The two-archive 2 algorithm (Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence, diversity, and complexity using diversity archive (DA) and convergence archive (CA). However, the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems. The traditional algorithm even cannot converge due to the weak selection pressure. Meanwhile, Two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the algorithm. To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions, an -domination based Two_Arch2 algorithm ( -Two_Arch2) for many-objective problems (MaOPs) is proposed in this paper. In -Two_Arch2, to decrease the computational complexity and speed up the convergence, a novel evolutionary framework with a fast update strategy is proposed; to increase the selection pressure, -domination is assigned to update the individuals in DA; to guarantee the uniform distribution of the solution, a boundary protection strategy based on indicator is designated as two steps selection strategies to update individuals in CA. To evaluate the performance of the proposed algorithm, a series of benchmark functions with different numbers of objectives is solved. The results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with Two_Arch2.

To balance the efficiency and accuracy of a global optimization algorithm in solving electromagnetic inverse problems, a Tabu search method assisted by using a Kriging surrogate model is proposed. To reduce the computational time and speed up the algorithm, the Kriging surrogate model is used to predict the objective space. To ensure the accuracy of the final optimal solution, a united trigger is developed to realize dynamically switching between the prediction and the direct objective computation. To utilize the variable space efficiently and provide proper sampling points to update the Kriging surrogate model, an evaluation list is used to evaluate the variable space. A typical mathematical function and electromagnetic inverse problems in low and high frequency are solved to testify the correctness and effectiveness of the proposed method.