Dynamic multiobjective optimization problems are challenging due to their fast convergence and diversity maintenance requirements. Prediction-based evolutionary algorithms currently gain much attention for meeting these requirements. However, it is not always the case that an elaborate predictor is suitable for different problems and the quality of historical solutions is sufficient to support prediction, which limits the availability of prediction-based methods over various problems. Faced with these issues, this article proposes a knowledge learning strategy for change response in the dynamic multiobjective optimization. Unlike prediction approaches that estimate the future optima from previously obtained solutions, in the proposed strategy, we react to changes via learning from the historical search process. We introduce a method to extract the knowledge within the previous search experience. The extracted knowledge can accelerate convergence as well as introduce diversity for the optimization of the future environment. We conduct a comprehensive experiment on comparing the proposed strategy with the state-of-the-art algorithms. Results demonstrate the better performance of the proposed strategy in terms of solution quality and computational efficiency.

Evolutionary algorithms have shown their promise in coping with many-objective optimization problems. However, the strategies of balancing convergence and diversity and the effectiveness of handling problems with irregular Pareto fronts are still far from perfect. To address these issues, this paper proposes an adaptive sorting-based evolutionary algorithm based on the idea of decomposition. Firstly, we propose an adaptive sorting-based environmental selection strategy. Solutions in each subpopulation (partitioned by reference vectors) are sorted based on their convergence. Those with better convergence are further sorted based on their diversity, then being selected according to their sorting levels. Secondly, we provide an adaptive promising subpopulation sorting-based environmental selection strategy for problems which may have irregular Pareto fronts. This strategy provides additional sorting-based selection effort on promising subpopulations after the general environmental selection process. Thirdly, we extend the algorithm to handle constraints. Finally, we conduct an extensive experimental study on the proposed algorithm by comparing with start-of-the-state algorithms. Results demonstrate the superiority of the proposed algorithm.

This paper aims at solving the sparse reconstruction (SR) problem via a multiobjective evolutionary algorithm. Existing multiobjective evolutionary algorithms for the SR problem have high computational complexity, especially in high-dimensional reconstruction scenarios. Furthermore, these algorithms focus on estimating the whole Pareto front rather than the knee region, thus leading to limited diversity of solutions in knee region and waste of computational effort. To tackle these issues, this paper proposes an adaptive decomposition-based evolutionary approach (ADEA) for the SR problem. Firstly, we employ the decomposition-based evolutionary paradigm to guarantee a high computational efficiency and diversity of solutions in the whole objective space. Then, we propose a two-stage iterative soft-thresholding (IST)-based local search operator to improve the convergence. Finally, we develop an adaptive decomposition-based environmental selection strategy, by which the decomposition in the knee region can be adjusted dynamically. This strategy enables to focus the selection effort on the knee region and achieves low computational complexity. Experimental results on simulated signals, benchmark signals and images demonstrate the superiority of ADEA in terms of reconstruction accuracy and computational efficiency, compared to five state-of-the-art algorithms.