The implicit parallelism of a population in evolutionary algorithms (EAs) provides an ideal platform for dealing with multiple tasks simultaneously. However, little effort has been made to explore what information among different tasks can be used as valuable knowledge to help the optimization of different tasks. This paper proposes a multiobjective multitask optimization evolutionary algorithm based on decomposition with dual neighborhoods (MTEA/D-DN), in which the neighborhood is used as a bridge to achieve knowledge transfer among different tasks. In MTEA/D-DN, each subproblem not only maintains a neighborhood (internal neighborhood) within its own task based on the Euclidean distance between weight vectors, but also keeps a neighborhood (external neighborhood) with the subproblems of other tasks via grey relation analysis in order to mine valuable information and communicate among tasks. Experimental studies show that our proposed algorithm outperforms five other state-of-the-art algorithms on a set of benchmark test instances and a real-world problem in steel plant.

In the blast furnace ironmaking process, accurate prediction of silicon content in molten iron is of great significance for maintaining stable furnace conditions, improving hot metal quality, and reducing energy consumption. However, most of the current research works employ linear correlation coefficient methods to select input features in modeling, which may not fully take the nonlinear and coupling relationships between features into account. Therefore, this article considers the input feature selection issue of silicon content prediction model from a new perspective and proposes a multiobjective evolutionary nonlinear ensemble learning model with evolutionary feature selection mechanism (MOENE-EFS), in which extreme learning machine is adopted as the base learner. MOENE-EFS takes the input feature scheme of each base learner as well as their network structure and parameters as decision variables and proposes a modified nondominated sorting differential evolution algorithm to optimize two conflicting objectives, i.e., accuracy and diversity of base learners, simultaneously. Through the optimization, a set of Pareto optimal base learners with high accuracy and strong diversity can be obtained. Moreover, different from the linear ensemble methods commonly used in classical evolutionary ensemble learning, this article proposes a nonlinear ensemble method to combine the obtained base learners based on differential evolution. Experimental results indicate that the two proposed strategies, i.e., evolutionary feature selection and nonlinear ensemble, are very effective in improving the accuracy and stability of the prediction model. MOENE-EFS also outperforms the other prediction models in both benchmark data and practical industrial data. Furthermore, analysis on the input features of all Pareto optimal base learners shows that the evolutionary feature selection is capable of selecting essential features and is consistent with human experience, which indicates it is a promising method to deal with the input feature selection issue in silicon content prediction.