Structural Optimization In Civil Engineering: ALiterature Review

Buildings 2021, 11, 663 of 27tazavi [19] proposed an auxiliary fuzzy decision mechanism to improve the performance ofinteractive search algorithm (ISA) for structural size and topology optimization. The combined algorithm, namely the fuzzy tuned interactive search algorithm (FTISA), achievesa lower computational cost and a higher solution accuracy. Degertekin [20] proposedtwo improved harmony search algorithms (i.e., efficient harmony search algorithm andself-adaptive harmony search algorithm) for size optimization of truss structures. Based onthe experimental results from several cases, the new algorithms are proved to have lowercomputational cost, higher convergence speed, and better optimization results than thetraditional harmony search algorithm. Furthermore, Zheng et al. [21] presented an explicittopology optimization method, namely transformable triangular mesh (TTM) method,for structural topology optimization, which is able to obtain the optimal solution moreeffectively compared with other state-of-the-art algorithms.These abovementioned studies in the field of structural optimization presented theachievements and potential of structural optimization to improve the efficiency and sustainability of the civil engineering industry. However, although a substantial number ofstudies as well as survey reports were published in this domain, none of them achieved acomprehensive review of the research developments on structural optimization. Therefore,this paper aims to comprehensively review the state-of-the-art literature on structuraloptimization in the field of civil engineering, including the analysis of the optimizationobjectives and their temporal and spatial trends, analysis of the optimization processeswith four major steps, and the discussions of research limitations and recommendations offuture works.The rest of this paper is organized as follows. Section 2 demonstrates the methodologyused for literature retrieval and Section 3 presents a statistical analysis of the selectedarticles. Then, the optimization objectives of the selected articles are categorized andanalyzed regarding the temporal and spatial trends in Section 4. Next, Section 5 providesan exhaustive review and analysis of the structural optimization process in four aspects, including structural analysis and modelling, optimization problem formulation, optimizationmethods, and computational tools and design platforms. Section 6 indicates the limitationsof the current research and based on which elaborates the potential future works. Finally,conclusions are drawn to conclude and summarize this study in Section 7.2. MethodologyA holistic approach was adopted in this paper to critically analyze the state-of-the-artliterature and present a comprehensive review on structural optimization in the field of civilengineering. Figure 1 elaborately depicts the overall methodology of this study, includingliterature retrieval and selection from a digital database, statistical analysis of the selectedliterature, review of optimization objectives with temporal and spatial trends, review ofoptimization process, limitations and future work recommendation, and conclusion. Thedetails of literature retrieval are presented in Section 2.1, and a brief introduction of thekeywords utilized for literature retrieval is presented in Section 2.2.2.1. Literature RetrievalThe database used for literature retrieval in this study is Google Scholar, whichcontains most of the academic literature published. Several search keywords including structural optimization, size, shape, topology, layout, optimal design, civil engineering structures, and metaheuristic algorithms, were adopted to facilitate the literatureretrieval. Then, the most relevant literature was manually selected from the search results.Through the above literature retrieval method, a total of 196 papers were selected, including154 research articles, 19 conference abstracts, 12 book chapters, 7 review articles, and 4 theses. Although structural optimization has a history of more than one hundred years, it isfirst applied in aerospace industry and the application in civil engineering industry is muchlater [22]. Moreover, with the advent of information technology, the optimization methodsused in recent studies have changed a lot compared with early studies. Therefore, the range

