Discrete versus continuous parametrization of bank credit rating systems optimization using differential evolution

Bank credit rating system is a clustering problem that aims to achieve the optimal classification of the clients' probability of defaults (PDs) into discrete buckets under a number of constraints. This global optimization problem can be parametrized either using continuous or discrete decision variables, and treated using basically the same differential evolution (DE) method that takes into account of real-world constraints imposed by the recent Basel Accord on Banking Supervision. This enables us to make interesting comparisons between continuous versus discrete parametrization of the same problem in terms of the efficiency, robustness and the rate of convergence. It turns out to be beneficial to use discrete parameters for all of these reasons. In addition we have also explored the use of the elitist as well as the classic strategies within the DE approach. The former choice turns out to perform better in terms of efficiency, robustness, and faster convergence, except when the number of required buckets is large.