文提出了一种基于算法优化算法(AOA)、基于折射对立学习和交叉策略的改进SCSO算法,称为沙猫算法优化算法(SC-AOA),该算法引入AOA来平衡探索和开发,减少陷入局部最优的可能性,使用交叉策略来提高收敛精度。通过10个基准功能、CEC 2014、CEC 2017、CEC 2022和8个工程问题对SC-AOA的有效性进行了基准测试。结果表明,SC-AOA具有较好的性能。
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引用次数: 0
Multi-threshold remote sensing image segmentation with improved ant colony optimizer with salp foraging 基于蚁群优化的多阈值遥感图像分割
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-16 DOI: 10.1093/jcde/qwad093
Yunlou Qian, Jiaqing Tu, Gang Luo, Ce Sha, Ali Asghar Heidari, Huiling Chen
Abstract Remote sensing images can provide direct and accurate feedback on urban surface morphology and geographic conditions. They can be used as an auxiliary means to collect data for current geospatial information systems, which are also widely used in city public safety. Therefore, it is necessary to research remote-sensing images. Therefore, we adopt the multi-threshold image segmentation method in this paper to segment the remote-sensing images for research. We first introduce salp foraging behavior into the continuous ant colony optimization algorithm (ACOR) and construct a novel ACOR version based on salp foraging (SSACO). The original algorithm's convergence and ability to avoid hitting local optima are enhanced by salp foraging behavior. In order to illustrate this key benefit, SSACO is first put up against 14 fundamental algorithms using 30 benchmark test functions in IEEE CEC2017. Then, SSACO is compared against 14 other algorithms. The experimental results are examined from various angles, and the findings convincingly demonstrate the main selling point of SSACO. We performed segmentation comparison studies based on 12 remote sensing images between SSACO segmentation techniques and several peer segmentation approaches to demonstrate the benefits of SSACO in remote sensing image segmentation. Peak signal-to-noise ratio, structural similarity index, and feature similarity index evaluation of the segmentation results demonstrated the benefits of the SSACO-based segmentation approach. SSACO is an excellent optimizer since it seeks to serve as a guide and a point of reference for using remote sensing image algorithms in urban public safety.
遥感影像可以为城市地表形态和地理状况提供直接、准确的反馈。它们可以作为当前地理空间信息系统收集数据的辅助手段,在城市公共安全中也得到了广泛的应用。因此,有必要对遥感图像进行研究。因此,本文采用多阈值图像分割方法对遥感图像进行分割进行研究。本文首先将salp觅食行为引入到连续蚁群优化算法(ACOR)中,构建了一个基于salp觅食的连续蚁群优化算法(SSACO)。采用海藻觅食行为增强了原算法的收敛性和避免局部最优的能力。为了说明这一关键优势,SSACO首先使用IEEE CEC2017中的30个基准测试函数与14种基本算法进行了比较。然后,将SSACO算法与其他14种算法进行比较。从多个角度对实验结果进行了检验,结果令人信服地证明了SSACO的主要卖点。通过对12幅遥感影像进行SSACO分割技术与几种同类分割方法的分割对比研究,验证了SSACO在遥感影像分割中的优势。峰值信噪比、结构相似度指数和特征相似度指数对分割结果的评价表明了基于ssac的分割方法的优越性。SSACO是一个优秀的优化者,因为它寻求成为在城市公共安全中使用遥感图像算法的指南和参考点。
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引用次数: 0
Effects of BIM prior knowledge on applying VR in construction education: Lessons from a comparison study BIM先验知识对VR在建筑教育中的应用的影响:一项比较研究的启示
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-12 DOI: 10.1093/jcde/qwad091
Xingbin Chen, Sining Li, Gengying Li, Bin Xue, Bingsheng Liu, Yuan Fang, Seo JoonOh, Inhan Kim, Jung In Kim
Abstract Applying BIM and VR in construction education is an effective way to achieve better study motivation, learnability, creativity, and observation of the real world. However, whether different levels of BIM prior knowledge affect students’ VR experimental learning, if at all, has not been examined. Therefore, this study employs a teaching intervention experiment to access the VR learning process based on the BIM prior knowledge. A total of 47 students, from the Department of Architecture and Civil Engineering, City University of Hong Kong, participated in the experiment. They were grouped according to whether they had taken the prior BIM tutorial section, with twenty-three participants in the group having completed the tutorial and twenty-four participants in the group that had not. Experiment materials were created and rendered via Autodesk Revit and Iris VR; the materials supported three tasks related to the underground design review scenarios and three other tasks about site planning review scenarios. After the experiment, a comparison study was done to discuss their differences based on VR task performances and satisfaction. The results revealed that the BIM prior knowledge mediated both the two-dimension and three-dimension navigations when students performed the tasks. Moreover, the relationship differences within the satisfactions showed that BIM prior knowledge effectively affected the learning outcomes. In conclusion, the comparison study implies that students’ BIM prior knowledge is efficacious in the students’ VR task performance and their VR satisfaction from cognitive and memory perspectives.
