Heuristic optimization of complex constrained portfolio sets with short sales

The problem of portfolio optimization which deals with the twin objectives of minimizing risk and maximizing expected portfolio return can turn complex when constraints that model investor preferences and market norms such as bounding, cardinality and class constraints, and short sales are included in it. A complex-constrained portfolio optimization such as this has been beyond the reach of solution using traditional optimization methods and therefore heuristic methods of solution have been investigated for their efficient solving. In this study we focus on the application of two heuristic methods viz., Evolution Strategy with Hall of Fame and Differential Evolution (rand/1/bin) for the efficient solving of the portfolio optimization problem with the aforementioned nontrivial constraints. Experimental results have been demonstrated on the Bombay Stock Exchange, India (BSE200 index, Period: July 2001-July 2006) and the results obtained by the heuristic methods have been compared with those of Quadratic Programming which becomes applicable on the simplified problem model and yields closed form solutions.