Pareto Set Prediction Assisted Bilevel Bi-objective Optimization

Bilevel optimization problems comprise an upper level optimization task with a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single objective at both levels using evolutionary computation, relatively little work has been reported on addressing problems with multiple objectives (BLMOP) at both levels. For highly non-linear or black-box BLMOPs, the existing evolutionary techniques typically employ nested search, which in its native form consumes large number of function evaluations. In this work, we propose to reduce this expense by predicting the lower level Pareto set for a candidate upper level solution directly, in lieu of performing optimization from scratch. Such prediction is significantly challenging for BLMOPs as it involves one-to-many mapping. To address this challenge, we supplement the dataset using a helper variable and construct a neural network, which can then be trained to map the variables in a meaningful manner. Then, we embed this initialization within a bilevel optimization framework, termed Pareto set prediction assisted evolutionary bilevel multi-objective optimization (PSP-BLEMO). Systematic experiments with existing state-of-the-art methods are presented to demonstrate its benefit in terms of solution quality and computational expense. The experiments show that the proposed approach is competitive across a range of problems, including both deceptive and non-deceptive problems.