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) This work has been supported by the French national research agency (ANR) within the SYSCOMM project ANR-08-SYSC-017. In addition, the author would like to thank his former employer ETH Zurich for the support during the literature research and Anne Auger for her assistance in writing the mandatory French title and abstract. ∗ INRIA Saclay—Île-de-France, projet TAO, Bat 490, Université Paris-Sud, 91405 Orsay Cedex, France, [email protected], http://www.lri.fr/∼brockho/ † The selection of the papers presented here is made as broad and objective as possible although such an overview can never be exhaustive. In particular, the author tried to collect all studies containing theoretical results on EMO published at the major conferences in the field, i.e., FOGA (1999–2009), EMO (2003–2009), GECCO, and CEC (2005–2009) as well as in all journal volumes of the IEEE Transactions on Evolutionary Computing and the Evolutionary Computation Journal. Furthermore, the EMOO web page http://www.lania.mx/∼ccoello/ EMOO/ built the basis of the selection.