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The Environmental and Economic Impact of Structural Optimization

: According to the well-known mathematician Leonhard Euler: “Nothing takes place within the universe in which the rule of maximum or minimum does not appear.” The development of optimization algorithms can be traced back to the days of Kepler, Newton, Lagrange and Cauchy and the concept of minimization much earlier to the days of Euclid. However, despite these early developments, very little progress on their use was achieved until the middle of 20 th century when digital computers made possible the application of the optimization algorithms and motivated further research, producing massive literature on the subject and development of new optimization techniques. Nevertheless, professional structural engineers and practitioners are highly sceptical in adopting such procedures in their professional life, while software applications implementing optimization techniques fall short of meeting their needs. Therefore, in this study the question that I will try to answer from an environmental and economic perspective is: “Is it worth performing structural optimization studies?”, and aim to prove that adopting optimization based design procedures will have drastic environmental impact and contribute on the economic development in construction industry.


INTRODUCTION
When Edison constructed the first long-lasting, high-quality light bulb in 1879; his successful design was the result of a long and effortful trial-and-error design procedure, the known as the Edisonian approach [1], targeting to identify the most filament material. Whereas Thomas Edison had no basic knowledge of how different materials resist on electric current, today's engineers are commonly armed with technical knowledge and experience concerning their domain. This enables them to generate good initial designs based on intuition before testing them to failure or to the design-code requirements. Design defects detected throughout the tests are then improved through the so-called make-it-and-break-it procedure.
Advances in computing power and in computer-aided engineering software packages now make it possible to produce virtual prototypes of potential designs before building and testing overengineered physical prototypes. This reduces the cost and time needed to perform every design iteration and provides better understanding of how a design performs. However, the potential of virtual prototyping approach remains restricted by two factors. First, every iteration needs an engineer to manually develop or modify a computer model of the system. Despite ever improving software packages, this is often still a cumbersome, fallible and lengthy procedure. The second factor concerns the success of this approach that still depends heavily on the restrictions of human intuition and skills. Despite how brilliant the design team is, the human mind often cannot predict or comprehend the results of adjusting multiple variables at an equivalent time in a very complicated system. This profound barrier, let alone time constraints, severely limits the quantity and types of design iterations that can be performed. Often the result is a far-optimal solution that is a design of the team's collective expertise.
The desire to extend productivity led naturally to the automation of the design iteration procedure.
Process automation software packages were introduced that might capture and execute automatically the standard manual procedure to generate and test a virtual prototype. Thus, every new design iteration can be performed much more quickly, and without worrying of manual errors. It shortly became obvious that exploration of the design space could also be automated by adding a smart iterative procedure over the design-evaluation process, and an instant market was created for all classical optimization algorithms. With the promise of reducing design time and cost whereas rising product quality, automated design optimization has tremendous potential. Starting with a sub-optimal or even random design, a numerical optimization algorithm could be used to iteratively adjust a set of pre-selected design parameters in an endeavour to realize a set of design targets.
Although since early 60's a large amount of excellent research studies have been published on the subject of optimization based structural engineering, where structural optimization was successfully been applied in various problems [2][3][4][5][6], structural engineering practice fall short behind of adopting optimization based design procedures. On the other hand, various engineering professions like mechanical and aerospace engineering implement optimization procedures into the everyday profession practice. For example in automotive industry, among other car manufactures, the R&D department of BMW has developed and standardized optimization procedures in the framework of various fields of simulation when developing a new diesel engine [7]. Additionally, in aeronautic industry, Airbus adopted an optimization-based procedure for designing the wing of A380 aircraft [8].
In addition, it should be taken into consideration that: (i) The building sector is the largest contributor to global greenhouse gas (GHG) emissions; buildings use about 40% of global energy, 25% of global water, 40% of global resources, and they emit almost 30% of GHG emissions, (ii) building sector is estimated to be worth 10% of global GDP (USD 7.5 trillion) and employs more than 110 million people, while (iii) CI is expected to expand by 85% to USD 15.5 trillion worldwide in 2030, with U.S., China and India accounting for almost 60% of this growth. Bearing in mind all issues mentioned above, the main objective of the present article is to answer the question: "Is it worth performing structural optimization studies?" from the environmental and economic perspective. For this purpose the global market of structural materials is reviewed, while the environmental and economic impact is assessed accompanied by two large-scale real-world test cases of design optimization techniques into structural engineering.

