Bilevel Evolutionary Multi-objective Algorithm with Multiple Lower-level Search Modes

In bilevel optimization, the upper-level optimization problem (ULOP) requires to be solved under the constraint of the inner lower-level optimization problem (LLOP). However, it is computationally expensive to always consider the constraint caused by the LLOP in a higher priority because heavy evaluation budgets are required for validating the constraint satisfaction. From this aspect, this paper investigates bilevel evolutionary multi-objective optimization with multiple lower-level search modes (BLEMO-MLS). Assisted by self-learning and reinforcement, BLEMO-MLS could adaptively adjust the priority of considering more on the upper-level objective optimization or the constraint caused by the LLOP. In BLEMO-MLS, three lower-level search modes are designed to handle the constraint caused by the LLOP. The former two search modes have higher priorities on the satisfaction of the constraint caused by the LLOP, where lower-level decisions of solutions are optimized by a hybrid lower-level search method, while the last search mode has a higher priority on the upper-level objective optimization with the constraint caused by the LLOP temporarily ignored. Through self-learning and reinforcement, BLEMO-MLS dynamically selects proper lower-level search modes in the bilevel optimization process, aiming to obtain approximate bilevel Pareto-optimal solutions fulfilling the constraint caused by the LLOP as much as possible. Compared with five existing bilevel evolutionary algorithms, BLEMO-MLS could effectively solve bilevel multi-objective optimization problems with function evaluations saved in both levels.