Pseudo label estimation based on label distribution optimization for industrial semi-supervised soft sensor

•A pseudo label estimation based on label distribution optimization PLELDO.•A semi-supervised ensemble soft sensor modeling method EnPLELDO.•Optimization problem considers prediction accuracy and variance, performance improvement, and Laplace regularization.•Multi-population strategy and transfer learning for enhancing fitness evaluation efficiency.•The proposed methods are evaluated through an industrial fed-batch fermentation process.