TREND OF THE GLOBAL STRUCTURAL MATERIALS MARKET:
CEMENT AND STEEL Before performing any techno-economic analysis, the structural material quantities produced annually and those required from the demand, need to be collected and analysed. In this direction, the evolution of the global cement production for years 1950 to 2016 as reported by US Geological Survey (USGS) [9] is presented in Figure 1   besides, a global transformation to a highly energy-efficient, low-carbon building sector must occur over the next decade to ensure a well below 2°C ambition. This is especially true in emerging economies, where there is a critical window of opportunity to address the largest new construction markets to avoid locking in inefficient buildings for decades [15,17]. Thus some priority actions were set by UNEP [15], one of which is to reduce embodied energy and emissions; i.e.
reduce the environmental impact of material use in the buildings & construction value chain.

STRUCTURAL OPTIMIZATION AND VALUE ENGINEERING
The Latin word "optimum" means ultimate-ideal; accordingly, "optimus" means the best. Therefore, to optimize refers to try to bring something closer to its ultimate state. The history of optimization, that is the quest for finding extreme points, dates back several hundreds of years during which remarkable progress has been made in developing new and more efficient methods. Euclid (300 BC) tackled with the problem of finding the shortest distance, which may be drawn from a point to a line, while Heron of Alexandria (100 BC) studied the optimization problem of light travelling between two points by the shortest path [18]. Many years later, Fermat (1657) developed a more general principle that light travels between two points in the minimum time [19], while Cauchy (1847) presented the first minimization method (the well-known Steepest Descent method) [20]. The progress on calculus provided the basis for the development of the optimization mathematical theory. The pioneering works of Courant (1943) on penalty functions [21], Dantzig (1951) on linear programming [22], Karush (1939) as well as that of Kuhn and Tucker (1951) on optimality conditions for constrained problems [23,24] established the modern era of numerical optimization.
The term structural optimization refers to the application of numerical optimization to the design process of engineering (load-carrying) structures, like building, automotive or aircraft structures.
Prior the implementation of computer-assisted optimization procedures, structural elements (like beams and plates) were optimally designed based on the calculus of variations [25]. The presentation of the finite element method (FEM) [26] was the reason for the dominance of computerized structural analysis and allowed the application of FEM-based numerical optimization procedures to structures. Schmit in his pioneering work [27] presented the first application where a simple three-bas truss structure was used for presenting the idea of structural synthesis. During the first years of computerized structural optimization, civil engineering truss structures were used for applying the new concept, with design variables being the cross-sectional areas of the bar elements. This class of structural optimization problems refers as sizing. In sizing optimization problems the aim is usually to minimize the weight of the structure under certain behavioural constraints on stresses and displacements as suggested by the design codes [28][29][30][31][32] in case of civil engineering structures. The design variables are most frequently chosen to be dimensions of the cross-sections of the structural elements, see for example the dimensioning approach of the skyscraper shown in Figure 7(a).
More recently, structural optimization research has focused on changing the shape (geometry) and topology (layout) of the structural system. In structural shape optimization problems (associated also with the so called parametric design) the aim is to improve the performance of the structure by modifying its shape, see for example the parametric design optimization of the structural system shown in Figure 7(b). The design variables are either some of the coordinates of the key points in the boundary of the structure or some other parameters that influence the geometry of the structure. Structural topology optimization, referred also as generalized shape design problem, can be considered as a procedure for optimizing the topological arrangement of material into the design domain, eliminating the material volume that is not needed, for example the design approach of the moment resisting frame (MRF) depicted in Figure 7(c) [33]. Several combinations of the three types of structural optimization have also been proposed.
In design, construction, and maintenance of any engineering system, engineers need to take several technological and managerial decisions at many stages. The ultimate goal of these choices is either to attenuate the effort required or to maximize the profit. Among others construction and material cost reduction can be achieved consistent with the desired performance, reliability, qual-ity and safety. Therefore, optimization is the act of getting an improved result under given circumstances. In structural engineering sizing optimization of the structural elements is considered as part of the so-called value engineering procedure when implemented in CI. Value engineering is outlined as the methodology to enhance the "value" of the product. It promotes the substitution of materials and procedures with more cost-effective alternatives, while not sacrificing practicality. Value engineering is the review of novel or existing products throughout the design stage to reduce costs and enhance functionality aiming to augment product's value.

