A novel semi-supervised learning method is proposed to better utilize labeled and unlabeled samples to improve classification performance. However, there is exists the limitation that Laplace regularization in a semi-supervised extreme learning machine (SSELM) tends to lead to poor generalization ability and it ignores the role of labeled information. To solve the above problems, a Joint Regularized Semi-Supervised Extreme Learning Machine (JRSSELM) is proposed, which uses Hessian regularization instead of Laplace regularization and adds supervised information regularization. In order to solve the problem of slow convergence speed and the easy to fall into local optimum of marine predator algorithm (MPA), a multi-strategy marine predator algorithm (MSMPA) is proposed, which first uses a chaotic opposition learning strategy to generate high-quality initial population, then uses adaptive inertia weights and adaptive step control factor to improve the exploration, utilization, and convergence speed, and then uses neighborhood dimensional learning strategy to maintain population diversity. The parameters in JRSSELM are then optimized using MSMPA. The MSMPA-JRSSELM is applied to logging oil formation identification. The experimental results show that MSMPA shows obvious superiority and strong competitiveness in terms of convergence accuracy and convergence speed. Also, the classification performance of MSMPA-JRSSELM is better than other classification methods, and the practical application is remarkable.

The transient search algorithm (TSO) is a new physics-based metaheuristic algorithm that simulates the transient behavior of switching circuits, such as inductors and capacitors, but the algorithm suffers from slow convergence and has a poor ability to circumvent local optima when solving high-dimensional complex problems. To address these drawbacks, an improved transient search algorithm (ITSO) is proposed. Three strategies are introduced to the TSO. First, a chaotic opposition learning strategy is used to generate high-quality initial populations; second, an adaptive inertia weighting strategy is used to improve the exploration ability, exploitation ability, and convergence speed; finally, a neighborhood dimensional learning strategy is used to maintain population diversity with each iteration of merit seeking. The Friedman test and Wilcoxon’s rank sum test were also used by comparing the experiments with recently popular algorithms on 18 benchmark test functions of various types. Statistical results, nonparametric sign tests, and convergence curves all indicate that ITSO develops, explores, and converges significantly better than other popular algorithms, and is a promising intelligent optimization algorithm for applications.

In the transmission and distribution system, the high-energy consumption of the low-voltage circuit breaker easily leads to the decrease of the distribution efficiency of the system. Therefore, on the basis of calculating the internal power consumption of circuit breakers, combining with several factors affecting the energy consumption of circuit breakers, the low-energy consumption mathematical model of circuit breakers is built, and an improved whale optimization algorithm (LA-WOA) is proposed for optimization. The Lévy flight mechanism and the adaptive weight factor are introduced into the traditional whale algorithm to enhance the global and local search ability of the algorithm and also improve the convergence speed and accuracy of the algorithm. The test function simulation experiment proves that the improved algorithm has better performance than other algorithms. Furthermore, the improved LA-WOA algorithm is used to iteratively solve the low-energy consumption mathematical model of the circuit breaker. The experimental results show that the improved algorithm obtains a lower-energy consumption value, which can effectively improve the design efficiency and accuracy of the circuit breaker.