Nikolaos D. Lagaros

Structural optimization using evolutionary algorithms

The objective of this paper is to investigate the efficiency of various evolutionary algorithms (EA), such as genetic algorithms and evolution strategies, when applied to large-scale structural sizing optimization problems. Both type of algorithms imitate biological evolution in nature and combine the concept of artificial survival of the fittest with evolutionary operators to form a robust search mechanism. In this paper modified versions of the basic EA are implemented to improve the performance of the optimization procedure. The modified versions of both genetic algorithms and evolution strategies combined with a mathematical programming method to form hybrid methodologies are also tested and compared and proved particularly promising. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.

Advanced solution methods in structural optimization based on evolution strategies

The objective of this paper is to investigate the efficiency of hybrid solution methods when incorporated into large‐scale optimization problems solved by evolution strategies (ESs) and to demonstrate their influence on the overall performance of these optimization algorithms. ESs imitate biological evolution and combine the concept of artificial survival of the fittest with evolutionary operators to form a robust search mechanism. In this paper modified multi‐membered evolution strategies with discrete variables are adopted. Two solution methods are implemented based on the preconditioned conjugate gradient (PCG) algorithm. The first method is a PCG algorithm with a preconditioner resulted from a complete Cholesky factorization, and the second is a PCG algorithm in which a truncated Neumann series expansion is used as a preconditioner. The numerical tests presented demonstrate the computational advantages of the proposed methods, which become more pronounced in large‐scale optimization problems and in a parallel computing environment.

Learning improvement of neural networks used in structural optimization

The performance of feed-forward neural networks can be substantially impaired by the ill-conditioning of the corresponding Jacobian matrix. Ill-conditioning appearing in feed-forward learning process is related to the properties of the activation function used. It will be shown that the performance of the network training can be improved using an adaptive activation function with a properly updated gain parameter during the learning process. The efficiency of the proposed adaptive procedure is examined in structural optimization problems where a trained neural network is used to replace the structural analysis phase and capture the necessary data for the optimizer. The optimizer used in this study is an algorithm based on evolution strategies.

Optimum Design of Shell Structures with Stiffening Beams

The optimum design of stiffened shell structures is investigated using a robust and efficient optimization algorithm where the total weight of the structure is to be minimized subject to behavioral constraints imposed by structural design codes. Evolutionary algorithms and more specifically the evolution strategies (ES) method specially tailored for this type of problems is implemented for the solution of the structural optimization problem. The discretization of the stiffened shell is performed by means of cost-effective and reliable shell and beam elements that incorporate the natural mode concept. Three types of design variables are considered: sizing, shape, and topology. A benchmark test example is examined where the efficiency and robustness of ES over other optimization methods is investigated. Two case studies of stiffened shells are subsequently presented, where a parametric study is undertaken to obtain the most efficient design compatible with the regulations suggested by design codes such as Eurocode. The important role of the stiffeners and how they can be optimally chosen to improve the performance of shell structures in terms of carrying capacity and economy is demonstrated.

Fragility Assessment of Steel Frames Using Neural Networks

A neural network–based methodology is proposed for the rapid evaluation of the seismic demand using data extracted from ground motion records. Limit-state fragilities for a moment-resisting steel frame are developed using Monte Carlo simulation. The proposed methodology allows taking into account uncertainties on both structural capacity and seismic demand with reduced computational cost. The use of neural networks is motivated by the approximate concepts inherent in the fragility assessment and the large number of time-consuming nonlinear response history analyses required for the accurate calculation of the probability of a limit-state being exceeded. The trained neural network is used to obtain the level of seismic demand, which is expressed in terms of maximum interstory drift. The methodology proposed is efficient and general in application.

Large scale structural optimization: Computational methods and optimization algorithms

SummaryThe objective of this paper is to investigate the efficiency of various optimization methods based on mathematical programming and evolutionary algorithms for solving structural optimization problems under static and seismic loading conditions. Particular emphasis is given on modified versions of the basic evolutionary algorithms aiming at improving the performance of the optimization procedure. Modified versions of both genetic algorithms and evolution strategies combined with mathematical programming methods to form hybrid methodologies are also tested and compared and proved particularly promising. Furthermore, the structural analysis phase is replaced by a neural network prediction for the computation of the necessary data required by the evolutionary algorithms. Advanced domain decomposition techniques particularly tailored for parallel solution of large-scale sensitivity analysis problems are also implemented. The efficiency of a rigorous approach for treating seismic loading is investigated and compared with a simplified dynamic analysis adopted by seismic codes in the framework of finding the optimum design of structures with minimum weight. In this context a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.

AUTOMATIC MINIMIZATION OF THE RIGIDITY ECCENTRICITY OF 3D REINFORCED CONCRETE BUILDINGS

The objective of this paper is to obtain the optimum design of 3D reinforced concrete buildings in terms of their performance under earthquake loading. This goal is achieved by considering the minimisation of the eccentricity between the mass centre and the rigidity centre of each storey layout as the optimisation objective in order to produce torsionally balanced structures. This problem is considered as a combined topology and sizing optimisation problem. The location and the size of the columns and the shear walls of the structure of each storey layout constitute the design variables. Apart from the constraints imposed by the seismic and reinforced concrete structure design codes, architectural restrictions are also taken into account. The test examples showed that a reduction in the structural cost of the building is achieved by minimising the eccentricity between the mass centre and the rigidity centre of each storey layout. Evolutionary optimisation algorithms and in particular a specially tailored algorithm based on Evolution Strategies is implemented for the solution of this type of structural optimisation problems.

A novel approach for the efficient simulation of highly skewed non-Gaussian stochastic fields

The problem of simulating non-Gaussian stochastic processes and fields has received considerable attention recently in the field of stochastic mechanics. This is due to the fact that several quantities involved in practical engineering problems (e.g. material and geometric properties of structural systems, soil properties in geotechnical engineering applications, wind loads, waves) exhibit non- Gaussian probabilistic characteristics [2].

Seismic Design Procedures in the Framework of Evolutionary Based Structural Optimization

Since the early seventies structural optimization has been the subject of intensive research and several different approaches have been advocated for the optimal design of structures in terms of optimization methods or problem formulation. Most of the attention of the engineering community has been directed towards the optimum design of structures under static loading conditions with the assumption of linear elastic structural behaviour. For a large number of real-life structural problems assuming linear response and ignoring the dynamic characteristics of the seismic action during the design phase may lead to structural configurations highly vulnerable to future earthquakes. Furthermore, seismic design codes suggest that under severe earthquake events the structures should be designed to deform inelastically due to the large intensity inertia loads imposed.