LIFE CYCLE ASSESSMENT
According to UNEP [15] GHG emissions are set to double by 2050 if CI carries on business as usual. The building sector consumes increasingly energy; since primarily newly built structures are constructed quicker than old ones are withdrawn. Figure 8 shows that buildings present the most impactful and also economical mitigation potential for GHG emissions globally [34]. Significant GHG emissions are generated through construction materials; broadly speaking, energy is consumed during the following activities: (i) manufacturing of building materials ("embedded" or "embodied" energy), (ii) transport of materials from production plants to construction sites ("grey" energy); (iii) construction of building ("induced" energy); (iv) operation of building ("operational" energy); and (v) demolition of building (and recycling of its parts).
In this direction, life cycle assessment (LCA) procedure has been established as a valuable tool for assessing the impacts of products occurred from their manufacturing process to consumption.
According to the International Standardization Organization (ISO) LCA procedure is referred as "Cradle to Grave". Furthermore, ISO has developed a detailed framework [35] for the implementation of this methodology into buildings. There is a plethora of productive-industrial procedures, during buildings' life cycle, which make them responsible for a large proportion of environmental impacts. Thus, it is essential to accumulate the impacts derived from every aspect of building's life cycle.
In this study the significance of design optimization into CI is assessed with respect to the embodied energy of the building, since it is correlated directly with the material use and will be implemented by means of a LCA framework. In particular, the global environmental revenue annually is calculated along with two test examples, which are examined in this study by means of LCA. Therefore, the comparative purpose of this work requires estimating the embodied energy's variations of CI output and thus only structural elements are included in the initial embodied energy, which are identified likewise in the recurring embodied energy of the building. Implementing the process presented in [36], embodied energy is divided in two parts: initial and recurring; used for rehabilitating the building and it is expressed with the following expression:

STRUCTURAL OPTIMIZATION DESIGN TOOLS
Design optimization refers to the act of generating improved designs in terms of cost, manufacturability or performance whereas not compromising safety. The implementation of optimum design formulations to real-world cases demands major computational effort, which may solely be addressed with the synergy of state-of-the-art technologies within the field. Therefore, tools developed for handling structural optimization problems primarily should serve four purposes: (i) correct numerical modelling of structural systems, (ii) reliable structural analysis for calculating response quantities like displacements and stresses, (iii) consistent to design codes and/or the design engineers design procedure for performing the constraints checks and (iv) effective optimization algorithms for achieving improved designs that satisfy design conditions and economic, manufacturability, performance or sustainability criteria.
Structural optimization has matured from a limited topic of academic nature, wherever researchers targeted on the design optimization of small-idealized structural components or systems, to become the premise in contemporary design of complicated structural systems. In recent years, few software packages have offered these tools accessible to professional engineers, decision-makers and students outside the structural optimization research community. These software packages typically targeted to aeronautic, mechanical or naval structural systems have incorporated the op-  [39] and recently MIDAS NFX presented its topology optimization capability [40]. However, these tools come short of meeting the requirements of professional structural engineers.
In the case of CI there are only a couple of software that offer design optimization solutions. More specifically, SCIA presented Engineer MOOT [41] which is a multi-objective optimization tool that achieves optimized structural designs using the internal forces' compliance for performing code checks and Optimization Computing Platform (OCP) [42,43]  Secondly, opinion leaders of the construction industry and managers must overcome some challenges if construction companies are to absorb structural optimization technology efficiently, one of which is that the users of optimization technology are often not willing (or able) to take the responsibility for implementing the optimization technology. This is possibly because design engineers might be sceptical on the safety of the optimized structural designs. For this purpose, the developers of the specialized software need to ensure that the results obtained through structural optimization software are, directly, comparable with those used in the original design, i.e. use the same FE simulation, material properties, loading conditions, design codes etc. [43]. In order to be convinced about the efficiency of structural optimization technology, a pilot operation across the board in a large organization needs to be conducted. However, pilot application should be treated carefully since novel and exotic technologies are especially vulnerable to hype.
Last but not least, although, structural engineers are sought out as policy leaders and problem solvers in many matters of the community, while they initiate and lead the development of emerging and exponential technology; they resist changing and might not identify direct personal benefit from the use of structural optimization technology. Roughly speaking CI is composed by three parts, the owner, the constructor and the designer; although the later one is to implement optimization technology in the design phase, only the first two parts have personal benefit from its adoption. Therefore, in order to help community earning from the outcomes of structural optimization technology, the State needs to impose its implementation through legal means.

