Comput Manag Sci (2011) 8:259–279 DOI 10.1007/s10287-009-0113-8 ORIGINAL PAPER Multiobjective evolutionary algorithms for complex portfolio optimization problems Konstantinos P. Anagnostopoulos · Georgios Mamanis Received: 23 October 2009 / Accepted: 4 November 2009 / Published online: 18 November 2009 © Springer-Verlag 2009 Abstract This paper investigates the ability of Multiobjective Evolutionary Algo- rithms (MOEAs), namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm (PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), for solving complex portfolio optimization prob- lems. The portfolio optimization problem is a typical bi-objective optimization prob- lem with objectives the reward that should be maximized and the risk that should be minimized. While reward is commonly measured by the portfolio’s expected return, various risk measures have been proposed that try to better reflect a portfolio’s risk- iness or to simplify the problem to be solved with exact optimization techniques efficiently. However, some risk measures generate additional complexities, since they are non-convex, non-differentiable functions. In addition, constraints imposed by the practitioners introduce further difficulties since they transform the search space into a non-convex region. The results show that MOEAs, in general, are efficient and reliable strategies for this kind of problems, and their performance is independent of the risk function used. Keywords Multiobjective optimization · NSGA-II · PESA · Portfolio selection · SPEA2 K. P. Anagnostopoulos · G. Mamanis (B ) Department of Production and Management Engineering, Democritus University of Thrace, Xanthi, Greece e-mail: gmamanis@pme.duth.gr K. P. Anagnostopoulos e-mail: kanagn@civil.duth.gr 123