Applications of Metaheuristic Optimization Algorithms in Civil Engineering

Much has been made of the parallels between engineering and art, and yet a unique economy of parts and adherence to a plethora of constraints from cost to market trends, from maintainability to robustness, and from project schedules safely distinguish engineering design from the arts and engineering projects from artworks. At the heart of this distinction lies the concept of “optimization” – the science of choosing design variable values within given constraints such that a function, e.g., total system cost, is minimized or, e.g., overall system reliability is maximized.

The whale optimization algorithm (WOA) is a recently developed swarm-based optimization algorithm inspired by the hunting behavior of humpback whales. This study attempts to enhance the original formulation of the WOA in order to improve solution accuracy, reliability, and convergence speed. The new method, called enhanced whale optimization algorithm (EWOA), is tested in the sizing optimization of skeletal structures. In this chapter, EWOA is also compared with WOA and other metaheuristic methods developed in the literature using four skeletal structure optimization problems. Numerical results compare the efficiency of the WOA and EWOA with the latter algorithm being superior to the standard implementation [1].

Space structures have become popular not only because of their topological attractiveness and greater reserves of strength compared to conventional structures but also their easy and fast construction. Double-layer grids are ideally suited for covering exhibition pavilions, assembly halls, swimming pools, hangars, churches, bridge decks, and many types of industrial buildings in which large unobstructed areas are required. Double-layer grids have been built successfully at a lower cost than equivalent conventional systems, providing at the same time additional advantages, such as greater rigidity, erection simplicity, and possibility of covering larger areas.

This chapter deals with the optimal design of double-layer Lamella domes, Suspen-Domes, and single-layer domes with relatively long spans including nonlinear structural behavior [1]. In recent years, much progress has been made in the optimal design of space structures by focusing on their linear behavior, neglecting nonlinearities which can result in uneconomic designs. In this study, geometric nonlinearity optimization is taken into account for the abovementioned domes. There are two main steps involved in the optimization of structural problems: analysis and design. In this chapter, OPENSEES [2] is employed for analysis, and enhanced colliding body is utilized in the design phase. All of the required programs for the optimization phase are coded in MATLAB [3]. The design variables include cross-sectional areas of the structural elements, the height of dome, the initial strain of cables, and the cross sections of cables in the Suspen-Dome. In order to illustrate the efficiency of the proposed methodology, three numerical examples including optimization of a single-layer dome with rigid-jointed, suspen-dome, and double-layer domes with 12 rings subjected to dead and snow loading are presented. The main contribution of the chapter is to utilize an efficient metaheuristic algorithm for optimization of domes. Optimal design of structures is usually achieved by considering the design variables to find an objective function which is the minimum weight while all of the design constraints are satisfied.

The increasing use of braced barrel vaults as a lightweight space structure is very common. Optimizing barrel vaults, therefore, can prove a worthwhile venture [1]. Metaheuristic algorithms explore the feasible region of the search space based on both randomization and some specified rules through a group of search agents. Nature-inspired phenomena are commonly used as a basis for the rules employed by these agents [2].

Barrel vault is one of the oldest architectural forms, used since antiquity. The brick architecture of the Orient or the masonry construction of the Romans provides numerous examples of the structural use of barrel vaults. The industrial and technological developments which have taken place during the last three decades have had a far-reaching effect upon contemporary architecture and modern engineering. New building techniques, new constructional materials, and new structural forms have been introduced all over the world. The architectural search for new structural forms has resulted in the widespread use of three-dimensional structures. The evolution of effective computer techniques of analysis is undoubtedly one of the reasons for the truly phenomenal acceptance of space structures. During recent years, architects and engineers have rediscovered the advantages of barrel vaults as viable and often highly suitable forms for covering not only low-cost industrial buildings, warehouses, large-span hangars, and indoor sports stadium but also large cultural and leisure centers. The impact of industrialization on prefabricated barrel vaults has proved to be the most significant factor leading to lower costs for these structures. A barrel vault consists of one or more layers of elements that are arched in one direction [1]. Barrel vaults are given different names depending on the way their surface is formed. The earlier types of barrel vaults were constructed as single-layer structures [2–4]. Nowadays, with increase of the spans, double-layer systems are often preferred. Whereas the single-layer barrel vaults are mainly under the action of flexural moments, the component members of double-layer barrel vaults are almost exclusively under the action of axial forces; the elimination of bending moments leads to a full utilization of strength of all the elements. Formex algebra is a mathematical system that provides a convenient medium for configuration processing. The concepts are general and can be used in many fields. In particular, the ideas may be employed for generation of information about various aspects of structural systems such as element connectivity, nodal coordinates, details of loadings, joint numbers, and support arrangements. The information generated may be used for various purposes, such as graphic visualization or input data for structural analysis. Double-layer barrel vaults have great number of structural elements, and utilizing optimization techniques has considerable influence on the economy.

Decks, interior beams, edge beams, and girders are parts of a steel floor system. If the deck is optimized without considering beam optimization, finding the best result is simple. However, a deck with a higher cost may increase the composite action of the beams and decrease the beam cost, thus reducing the total expense. Also, a different number of floor divisions can improve the total floor cost. Increasing beam capacity by using castellated beams is another efficient cost-saving method. In this study, floor optimization is performed and these three issues are discussed. Floor division number and deck sections are some of the variables. Also, for each beam, profile section of the beam, beam-cutting depth, cutting angle, spacing between holes, and number of filled holes at the ends of castellated beams are other variables. Constraints include the application of stress, stability, deflection, and vibration limitations according to the load and resistance factor (LRFD) design. The objective function is the total cost of the floor consisting of the steel profile, cutting and welding, concrete, steel deck, shear stud, and construction costs. Optimization is performed by enhanced colliding bodies optimization (ECBO). Results show that using castellated beams, selecting a deck with a higher price and considering the different number of floor divisions can decrease the total cost of the floor (Kaveh and Ghafari [1]).