WHAT IF DESIGN OPTIMIZATION PROCEDURES WERE APPLIED IN STRUCTURAL ENGINEERING PRACTICE
In this section the environmental and economic impact globally is assessed, the benefits for the structural engineers is also discussed and two indicative test examples are presented in the following parts of the section. Although the techno-economic analysis performed in the current study relies on embodied energy only; it will be shown that by means of structural optimization the environmental and economic merits are enormous.

Environmental and economic impact
Without loss of generality of the conclusions derived, the case of building structures is considered herein that represent the 75% of the construction industry activity. In order to examine the influence of design optimization procedures in structural engineering practice and thus the environmental and economic impact, some scenarios are examined: (i) assume that via design optimization procedures an average reduction on material requirements equal to 5% or 10% is achieved and (ii) assume that globally 0.1%, 0.5% or 5% of the construction industry related to the buildings market adopts optimization techniques during the design procedure.  Table 1 for years 2015, 2016 and projected values for 2030 and 2050 (according to UNEP [15]). Based on these quantities of materials the environmental and economic impact is presented analytically below. For the purposes of this parametric study instead of making the calculations for cement it is performed for concrete. Typically, a concrete mix contains about 10% to 15% cement [44]; therefore, in order to derive the corresponding concrete quantities it is assumed that concrete on average contains 12.5% cement. Table 2 presents the reduction with respect to annual material demand for the building sector of CI (in million m 3 of concrete and million kgr of steel). Tables 3 and 4 depict the environmental impact, calculated as reduced requirements in terms of trillion BTU energy consumption (see Table 2) and million metric tons of GHG CO2e emissions (see Table 3) when design optimization procedures are adopted. These values correspond to year 2016 based on the material consumption [15] and for years 2030 and 2050 based on predictions of CI evolution described analytically previously. These quantities are derived for explicit values for the energy and CO2e coefficients obtained from the Inventory of Carbon and Energy of the University of Bath [45]. for concrete and corresponds to 30% cement replacement with fly ash [45].
In order to underline the significance for adopting optimization procedures in the structural engineering design practice the annual GHG emissions for 24 cities (indicatively selected) around the world in million metric tons of CO2e is presented in Table 5, obtained by the Carbon Disclosure Project (CDP) open data portal [46]. Indicatively, for the scenario that on average 5% material use reduction is achieved by the 0.50% of CI that implement optimization-based design procedures, the environmental benefit corresponds to reduction of 0.30 million metric tons of CO2e for year 2016, it can be observed that this mass of CO2e corresponds to the quantity that cities like Adelaide, Lausanne, Reykjavík or Udine emit annually. Accordingly, for the scenario that on average 10% material use reduction is achieved by the 5% of CI that implement optimization-based design procedures, the environmental benefit corresponds to reduction of 6.04 million metric tons of CO2e for year 2016, it can be observed that this mass of CO2e corresponds to the quantity that cities like Athens, Milan, Paris or Pittsburgh emit annually.
The economic impact when adopting design optimization procedures in CI is presented in Table   6, corresponding to annual profit in billion USD.

Real-world design test examples
In order to present the capabilities of computerized structural optimization design procedures, two real-world test examples are considered, a high-rise building and an athletic stadium. More analytical results regarding the environmental impact of design optimization procedures with reference to structural systems of high-rise buildings can be found in the recent work by Lagaros et al. [49], where different structural systems of high-rise buildings are compared.

