A PSO-based framework for nonsmooth portfolio selection problems

We propose a Particle Swarm Optimization (PSO) based scheme for the solution of a mixed-integer nonsmooth portfolio selection problem. To this end, we first reformulate the portfolio selection problem as an unconstrained optimization problem by adopting an exact penalty method. Then, we use PSO to manage both the optimization of the objective function and the minimization of all the constraints violations. In this context we introduce and test a novel approach that adaptively updates the penalty parameters. Also, we introduce a technique for the renement of the solutions provided by the PSO to cope with the mixed-integer framework