Optimization techniques aim to identify optimal solutions for a given problem. In single-objective optimization, the best solution corresponds to the one that maximizes or minimizes the objective function. However, when dealing with multi-objective optimization, particularly when the objectives are conflicting, identifying the best solution becomes significantly more complex. In such cases, exact or analytical methods are often impractical, leading to the widespread use of heuristic and metaheuristic approaches to identify optimal or near-optimal solutions. Recent advancements have led to the development of various nature-inspired metaheuristics designed to address these challenges. Among these, the Whale Optimization Algorithm (WOA) has garnered significant attention. An adapted version of the WOA has been proposed to handle multi-objective optimization problems. This work extends the WOA to tackle multi-objective optimization by incorporating a decomposition-based approach with a cooperative mechanism to approximate Pareto-optimal solutions. The multi-objective problem is decomposed into a series of scalarized subproblems, each with a well-defined neighborhood relationship. Comparative experiments with seven state-of-the-art bio-inspired optimization methods demonstrate that the proposed decomposition-based multi-objective WOA consistently outperforms its counterparts in both real-world applications and widely used benchmark test problems.

This paper presents an online model-free sensor fault-tolerant control scheme capable of tolerating the most common faults affecting an induction motor. This approach involves using neural networks for fault detection to provide the controller with sufficient information to counteract adverse consequences due to sensor faults, such as degradation in performance, reliability, and even failures in the control system. The proposed approach does not consider the knowledge of the nominal model of the system or when the fault may occur. Therefore, a high-order recurrent neural network trained online by the Extended Kalman Filter is used to obtain a mathematical model of the system. The obtained model is used to synthesize a discrete-time sliding mode control. Then, the fault-detection and -isolation stage is performed by independent neural networks, which have as input the signal from the current sensor and the position sensor, respectively. In this way, the neural classifiers continuously monitor the sensors, showing the ability to know the sensor status. The combination of controller and fault detection maintains the operation of the motor during the time of the fault occurrence, whether due to sensor disconnection, degradation, or connection failure. In fact, the MLP neural network achieves an accuracy between 95% and 99% and shows an AUC of 97% to 99%, and this neural network correctly classifies true positives with acceptable performance. The Recall value is high, between 97% and 99%, and the F1 score confirms a good performance. In contrast, the CNN shows a higher accuracy, between 96% and 99% in accuracy and 98% to 99% in AUC. In addition, its Recall and F1 reflect a better balance and capacity to handle complex data, demonstrating its superiority to MLP in fault classification. Therefore, neural networks are a promising approach in areas such as fault-tolerant control.