在建筑教学中应用BIM和VR是提高学生学习积极性、可学习性、创造性和对现实世界观察能力的有效途径。然而,不同水平的BIM先验知识是否会影响学生的VR实验学习,如果有的话,还没有研究。因此,本研究采用教学干预实验的方式来获取基于BIM先验知识的VR学习过程。来自香港城市大学建筑及土木工程系的47名学生参加了这项实验。他们根据是否参加了之前的BIM教程部分进行分组,其中23名参与者完成了教程,24名参与者没有完成教程。通过Autodesk Revit和Iris VR创建和渲染实验材料;这些材料支持与地下设计评审方案相关的三个任务和与场地规划评审方案相关的另外三个任务。实验结束后,进行了对比研究,讨论了他们在VR任务表现和满意度方面的差异。结果表明,BIM先验知识在学生执行任务时对二维和三维导航都有中介作用。此外,满意度内部的关系差异表明BIM先验知识有效地影响了学习结果。综上所述,对比研究表明,从认知和记忆的角度来看,学生的BIM先验知识对学生的VR任务表现和VR满意度是有效的。
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引用次数: 0
Inherent Irreversibility in Unsteady MHD Nanofluid Flow Past a Slippery Permeable Vertical Plate with Fractional Order Derivative 非定常MHD纳米流体流过具有分数阶导数的光滑可渗透垂直板的固有不可逆性
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-10 DOI: 10.1093/jcde/qwad090
Zafar Hayat Khan, O D Makinde, M Usman, R Ahmad, W A Khan, Zaitang Huang
Abstract This study focuses on fractional order derivatives for the unsteady flow of MHD methanol-iron oxide nanofluid over a permeable vertical plate. The study incorporates fractional order derivatives to exhibit the system mathematically. The concluding model, which consists of the system of PDEs, has been solved via the Finite Difference Method, and graphical illustrations demonstrate the effects of key parameters on the flow field. Velocity and temperature profiles provide insights into nanofluid behavior. Additionally, essential quantities such as skin friction coefficient, Nusselt number, Bejan number, and entropy generation rate have been depicted graphically. Comparison with previous studies authenticates the accuracy of the anticipated model, contributing to new intuitions into MHD nanofluid flow over a permeable vertical plate. It is worth noting that the current model, incorporating fractional order derivatives, contributes to understanding the physical characteristics of MHD CH3OH-Fe3O4 nanofluid flow over a permeable vertical plate, research that has not been extensively explored before.
摘要本文研究了MHD甲醇-氧化铁纳米流体在可渗透垂直板上的非定常流动的分数阶导数。该研究采用分数阶导数来数学地展示系统。用有限差分法对由偏微分方程系统组成的结论模型进行了求解,并用图形说明了关键参数对流场的影响。速度和温度剖面提供了对纳米流体行为的深入了解。此外,基本的数量,如皮肤摩擦系数,努塞尔数,贝尚数,和熵生成率已被描绘成图形。与先前研究的对比验证了预期模型的准确性,有助于对MHD纳米流体在可渗透垂直板上的流动有新的直观认识。值得注意的是,目前的模型纳入了分数阶导数,有助于理解MHD CH3OH-Fe3O4纳米流体在可渗透垂直板上流动的物理特征,这一研究此前尚未得到广泛探索。
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引用次数: 1
Modified Beluga Whale Optimization with Multi-strategies for Solving Engineering Problems 基于多策略的改进白鲸优化工程问题求解
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-05 DOI: 10.1093/jcde/qwad089
Heming Jia, Qixian Wen, Di Wu, Zhuo Wang, Yuhao Wang, Changsheng Wen, Laith Abualigah
Abstract The Beluga Whale Optimization(BWO) Algorithm is a recently proposed metaheuristic optimization algorithm that simulates three behaviors: beluga whales interacting in pairs to perform mirror swimming, population sharing information to cooperate in predation and whale fall. However, the optimization performance of the BWO algorithm still needs to be improved to enhance its practicality. This paper proposes a modified beluga whale optimization(MBWO) with a multi-strategy. It was inspired by beluga whales' two behaviors: group gathering for foraging and searching for new habitats in long-distance migration. This paper proposes a group gathering strategy (GAs) and a migration strategies (Ms). The group aggregation strategy can improve the local development ability of the algorithm and accelerate the overall Rate of convergence through the group aggregation fine search; The migration strategy randomly moves towards the periphery of the population, enhancing the ability to jump out of local optima. In order to verify the optimization ability of MBWO, this article conducted comprehensive testing on MBWO using 23 benchmark functions, IEEE CEC2014, and IEEE CEC2021. The experimental results indicate that MBWO has a strong optimization ability. This paper also tests MBWO's ability to solve practical engineering optimization problems through five practical engineering problems. The final results prove the effectiveness of MBWO in solving practical engineering optimization problems.
