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The uncertainty of the interval variable is represented by interval factor, and the interval variable is described as its mean value multiplied by its interval factor. Based on interval arithmetic rules, an analytical method of interval finite element for uncertain structures but not probabilistic structure or fuzzy structure is presented by combining the interval analysis with finite element method. The static analysis of truss with interval parameters under interval load is studied and the expressions of structural interval displacement response and stress response are deduced. The influences of uncertainty of one of structural parameters or load on the displacement and stress of the structure are examined through examples and some significant conclusions are obtained.

This paper demonstrates the use of genetic algorithms (GAs) for size optimization of trusses. The concept of rebirthing is shown to be considerably effective for problems involving continuous design variables. Some benchmark examples are studied involving 4‐bar, 10‐bar, 64‐bar, 200‐bar and 940‐bar two‐dimensional trusses. Both continuous and discrete variables are considered.

Reliability-based design optimizations (RBDOs) of engineering structures involve complex non-linear/non-differentiable performance functions, including both continuous and discrete variables. The gradient-based RBDO algorithms are less than satisfactory for these cases. The simulation-based approaches could also be computationally inefficient, especially when the double-loop strategy is used. This paper aims to present a pseudo-double loop flexible RBDO, which is efficient for solving problems, including both discrete/continuous variables.

The method is based on the hybrid improved binary bat algorithm (BBA) and weighed simulation method (WSM). According to this method, each BBA’s movement generates proper candidate solutions, and subsequently, WSM evaluates the reliability levels for design candidates to conduct swarm in a low-cost safe-region.

The accuracy of the proposed enhanced BBA and also the hybrid WSM-BBA are examined for ten benchmark deterministic optimizations and also four RBDO problems of truss structures, respectively. The solved examples reveal computational efficiency and superiority of the method to conventional RBDO approaches for solving complex problems including discrete variables.

Unlike other RBDO approaches, the proposed method is such organized that only one simulation run suffices during the optimization process. The flexibility future of the proposed RBDO framework enables a designer to present multi-level design solutions for different arrangements of the problem by using the results of the only one simulation for WSM, which is very helpful to decrease computational burden of the RBDO. In addition, a new suitable transfer function that enhanced convergence rate and search ability of the original BBA is introduced.

This paper aims to present a new physically inspired meta-heuristic algorithm, which is called Plasma Generation Optimization (PGO). To evaluate the performance and capability of the proposed method in comparison to other optimization methods, two sets of test problems consisting of 13 constrained benchmark functions and 6 benchmark trusses are investigated numerically. The results indicate that the performance of the proposed method is competitive with other considered state-of-the-art optimization methods.

In this paper, a new physically-based metaheuristic algorithm called plasma generation optimization (PGO) algorithm is developed for solving constrained optimization problems. PGO is a population-based optimizer inspired by the process of plasma generation. In the proposed algorithm, each agent is considered as an electron. Movement of electrons and changing their energy levels are based on simulating excitation, de-excitation and ionization processes occurring through the plasma generation. In the proposed PGO, the global optimum is obtained when plasma is generated with the highest degree of ionization.

A new physically-based metaheuristic algorithm called the PGO algorithm is developed that is inspired from the process of plasma generation.

The results indicate that the performance of the proposed method is competitive with other state-of-the-art methods.

The purpose of this paper is to propose and analyze the use of local surrogate models to improve differential evolution’s (DE) overall performance in computationally expensive problems.

DE is a popular metaheuristic to solve optimization problems with several variants available in the literature. Here, the offspring are generated by means of different variants, and only the best one, according to the surrogate model, is evaluated by the simulator. The problem of weight minimization of truss structures is used to assess DE’s performance when different metamodels are used. The surrogate-assisted DE techniques proposed here are also compared to common DE variants. Six different structural optimization problems are studied involving continuous as well as discrete sizing design variables.

The use of a local, similarity-based, surrogate model improves the relative performance of DE for most test-problems, specially when using r-nearest neighbors with r = 0.001 and a DE parameter F = 0.7.

The proposed methods have no limitations and can be applied to solve constrained optimization problems in general, and structural ones in particular.

The proposed techniques can be used to solve real-world problems in engineering. Also, the performance of the proposals is examined using structural engineering problems.

The main contributions of this work are to introduce and to evaluate additional local surrogate models; to evaluate the effect of the value of DE’s parameter F (which scales the differences between components of candidate solutions) upon each surrogate model; and to perform a more complete set of experiments covering continuous as well as discrete design variables.

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.

First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.

The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.

Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.

The early detection of cracks, corrosion and structural failure in aging structures is one of the major challenges in the civil, mechanical and aircraft industries. Common inspection techniques are time consuming and hence can have strong economic implications due to downtime. The paper aims to discuss these issues.

As a result, during the past decade a number of methodologies have been proposed for detecting crack in structure based on variations in the structure's dynamic characteristics. This work showcases the efficacy of particle swarm optimization (PSO) and genetic algorithm (GA) in damage assessment of structures.

Efficiency of these tools has been tested on structures like beam, plane and space truss. The results show the effectiveness of PSO in crack identification and the possibility of implementing it in a real-time structural health monitoring system for aircraft and civil structures.

The methodology presented establishes the PSO as robust and competent tool over GA for crack identification using changes in natural frequencies.

In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

Trusses constitute a fertile field to demonstrate the application of optimization techniques because of the possibility of several different configurations. Using such techniques allows the search for designs that minimize the use of material to safely comply with the imposed loads. Truss optimization can be classified into three categories: cross-section, shape, and topology. The purpose of this paper is to present a numerical and experimental study developed to minimize the weight of aluminum trusses, taking both the cross-sectional dimensions of the elements and the nodal coordinates as design variables.

Initially, several numerical computer simulations were performed with an optimization program developed by combining the displacement method and a simulated annealing optimization method. Subsequently, two aluminum trusses were selected and built in order to validate the numerical results obtained.

Experimental tests verified the excellent performance of the optimized model.

In addition, it was concluded that significant savings could be obtained from the application of the proposed formulation.