Buildings 2021, 11, 664 of 27Buildings 2021, 11, x FOR PEER REVIEWof publication4 of29year of the selected papers is set from 1970 to 2020 in order to analyzeandsummarize the latest achievements of research on civil engineering structural optimization.Figure 1.FigureThe researchmethodologyof this study.1. The researchmethodologyof this study.2.1.2.2. LiteratureKeywords Retrievalfor Literature RetrievalThedatabaseliteratureretrievalin thisforstudyis GoogleScholar,whichAs mentioned usedabove,foreightkeywordsare ordsincludingDuring the process of choosing suitable keywords, “civil engineering structural ogy,layout,optimaldesign,civiltion” is firstlysearched size,in ted dtofacilitatetheliteratureretrieval.find the state-of-the-art techniques in this field and based on which some other keywordsThen,themost relevantliteraturemanually selectedfromsearch results.Throughsuch sarethesummarizedfor of196paperswereselected,includingretrieval. Through these steps, a set of keywords which are sufficient to cover most of 154theresearch19 conferencearticles inarticles,this domaincould beabstracts,obtained.12 book chapters, 7 review articles, and 4 theses.Although structural optimization has a history of more than one hundred years, it is first3. StatisticalAnalysisindustryof Selectedappliedin aerospaceand Literaturethe application in civil engineering industry is muchlater [22].Moreover, withthe adventof informationtechnology,The distributionof papersregardingthe publicationyearstheis optimizationpresented in methodsFigure 2,usedrecent thestudieshaveintochangeda lotcomparedwith earlyTherefore,thewhichindividestimelinefive timeperiods.It is obviousthatstudies.the numberof papersrangeof publicationyear ofexperiencesthe selectedapapersis setincreasefrom 1970tothe2020in orderto analyzeon l theandsummarizethe oflatestofafterresearchon civilengineeringstructuralselectedpapers, 88%themachievementswere published2000, and73% ofthem were publishedoptimization.after 2010, indicating that this theme has attracted increasing attention from researchers.2.2. Keywords for Literature RetrievalAs mentioned above, eight keywords are utilized for searching relevant publications.During the process of choosing suitable keywords, “civil engineering structuraloptimization” is firstly searched in Google Scholar. Then several review articles areselected to find the state-of-the-art techniques in this field and based on which some otherkeywords such as topology optimization and metaheuristic algorithms are summarized

Buildings 2021, 11, 66which dividesthe timelineintooffivetime periods.3. StatisticalAnalysisSelectedLiteratureIt is obvious that the number of paperson structural optimizationexperiencessignificantoverthe years.Amongall the 2,The distributionof papers aregardingtheincreasepublicationyearsis presentedin Figureselected mwerepublishedwhich divides the timeline into five time periods. It is obvious that the number of papersafter 2010,onindicatingthis themehas uralthatoptimizationexperiencesa significantincreaseover theyears.Among all the5 of 27selected papers, 88% of them were published after 2000, and 73% of them were publishedafter 2010, indicating that this theme has attracted increasing attention from researchers.Figure 2. Distribution of the selected articles regarding the publication year.Figure 2. Distribution of the selected articles regarding the publication year.Figure 2. Distribution of the selected articles regarding the publication year.These selected papers are also analyzed based on the journals they are published in.These selected papers are also analyzed based on the journals they are publishedFigure 3 showsthe selectedtop tenpapersjournalspublish basedthe mostarticlesintheythe arefieldof civilin.Theseare thatalso analyzedon thejournalspublishedin. Figure 3 shows the top ten journals that publish the most articles in the field ofFigure3 showsoptimization.the top ten journalsthehavemost publishedarticles in thefield ofof 82civilengineeringstructuralThe topthattenpublishjournalsa totalcivil engineering structural optimization. The top ten journals have published a total alshavepublishedatotalofpapers.The Thejournalof Computersrankedfirstwith21 paperspublished,8282 papers.journalof ComputersandandStructuresStructures isisrankedfirstwith21 sciplinaryMultidisciplinaryOptimizationand ural andOptimizationand EngineeringStructures,each published,of zationandEngineeringStructures,eachof whichwhichalsoalsopublishedpublishedmorethan10 papers.morethan10 papers.of which also published more than 10 papers.Figure 3. Number of selected articles published in the top ten journals.Figure 3. Number of selected articles published in the top ten journals.Figure 3. Number of selected articles published in the top ten journals.Moreover, the retrieved articles are classified according to the geographical locationof the first author’s research institution, and the distribution of geographical locations isshown in Figure 4. The top three continents are Asia, Europe, and North America, whichhave published 79, 66, and 36 papers, respectively, which altogether account for 92% of thetotal number of the collected papers.