Tubular steel monopole structures are widely used for supporting antennas in telecommunication industries. This research presents two recently developed metaheuristic algorithms, so-called colliding bodies optimization (CBO) and its enhanced version (ECBO), for size optimization of monopole steel structures. The optimal design procedure aims to obtain minimum weight of monopole structures subjected to the TIA-EIA222F specification. Two monopole structure examples are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the CBO and ECBO in creating optimal design for this problem. The outcomes of the ECBO are also compared to those of the standard CBO to illustrate the importance of the enhancement of the CBO algorithm [1].

It is well known that damaged structural members may alter the behavior of the structures considerably. Careful observation of these changes has often been viewed as a means to identify and assess the location and severity of damages in structures. Among the responses of a structure, natural frequencies and natural modes are both relatively easy to obtain and independent from external excitation and, therefore, can be used as a measure of the structural behavior before and after an extreme event which might have led to damage in the structure. This chapter applies charged system search algorithm to the problem of damage detection using vibration data. The objective is to identify the location and extent of multi-damage in a structure. Both natural frequencies and mode shapes are used to form the required objective function. To moderate the effect of noise on measured data, a penalty approach is applied. A variety of numerical examples including beams, frames, and trusses are examined. The results show that the present methodology can reliably identify damage scenarios using noisy measurements and incomplete data [1].

In this chapter a simple and robust approach is presented for spectral matching of ground motions utilizing the wavelet transform and an improved metaheuristic optimization technique. For this purpose, wavelet transform is used to decompose the original ground motions to several levels, where each level covers a special range of frequency, and then each level is multiplied by a variable. Subsequently, the enhanced colliding bodies optimization (ECBO) technique is employed to calculate the variables such that the error between the response and target spectra is minimized. The application of the proposed method is illustrated through modifying 12 sets of ground motions [1].

In this chapter three recently developed metaheuristic optimization algorithms, known as colliding bodies optimization (CBO), enhanced colliding bodies optimization (ECBO), and tug of war optimization (TWO), are utilized for optimum nodal ordering to reduce bandwidth, profile, and wavefront of sparse matrices. The bandwidth, profile, and wavefront of some graph matrices, which have equivalent pattern to structural matrices, are minimized using these methods. Comparison of the achieved results with those of some existing approaches shows the robustness of these three new metaheuristic algorithms for bandwidth, profile, and wavefront optimization [1].

Structural optimization involves a large number of structural analyses. When optimizing large structures, these analyses require a considerable amount of computational time and effort. However, there are specific types of structure for which the results of the analysis can be achieved in a much simpler and quicker way due to their special repetitive patterns. In this chapter, frequency constraint optimization of cyclically repeated space trusses is considered. An efficient technique is used to decompose the large initial eigenproblem into several smaller ones and thus to decrease the required computational time significantly (Kaveh and Zolghadr [1]).

High number of design variables, large size of the search space, and control of a great number of design constraints are major preventive factors in performing optimum design of real-world structures in a reasonable time. This chapter presents an accurate and efficient technique for optimal design of truss towers with large number of design variables to illustrate its applicability to optimum design of practical structures [1].

In this chapter the recently developed physically inspired non-gradient algorithm is employed for structural optimization with frequency constraints. The algorithm being called vibrating particles system (VPS) mimics the free vibration of single degree of freedom systems with viscous damping. Truss optimization with frequency constraints is believed to represent nonlinear and non-convex search spaces with several local optima and therefore is suitable for examining the capabilities of the new algorithms. A set of five truss design problems are considered for evaluating the VPS in this article. The numerical results demonstrate the efficiency and robustness of the new method (Kaveh and Ilchi Ghazaan [1]).

This chapter investigates discrete design optimization of reinforcement concrete frames using the recently developed metaheuristic called Enhanced Colliding Bodies Optimization (ECBO) and the Non-dominated Sorting Enhanced Colliding Bodies Optimization (NSECBO) algorithm. The objective function of algorithms consists of construction material costs of reinforced concrete structural elements and carbon dioxide (\( {\mathrm{CO}}_2 \)) emissions through different phases of a building life cycle that meets the standards and requirements of the American Concrete Institute’s Building Code. The proposed method uses predetermined section database (DB) for design variables that are taken as the area of steel and the geometry of cross sections of beams and columns. A number of benchmark test problems are optimized to verify the good performance of this methodology. The use of ECBO algorithm for designing reinforced concrete frames indicates an improvement in the computational efficiency over the designs performed by Big Bang–Big Crunch (BB–BC) algorithm. The analysis also reveals that the two objective functions are quite relevant and designs focused on mitigating \( {\mathrm{CO}}_2 \) emissions could be achieved at an acceptable cost increment in practice. Pareto results of the NSECBO algorithm indicate that both objective yield similar solutions [1].

In this chapter, two recently developed metaheuristic algorithms, so-called CBO and ECBO, are employed for construction site layout planning. Results show that both of these algorithms have the capability of solving this kind of problem. Two case studies are presented to show the applicability and performance of the utilized methods [1].