Effective Identification of Lower-Level Optimal Solutions via Discriminator of Conditional Generative Adversarial Network
提出一种改进的条件生成对抗网络训练机制，利用多个生成器构建参考分布，使判别器能有效识别下层最优解，从而改变双层多目标优化问题的嵌套结构，实现上下层同步优化，显著降低计算开销。
Bilevel multiobjective optimization problem (BLMOP) can be seen as a special constrained multiobjective optimization problem (CMOP), where the optimality constraint of the lower-level (LL) problem cannot be easily and quickly checked, but must be verified by solving the LL problem. If there was a relatively simple alternative formulation for effectively identifying LL optimal solutions, the abovementioned special constraint could become as simple as the usual constraints and the nested optimization structure of BLMOP would be altered, which can greatly improve efficiency and effectively find LL optimal solutions with excellent upper-level (UL) performance. In this article, we improve the training mechanism for conditional generative adversarial network (cGAN) by introducing multiple generators to construct a reasonable reference distribution, so as to prevent the discriminator from performance degradation. With a discriminator identifying LL optimal solutions effectively, the nested optimization structure of BLMOP is altered by adding the objective that maximizing the discriminator output score into the UL objectives and removing the LL optimality constraint, realizing synchronous optimization of UL and LL vectors. The cooperation of generators and discriminator greatly reduces the computational overhead for solving BLMOPs. The proposed algorithm has achieved the best or competitive results in comparison with 6 state-of-the-art algorithms and a nested method on benchmark problems and a real-world problem, whose effectiveness has been demonstrated.