Feature Extraction for Recommendation of Constrained Multiobjective Evolutionary Algorithms

The evolutionary algorithm recommendation is catching increasing attention when solving practical application problems since different algorithms often perform differently on different problems. To achieve the algorithm recommendation, extracting effective features to accurately characterize the problems is necessary, which is related to the feature extraction problem. So far, most feature extraction methods focus on single-objective optimization problems, and only a few studies are conducted on multiobjective optimization problems and constrained optimization problems, let alone constrained multiobjective optimization problems (CMOPs) that are widely encountered in the real world. To fill the gap, this article proposes an evolution-based constrained multiobjective feature extraction method (ECMOFE), in which the information generated in the evolutionary process is leveraged to form the feature matrix. To be specific, we create two populations to, respectively, optimize constraints and objectives for some generations. Furthermore, two complementary evolutionary operators are used to generate offspring for each population. In the environmental selection, the successful rate of offspring individuals generated by each operator of each population is recorded to form the feature matrix. Then, a dimension reduction method is designed to compress the size of the feature matrix. By the above process, the feature vector that can reflect the global relationship between constraints and objectives and the difficulty of the CMOP is formed. Based on the formed features, several algorithm recommendation methods are built on the basis of classifiers. The results based on multiple metrics show the effectiveness of the proposed ECMOFE.