Conditional Generative Adversarial Network-Based Bilevel Evolutionary Multiobjective Optimization Algorithm

In bilevel multiobjective optimization problems (BLMOPs), the mapping from an upper-level vector to the corresponding lower-level optimal vectors is a complex set valued mapping. Existing methods require numerous surrogate models to fit such a set valued mapping by grouping the lower-level optimal vectors, and the effects are not satisfactory because the correlation among lower-level optimal vectors corresponding to the same upper-level vector is disregarded. In this article, introducing conditional generative adversarial network (cGAN), we use only one surrogate model to effectively fit such a set valued mapping, which extracts knowledge from lower-level optimal vectors corresponding to the same upper-level vector. Then, a BLMOP is transformed into a single-level constraint multiobjective optimization problem (CMOP). By adaptively allocating computational resources to optimize the CMOP, promising upper-level vectors are obtained. Furthermore, a lower-level search is executed for these promising upper-level vectors, thus obtaining high-quality solutions. Because of the excellent performance of cGAN and the lower-level search conducted only for promising upper-level vectors, the computational overhead is greatly reduced. The proposed algorithm has achieved the best results in comparison with five state-of-the-art algorithms on benchmark problems and a real-world problem, whose effectiveness has been demonstrated.