Explainable nature-inspired optimization via virtual and actual multi-objective strategies to establish a smart earthquake early warning system

Geosynthetic-reinforced soil (GRS) structures are considered for reducing displacement and providing economical reinforcement solutions. The risk assessment of these structures against earthquakes, based on the prediction of seismic sliding displacement, is a major challenge in this field. Multi-objective optimization is a powerful machine learning tool for selecting efficient features for high-performance forecasting. This research investigates two strategies based on swarm intelligence and genetic programming for a comprehensive evaluation. These frameworks integrate multiobjective optimization algorithms and Newmark methods for utilizing effective physics-informed features. The first strategy is virtual multi-objective (VMO) optimization by applying particle swarm optimization (PSO) based on minimizing one function via variations of other functions. In this approach, the error function, as a computational error object, is minimized versus the nomination of interpretable feature space as a computational cost object through the virtual Pareto front. The second strategy is actual multi-objective (AMO) optimization by exploiting nondominated sorting genetic algorithm II (NSGA-II) based on minimizing several functions simultaneously with two various approaches, including bi-objective and many-objective algorithms through actual Pareto-optimal solutions. In this approach, the computational error value, computational cost value, and computational time value are minimized at the same time. The main novelty of the first technique is low computational complexity, resulting in high speed due to definite search space dimension-based exploration and exploitation to forecast seismic sliding displacement, whereas the major achievement of the second technique is high computational accuracy due to multiobjective structure-assisted exploitation and exploitation. Through numerical validation by employing the Newmark methods, the resultant model predicts the seismic sliding displacement of these structures using two algorithms efficiently. Nevertheless, both strategies have good performance for intelligent forecasting. The actual many-objective optimization algorithm is a more effective switchable machine learning tool based on the proposed adaptable performance index for developing a smart earthquake early warning software that can precisely detect imminent natural hazards.