Structural Optimization with Swarm-based Algorithms

The purpose of the present dissertation is not only to introduce different methods for solving optimization problems, but also to expose a new strategy to deal with constrained structural optimization problems which combines modern Artificial Intelligence and machine learning methods. In the first introductory part, the classical resolution methods are exposed mainly focusing on the Lagrange multiplier rule and the most used mathematical programming methods of the past. These approaches, based on the calculation of the gradient of the objective function, usually solve optimization problems in a sequential way. Afterwards, an overview of the most popular modern meta-heuristic approaches to solve optimization problems is presented. Inspired by Nature, these methods are included within the framework of Soft Computing, which is a still very active research sub-field of Artificial Intelligence. The attention is mainly focused on the Particle Swarm Optimization (PSO) algorithm which is based on the emerging intelligent convergent behaviour of a swarm influenced by social and cognitive interactions that are inspired by natural bird flocking behaviour. Originally formalized in 1995, the PSO is nowadays still under study to improve the search process performances. For this reason, many variants and several constraint handling strategies have been developed during the recent years. Although the penalty functions still remain the most adopted indirect method to deal with constrained problems, due to their several drawbacks, in this Thesis a new non-penalty constraint handling approach is discussed. The PSO is thus combined with a constraint handling technique to preserve the feasibility of candidate solutions, which is based on the predictive model generated by the Support Vector Machine (SVM), a machine learning method usually adopted for classification problems. Because of its generality, the constraint handling with SVM appears to be more adaptive both to non-linear and discontinuous boundary. However, to improve the performance of the algorithm, e.g. when the feasible region is little and narrow, a relaxation function of the constraints is also adopted to enlarge the actual search region. In the final part of the present work, to assess the convergence properties of the new PSO-SVM algorithm, two numerical benchmark literature problems, which statements are located into the Appendix A, are discussed and compared in terms of objective function value with the well-known meta-heuristic genetic algorithm (GA) and with a PSO penalty-based. Subsequently, two structural examples are discussed concerning respectively the size optimization of constant cross section simply supported beam and the shape and size optimization of a planar steel warren truss beam with hollow core section profiles. In particular, this latter example highlights not only the importance of the optimization process to get the highest structural performances with the minimum costs, but also that the optimization algorithms represent, from the technical point of view, an essential tool for civil engineers, which strongly influences the decision process during the design phase. Therefore, the optimization algorithms are valuable and essential tools, which support the designers to identify the best technical solution among the infinite possibilities.