Moreover, the retrieved articles are classified according to the geographical locationof the first author’s research institution, and the distribution of geographical locations isshown in Figure 4. The top three continents are Asia, Europe, and North America, which6 of 27have published 79, 66, and 36 papers, respectively, which altogether account for 92% ofthe total number of the collected papers.Buildings 2021, 11, 66Figure 4. Distribution of selected articles by the continent of the first author’s research institution.Figure 4. Distribution of selected articles by the continent of the first author’s research institution.4. Objectives of Structural Optimization4. Objectivesof StructuralOptimization4.1. Categoriesof OptimizationObjectives4.1.of ectives ofthe selected papers on structural optimization can beThetheoptimizationobjectivesof the selected papers on structural optimization can bedivided intofollowing es:1.Cost minimization: the objective of the structural optimization design is to minimizeCost cost,minimization:the objectiveof thebystructuraldesignis to minimizethe totalwhich is usuallyachievedreducingoptimizationthe weight orthe ingtheweightorthevolumeof thethe structure;structure;2.Structural performance improvement: the objective of the structural tivesuchof thedesignis to improvecertain improvement:properties of theas lior, aerodynamic performance, dynamic seismic performance, in orderto meetbehavior,theaerodynamicperformance,dynamic seismic performance, in order to meet therequirements indifferent environments;in differentenvironments;the objective of the structural optimization3. requirementsEnvironmentalimpact minimization:Environmentalimpactminimization:the objectivethe structuraloptimizationdesign is to reduce the greenhousegas emissionor energyofconsumptionto improvedesignis to reduce performancethe greenhousegasstructure;emission or energy consumption to improve thethe environmentalof thestructure,and;Multi-objective:performancethe objectiveofofthestructuraloptimizationcontains more than one of the4. raloptimizationcontains more than one of theabove three objectives.above three objectives.Table 1 presents a summary of the four categories of optimization objectives and someTable 1 presents a summary of the four categories of optimization objectives andrelevant literature from the selected papers for further analysis.some relevant literature from the selected papers for further analysis.Table 1. Summary of the four categories of optimization objectives with their respective relevant articles in the field ofTable 1. Summary of the four categories of optimization objectives with their respective relevantstructural optimization.articles in the field of structural optimization.Optimization ObjectivesOptimizationRelevant ArticlesRelevant ArticlesBarbieri, Cinquini [23]; Lin, Che [24]; ZhouOptimization for minimizing the total cost ofand Rozvany [25]; Liang, Xie [26]; GhasemiCost minimizationcivil engineering structures, which is usuallyand Dizangian [27]; Ho-Huu, Nguyen-ThoiOptimizationforreducingminimizingthe totalcostachieved bystructureweightor Barbieri,volume Cinquini [23]; Lin, Che [24]; Zhou and Rozvany[28]; Zhao, Xu [29]of civil engineering structures, which isRahmatallaandSwan [30];and 7]; HoCost minimizationOptimization for improving certain properties ofStructural performance usually achieved by reducing structure[31]; Achtziger [32]; Wang [33]; Guest andcivil engineering structures in order to Huu,adapt Nguyen-Thoi [28]; Zhao, Xu [29]improvementMoen [34]; Uroš, Gidak [35]; Martin andfunctional requirementsweight or volumeDeierlein [36]Optimization for reducing the environmentalYi and Malkawi [37]; Brown and Mueller [38];Environmental impactimpacts of civil engineering structures, such asPenadés-Plà, García-Segura [39]; Mayencourtminimizationgreenhouse gas emission and energyand Mueller [40]consumptionBremicker, Chirehdast [41]; Ohsaki and SwanOptimization considering more than one of theMulti-objective[42]; Paik and Raich [43]; Munk, Vio [44];above objectivesChoi, Oh [3]; Xia, Langelaar [45]ObjectivesDescriptionDescription

