Keywords: structural optimization, evolution strategies, genetic algorithms, discrete and continuous formulations, trusses and frames.

Recently, a group of global and heuristic search and optimization techniques known as evolutionary algorithms (EAs) have attracted a substantial interest from the researchers in almost all fields of optimization. Evolutionary strategies (ESs), together with genetic algorithms (GAs) and evolutionary programming (EP), are known as the three main instances of these techniques. The underlying idea in all the three algorithms is the same, that is, they are based on mimicking natural evolution and adaptation within a population, which consists of a number of individuals representing a possible solution to a given problem. Depending on the particular algorithm some of the probabilistic operators, such as recombination, mutation, selection, etc., are used to evolve the population such that the individuals attain increasingly better fitness values, where fitness of an individual is a measure of how good the solution is.

Amongst EAs, mostly GAs have been applied to a variety of complex real-world problems, including those of structural optimization, and are shown to be very successful in producing useful solutions. However, the use of ESs especially in optimum structural design problems is very limited [1,2,3]. The main concern of this paper is to explore the potential use of ESs in structural optimization; in particular, the discrete and continuous variable based weight optimum design of trusses and frames. As in most optimum structural design problems, this problem is posed as a typical non-linear programming problem with a number of possibilities for the objective function, a very large number of constraints and mixed design variables, creating a large and complex search space. The paper focuses on the suitability (advantages and certain drawbacks) of using ESs in such a problem and discusses and comments on the main components of ESs for computer implementation, which are tested on selected numerical examples producing very successful results.

In the light of the three illustrative examples discussed in the paper, it is shown that the ES is a promising algorithm in dealing with discrete, continuous and mixed structural optimization problems resulting in complex design spaces. The underlying reason for the encouraging performance observed in this study is attributed to the initial design independency and global nature of the algorithm, which are common to all evolutionary algorithms, and in fact which reflect their advantages over the gradient-based techniques. Additionally, the self-adaptation of strategy parameters in ES emerges as the most striking property of the algorithm. As noted in the paper, the evolutionary operators i.e., mutation and recombination are not only applied to design variables but also to strategy parameters. Accordingly, depending on the characteristics of the design space, strategy parameters adapt themselves during the search process. Nevertheless, still the main disadvantage of ES, and in fact of all the algorithms mimicking natural processes, is that the number of evaluations to reach an optimum solution is generally high. This drawback is reasonably acceptable for discrete problems where gradient-based methods cannot compete. The integration of approximate analysis techniques to the algorithm may be considered as a remedy to decrease the computational effort, especially in dealing with continuous problems.

1

Thierauf, G., Cai, J., "Parallel Evolution Strategy for Solving Structural Optimization", Engineering Structures, 19, 318-324, 1997. doi:10.1016/S0141-0296(96)00076-4

2

Papadrakakis, M., Lagaros, N.D., "Advanced Solution Methods in Structural Optimization based on Evolution Strategies", Engineering Computations, 15, 12-34, 1998. doi:10.1108/02644409810200668

3

Lagaros, N.D., Papadrakakis, M., Kokossalakis, G., "Structural Optimization using Evolutionary Algorithms", Computers & Structures, 80, 571-589, 2002. doi:10.1016/S0045-7949(02)00027-5

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