(a) High-rise building test example
In this part of the study, the high-rise reinforced concrete (RC) building shown in Figure 9 has been considered in order to perform a specially tailored structural based value engineering study.
The building, that is to be constructed in the Persian Gulf area, is a 50 storey skyscraper where each storey height is equal to 10.7 meters, resulting into a total height of 535 meters and the dimensions of the building's layout are 50.0 × 50.0 square metres. Figure 9 shows the structural system that was chosen by the designers where outriggers are used every 7 to 17 storeys, i.e. more specifically in storeys 17, 25, 34 and 41. It is a real-world case that due to increased material cost the owners of the building postulated cost reduction, thus the contractors of the owners implemented a value engineering based design process for improving their initial design in terms of material requirements; we took over the structural design optimization part.
The structural system is composed by five types of structural elements: columns, perimeter beams, core shear walls, slabs and outriggers whose reference dimensions are provided in Table 7 The building is optimally designed to meet the ACI 318-11 [50] requirements, while an additional deformation constraint related to the roof displacement is also taken into account (roof displacement < 1.0 meter). For the formulation of the optimization problem the structural members are divided into groups having the same cross-sectional properties. Table 7 provides also information regarding the upper and lower bounds (box constraints) of the design variables (DVi, i=1,2,…,9).
The material cost is considered as the objective function to be minimized. For solving of the optimization problem the Differential Evolution (DE) metaheuristic optimization algorithm is used, as implemented in the OCP optimization software [42]. The optimized design achieved and reference one are presented in Table 7 along with the material cost, energy requirements and GHG CO2 emissions. Comparing the two designs it can be seen that there are differences to almost all the design variables considered to formulate the optimization problem leading to environmental benefit of 11.2% and 12.7% with reference to the energy consumption and GHG CO2 emissions, respectively; on the other hand the cost reduction achieved is of the order of 8%. The total gross floor area of the Jinan Olympic sports centre is equal to 678,000 square metres where that of the stadium is equal to 154,000 square metres. The stadium height is 52 meters and the structural system is composed mainly by reinforced concrete elements and suspended steel truss members. The structural system is composed by five types of structural elements: columns, beams, shear walls, slabs and truss members whose reference dimensions are provided in Table   8; all dimensions are considered as optimizable. The space frame of the stadium is shown in Figure   10 and pairing dead, live loads as well as wind and earthquake loading conditions; the latter ones as imposed by the Chinese Design codes [32,53].
The stadium has been optimally designed to meet ACI 318-14 [29] and AISC 360-10 [54], requirements. For the formulation of the optimization problem the members are divided into groups having the same structural properties, resulting into 61 design variables in total. Table 9 provides information regarding the upper and lower bounds (box constraints) of the design variables (DVi, i=1,2,…,61). Similar to the high-rise building test example, the material cost is considered as the objective function to be minimized. For solving of the optimization problem at hand the Projected Quasi-Newton (PQN) derivative free optimization algorithm is used, as implemented in OCP optimization software [42]. The optimized design achieved and reference one are presented in Table   8 along with the material cost, energy requirements and GHG CO2 emissions. Comparing the two designs it can be observed that solving the optimization problem led to environmental benefit of 19.2% with respect to both energy consumption and GHG CO2 emissions, respectively; on the other hand the cost reduction achieved is equal to 19.1%.

CONCLUSIONS
The objective of this work is to present the environmental and economic benefits if design optimization techniques are adopted in structural engineering practice. In this direction        Initial Design Optimized Design Figure 8. Estimated economic mitigation potential by sector and region using technologies and practices expected to be available in 2030. The potentials do not include non-technical options such as lifestyle changes [34].   Table 2. The reduction on the annual material demand for building construction in million m 3 of concrete and million kgr of steel; for different scenarios on average material use reduction achieved and percentage of optimization-based design technology by CI.
Year Usage reduction CI market (%) 0.10% 0.50% 5.00% Table 3. The annual environmental benefit achieved in terms of energy consumption due to the material use reduction (in trillion BTU); for different scenarios on average material use reduction achieved and percentage of optimization-based design technology by CI.   Table 6. The annual economic profit achieved due to the material use reduction (in billion USD); for different scenarios on average material use reduction achieved and percentage of optimization-based design technology by CI.    Table 9. Jinan stadium test example: box constraints (dimensions in mm).