Multi-objectiveBuildings 2021, 11, 66of the above objectivesand Raich [43]; Munk, Vio [44]; ChoiLangelaar [45]Figure 5 presents the percentage of the selected articles for each7 of 27objective. It is found that most researchers are from the standpoint of projecand focus on the objective of cost minimization, accounting for 62% of the seAnotherof thecollectedofarticlesaimingthe structuralFigure 522%presentsthe percentagethe selectedarticles tofor improveeach optimizationobjective. perfoItonis structuralfound that mostresearchers arefrom the 14%standpointproject stakeholdersoptimization,whereasof theof articlesengage n,accountingfor62%oftheselectedarticles.for more than one goal. Few studies concentrate on reducing the environmAnother 22% of the collected articles aiming to improve the structural performance basedcivilengineeringstructuresalone,only inaccount2% of theonstructuraloptimization,whereas 14%of the whicharticles engagestructuralforoptimizationfor selectereasonmightbe studiesthat concentratereducingon greenhousegas emissionsand embmorethan onegoal. Fewreducing the environmentalimpact of r2%oftheselectedarticles.Thereasonconsumption will result in a reduction of the total cost of structures at the smight be that reducing greenhouse gas emissions and embodied energy consumptionTherefore,more commonis to considerwillresult in aareductionof the totalapproachcost of structuresat the samecosttime minimization[39]. Therefore, andminimizationsimultaneously,whichis categorizedaimpactmore commonapproach is to considercost minimizationand environmentalimpact as lti-objectiveoptimizationinoptimization in this study.this study.Figure 5. Number and proportion of articles for each optimization objective.Figure 5. Number and proportion of articles for each optimization objective.4.2. Temporal Trends of Optimization ObjectivesOver the years, the overall tendency of research on civil engineering structural opti4.2. TemporalTrendsof OptimizationObjectivesmizationexperiencesan upwardtrend, while theproportion of articles with each objectivehas trends infield ofOver the years, the overall tendencyof ofresearchonthecivilengineestructural optimization over time, the number and proportion of the selected papers withoptimization experiences an upward trend, while the proportion of artieach optimization objective in the five time periods are shown in Figure 6a,b, respectively.objectivehas mostbeenofconstantlychanging.To analyze Therethe changesof researcBefore 2000,the articles focuson cost minimization.are 16 talnumberofpapersbefore2000.field of structural optimization over time, the number and proportion oSince weight or volume of a structure constitutes a considerable part of the cost [46], cost repapers with each optimization objective in the five time periods are shownduction was achieved by reducing the total weight or volume of the structure in all of theserespectively.earlystudies collected. In addition to cost minimization, a few studies also concentrate hich account for ThereBefore2000, improvementmost of thefocusoptimization,on cost minimization.17% and 13% of the selected articles, respectively. All of the articles aiming at structuralrelated to this theme, which account for 70% of the total number of papeperformance improvement collected in this period are based on topology optimization,Sinceor volumeis achievedof a structureconstitutesa considerableinwhichweightdesign optimizationby eliminatingsubsystemswith negligible partcon- of gprescribedcriteria[31].Itisworthreduction was achieved by reducing the total weight or volume of the strnoting that there was not a uniform structural performance indicator in these studies, andvarious performance indicators such as compliance [32,47], and maximum displacement ormoment [48] were applied for optimization. For multi-objective structural optimization,the earliest study retrieved in this paper conducted a mean compliance minimization and aweight minimization separately, and then combined these two types of optimizations [41].A more common form of multi-objective optimization is to consider two objectives at thesame time. Some researchers proposed a multiplier to convert multi-objective problems to

Buildings 2021, 11, 66competition with each other [43,51]. However, due to some limitations such ascomputational complexity [50] and uncertainty of the solution [51], the number of studiesrelevant to this theme is limited, which only accounts for 14% of the total selected articles.According to Figure 6a, the number of articles with multi-objective has been fluctuating8 of 27in the time periods after 2000. Moreover, one thing that must be pointed out is thatalthough only four articles (2%) aim to reduce the environmental impact of the structures,three out of the four articles were published from 2016 to 2020, which suggests that thissingle-objectiveproblems[49] and othersa Paretosolution forachievingthememay becomemore popularin theadoptedfuture ization objectives simultaneously [50].in the field of structural engineering [39].(a)(b)Figure 6. Number and proportion of articles with each objective in each time period: (a) number of articles, and (b)proportion of articles.The number of articles in the field of structural optimization increases rapidly after2000, especially in the fourth time period, from 17 articles between 2006 and 2010 to 66 articles between 2011 to 2015, while the proportion of articles with each objective has beenchanging over the years. According to Figure 6a,b, it is obvious that cost minimization hasalways been the hottest research theme, and the number of articles on this theme keepsincreasin

Multi-objective optimization: simultaneously considers two or more of the above . [12]. Another example of structural optimization applied on a large-scale civil engineering structure is the Shenzhen CITIC Financial Center in Shenzhen, China. . literature and present a comprehensive review on structural optimization in the field of civil