Using harmony search with multiple pitch adjustment operators for the portfolio selection problem

Portfolio selection is an important problem in the financial markets that seeks to distribute an amount of money over a set of assets where the goal is to simultaneously maximize the return and minimize the risk. In this work, we propose a harmony search algorithm (HSA) for this problem. HSA is a population based algorithm that mimics the musician improvisation process in solving optimization problems. At each iteration, HSA generates a new solution using a memory procedure which considers all existing solutions and then perturbs them using a pitch adjustment operator. To deal with different instances, and also changes in the problem landscape, we propose an improved HSA that utilizes multiple pitch adjustment operators. The rationale behind this is that different operators are appropriate for different stages of the search and using multiple operators can enhance the effectiveness of HSA. To evaluate and validate the effectiveness of the proposed HSA, computational experiments are carried out using portfolio selection benchmark instances from the scientific literature. The results demonstrate that the proposed HSA is capable of producing high quality solutions for most of the tested instances when compared with state of the art methods.