摘要白鲸优化算法(Beluga Whale Optimization Algorithm, BWO)是最近提出的一种元启发式优化算法,它模拟了三种行为:白鲸成对互动进行镜像游泳、种群共享信息合作捕食和鲸鱼摔倒。但是,BWO算法的优化性能还有待提高,以增强其实用性。提出了一种改进的多策略白鲸优化算法。它的灵感来自于白鲸的两种行为:集体觅食和长途迁徙中寻找新栖息地。提出了一种群体聚集策略(GAs)和迁移策略(Ms)。群聚集策略通过群聚集精细搜索提高了算法的局部发展能力,加快了整体收敛速度;迁移策略随机向种群外围移动,增强了跳出局部最优的能力。为了验证MBWO的优化能力,本文使用23个基准函数,IEEE CEC2014和IEEE CEC2021对MBWO进行了全面的测试。实验结果表明,MBWO具有较强的优化能力。本文还通过五个实际工程问题来检验MBWO解决实际工程优化问题的能力。最后的结果证明了MBWO在解决实际工程优化问题中的有效性。
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引用次数: 0
Erken Tasarım Aşamasında Mimarlık Öğrencilerinin Fiziksel ve Bilgisayar Destekli Modelleme Kullanım Tercihleri 建筑系学生在早期设计阶段使用实物模型和计算机辅助模型的偏好
2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-30 DOI: 10.53710/jcode.1307294
Buket SAMANCI, Özge TAŞPINAR, Yaşar Emir KARCI, Başak CENGİZ, Selen OZDOGAN, Dilek YILDIZ, Michael Stefan BİTTERMANN
Preferences for using physical mock-up modeling or computer-aided design (CAD) among architecture students in the early design phase are analyzed. The data is obtained from a questionnaire, consisting of eight multiple-choice questions and one open-ended question. The respondents are architecture students; the majority of them are still in their undergraduate studies. As quantitative analysis methods hypothesis tests based on the probability distributions known as the z-distribution, and the Chi-squared distribution were carried out. Generally, it was investigated which modeling technique is more efficient in the early design phase. Moreover, according to the age groups of respondents, the difference in the preference among mock-up and CAD is identified. Explicitly, younger students prefer CAD, while other ones prefer mock-up representation. The reasons for the difference are analyzed. Since the choice for mock-up modeling or CAD modeling can have a strong impact on the design processes of both, students and professionals, the result of the study is relevant, because it gives a hint about probable future architecture practice.
分析了建筑学生在早期设计阶段使用实体模型建模或计算机辅助设计(CAD)的偏好。数据来自一份问卷,包括八个选择题和一个开放式问题。受访者是建筑系学生;他们中的大多数人仍在本科学习。作为定量分析方法,假设检验是基于概率分布即z分布和卡方分布进行的。一般来说,在设计的早期阶段,研究哪种建模技术更有效。此外,根据受访者的年龄组别,我们发现他们对实体模型和CAD的偏好有何不同。显然,年龄较小的学生更喜欢CAD,而其他学生更喜欢实物模型。分析了造成这种差异的原因。由于模型建模或CAD建模的选择可以对学生和专业人员的设计过程产生强烈的影响,因此研究结果是相关的,因为它给出了可能的未来建筑实践的提示。
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引用次数: 0
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