Evolutionary Multi/Many-Objective Optimisation via Bilevel Decomposition

Decomposition of a complex multi-objective optimisation problem (MOP) to multiple simple subMOPs, known as M2M for short, is an effective approach to multi-objective optimisation. However, M2M facilitates little communication/collaboration between subMOPs, which limits its use in complex optimisation scenarios. This paper extends the M2M framework to develop a unified algorithm for both multi-objective and many-objective optimisation. Through bilevel decomposition, an MOP is divided into multiple subMOPs at upper level, each of which is further divided into a number of single-objective subproblems at lower level. Neighbouring subMOPs are allowed to share some subproblems so that the knowledge gained from solving one sub-MOP can be transferred to another, and eventually to all the sub-MOPs. The bilevel decomposition is readily combined with some new mating selection and population update strategies, leading to a high-performance algorithm that competes effectively against a number of state-of-the-arts studied in this paper for both multi- and many-objective optimisation. Parameter analysis and component analysis have been also carried out to further justify the proposed algorithm.