Metaheuristic Approaches to Realistic Portfolio Optimization
  We investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium.   It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times. This approach also copes easily with extensive modifications such as the addition of more intricate constraints, discontinuous variables and more complex objective functions.   The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and should be examined critically. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. The number of assets in a portfolio invariably increases as a result of constraints, costs and their combination.   The implementation of cardinality constraints is essential for finding the best-performing portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features. 
Franco Busetti