Machine-Learning-Based Constraint Handling for Particle Swarm Optimization Within Structural Optimization

Despite their historical roots and formally rigorous mathematical framework, mathematical programming is often not sufficient to effectively deal with real-world complex optimization problems. For instance, focusing on the structural optimization field, heuristic and meta-heuristic computational intelligence methods represented a promising solution for addressing many real-world challenges since their early conception. Several algorithms have been formulated inspired by mimicking natural phenomena, such as Genetic Algorithms or Simulated Annealing, among others. The lack of a strong mathematical basis motivated the idea of always simultaneously implementing different soft-computing techniques both for comparisons and mutual validation, and also because due to the No-Free Lunch, which demonstrated that the perfect algorithm able to solve any optimization problem does not exist. The study of the animal’s world behavior, i.e. bird flocking or fish schooling, is the main idea behind one of the nowadays still most widely adopted meta-heuristic algorithms, i.e. the particle swarm optimization (PSO) technique. In the beginning, PSO was formulated to solve unconstrained optimization problems only, and later numerous scholars attempted to introduce some new constraint handling mechanisms in order to exploit the PSO's powerful optimization capabilities even with most likely real-world constrained problems. In this study, the authors focused on the constraint handling problem in PSO for solving structural optimization tasks, by leveraging the nowadays new compelling Machine Learning tools offered by the digital revolution currently in progress. Specifically, the authors formulated a new constraint-handling method based on the support vector machine (SVM) classifier to progressively update the feasible search region while the swarm explores the search space. This novel technique has been tested on a structural optimization conceptual design problem of a Warren truss steel bridge.