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Firstly formulated to solve unconstrained optimization problems, the common way to solve constrained ones with the metaheuristic particle swarm optimization algorithm (PSO) is represented by adopting some penalty functions. In this paper, a new nonpenalty-based constraint handling approach for PSO is implemented, adopting a supervised classification machine learning method, the support vector machine (SVM). Because of its generality, constraint handling with SVM appears more adaptive both to nonlinear and discontinuous boundary. To preserve the feasibility of the population, a simple bisection algorithm is also implemented. To improve the search performances of the algorithm, a relaxation function of the constraints is also adopted. In the end part of this paper, two numerical literature benchmark examples and two structural examples are discussed. The first structural example refers to a homogeneous constant cross-section simply supported beam. The second one refers to the optimization of a plane simply supported Warren truss beam. The obtained results in terms of objective function demonstrate that this new approach represents a valid alternative to solve constrained optimization problems even in structural optimization field. Furthermore, as demonstrated by the Warren truss beam problem, this new algorithm provides an optimal structural design which represents also a good solution from the technical point of view with a trivial rounding-off that does not jeopardize significantly the optimization design process.

This work focuses on the proposal and the evaluation of a new consolidation system for prestressed reinforced concrete (PRC) beams of girder bridges. The system consists of two arch-shaped steel trusses placed alongside the lateral faces of the beam to beconsolidated. The arches develop longitudinally along the entire span of the beam and in elevation using the available height of the PRC cross section. The consolidation system is characterized by its own external constraints, independent from those serving the pre-existing element. The efficiency of the system with respect to parameters variability is described also focusing on the ratio between the load discharged by the consolidation system and the total applied load. Referring to a case study, the consolidation of a PRC beam is presented adopting the proposed system with respect to the usually adopted external prestressing technique. The cross sections properties of the steel arch shaped trusses are defined by means of a structural optimization process using a genetic algorithm, identifying the minimum steel consumption. Finally, a preliminary cost-benefit analysis is performed for the proposed solution for a comparison with other commonly adopted techniques.

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The present paper discusses about optimal shape solution for a non-prismatic planar beam. The proposed model is based on the standard Timoshenko kinematics hypothesis (i.e., planar cross-section remains planar in consequence of a deformation, but it is able to rotate with respect to the beam center-line). The analytical solution for this type of beam is thus used to obtain deformations and stresses of the beam, under different constraints, when load is assumed as the sum of a generic external variable vertical one and the self-weight. The solution is obtained by numerical integration of the beam equation and constraints are posed both on deflection and maximum stress under the hypothesis of an ideal material. The section variability is, thus, described assuming a rectangular cross section with constant base and variable height which can be described in general with a trigonometric series. Other types of empty functions could also be analyzed in order to find the best strategy to get the optimal solution. Optimization is thus performed by minimizing the beam volume considering the effects of non-prismatic geometry on the beam behavior. Finally, several analytical and numerical solutions are compared with results existing in literature, evaluating the solutions’ sensibility to some key parameters like beam span, material density, maximum allowable stress and load distribution. In conclusion, the study finds a critical threshold in terms of emptying function beyond which it is not possible to neglect the arch effect and the curvature of the actual axis for every different case study described in this work. In order to achieve this goal, the relevance of beam span, emptying function level and maximum allowable stress are investigated.

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method.

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This paper discusses the size and shape optimization of a guyed radio mast for radiocommunications. The considered structure represents a widely industrial solution due to the recent spread of 5G and 6G mobile networks. The guyed radio mast was modeled with the finite element software SAP2000 and optimized through a genetic optimization algorithm (GA). The optimization exploits the open application programming interfaces (OAPI) SAP2000-Matlab. Static and dynamic analyses were carried out to provide realistic design scenarios of the mast structure. The authors considered the action of wind, ice, and seismic loads as variable loads. A parametric study on the most critical design variables includes several optimization scenarios to minimize the structure’s total self-weight by varying the most relevant parameters selected by a preliminary sensitivity analysis. In conclusion, final design considerations are discussed by highlighting the best optimization scenario in terms of the objective function and the number of parameters involved in the analysis.