State of the art and future challenges in evolutive algorithms for structural optimization 

Giuseppe Carlo Marano (Politecnico di Torino, Italy) 

Although structural engineering problems are often characterized by significant levels of complexity, they are generally approached and solved by combining several practitioners’ skills, such as mathematical elaborations and physical sense, but also using intuition and experience. This is also the case of problems in large and spatial structures whose solution is generally based on the so-called “engineer’s judgment” as they are quite difficult to be properly described with simply models, that are able to synthetize structural complexity in few mechanical parameters that have a clear meaning in designers’ mind. On the contrary the level of interconnection between a large number of parameters (kinematic, sectional, geometric and so on) usually needs of complex FEM models, accurate but difficult to be used for a synthesis at design stage. Support to early structural design stages should improve the global project’s quality, and in this way structural optimization tools are the natural chose. Optimization is an approach used in many engineering disciplines, and structural engineering is one among them. Topology, geometry and size optimization should be applied to different kinds of structures such as frames, trusses, plates, and shells to achieve minimum cost, weight, or other specific goals. Most design applications in structural engineering involve selecting values for a set of design variables (discrete, continuous or often hybrid) that best describe the behaviour and performance of the particular problem while satisfying the requirements and specifications imposed by codes of practice. A basic understanding of optimization problem specifications and the capabilities and incapability of solution techniques is vital for designers in in this field. In last decades many different kinds of structural optimization problems and solution techniques has been proposed in structural optimization problems, that usually present some serious drawbacks mostly depending on nonlinearity of their objective(s) and constraint(s). They usually have many local minimums, which make them complex and difficult to solve using classical methods. However, no single classic method has been found to be entirely efficient and robust for the wide range of structural optimization problems for complex structures. 

However, heuristic theories and algorithms within the framework of “soft computing” can provide a more rational and systematic way to approach and solve those problems. As a matter of fact, the algorithms have been recently utilized in several branches of structural optimization, and the growing interest from scientific as well as technical community demonstrates that this is a very promising way for a new approach in complex structure design.

This work proposes a state-of-the-art of Genetic algorithms, genetic programming, evolutionary programming, differential evolution and others that are subsets of Evolutionary algorithms (EAs). They have attained intense attention since 1980’s, belonging to a large family of stochastic optimization methods called metaheuristics. These methods do not need any information about shape or smoothness of the function they optimize and on constraints. In a synthetic description they evolve a set of promising candidate solutions (population of individuals) thought finite steps (generation). During each step a new set of individuals is generated and a part or the whole former population is replaced according to some selection criterion Therefore, they are successfully applied especially in areas where smooth optimizations cannot be used, such as complex structural optimization. However, must be stressed that they are not guaranteed to find the optimum: usually, they only converge to some “near-optimal” solution, that has a great importance for early design decision support.

In this work are described the main steps and procedures of evolutive algorithms for structural optimization, their advantages and weakness, and finally further developing in this field are described.

Giuseppe Carlo Marano