PSO and Harmony Search Algorithms for Cardinality Constrained Portfolio Optimization Problem

Markowitz cardinality constraint mean-variance (MCCMV) model is a well studied and important one in the portfolio optimization literature. It is formulated as mixed integer quadratic programming problem (MIQP) which belongs to class of NP-hard problems, thus various heuristic and meta-heuristic algorithms are applied to solve it. In this paper, two modified versions of particle swarm optimization (PSO) and harmony search (HS) algorithms are applied to solve the underlying problem. In the proposed PSO algorithm, modifications in inertia weight and learning coefficients are done and in the modified HS algorithm, modifications in harmony memory consideration rate, pitch adjustment rate, and bandwidth are done. Experimental results on five data sets that includes 31 assets up to 225 assets show that the modified HS algorithm is much faster than the modified PSO, specially on large data sets.