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Theoretical Aspects of Evolutionary Multiobjective Optimization---A Review

Optimization problems in practice often involve the simultaneous optimization of 2 or more conflicting objectives. Evolutionary multiobjective optimization (EMO) techniques are well suited for tackling those multiobjective optimization problems because they are able to generate a set of solutions that represent the inherent trade-offs between the objectives. In the beginning, multiobjective evolutionary algorithms have been seen as single-objective algorithms where only the selection scheme needed to be tailored towards multiobjective optimization. In the meantime, EMO has become an independent research field with its specific research questions---and its own theoretical foundations. Several important theoretical studies on EMO have been conducted in recent years which opened up a better understanding of the underlying principles and resulted in the proposition of better algorithms in practice. Besides a brief introduction about the basic principles of EMO, the main goal of this report is to give a general overview of theoretical studies published in the field of EMO and to present some of the theoretical results in more detail. Due to space limitations, we only focus on three main aspects of previous and current research here: (i) performance assessment with quality indicators, (ii) hypervolume-based search, and (iii) rigorous runtime analyses and convergence properties of multiobjective evolutionary algorithms.