Binary differential evolution strategies

Differential evolution has shown to be a very powerful, yet simple, population-based optimization approach. The nature of its reproduction operator limits its application to continuous-valued search spaces. However, a simple discretization procedure can be used to convert floating-point solution vectors into discrete-valued vectors. This paper considers three approaches in which differential evolution can be used to solve problems with binary-valued parameters. The first approach is based on a homomorphous mapping, while the second approach interprets the floating-point solution vector as a vector of probabilities, used to decide on the appropriate binary value. The third approach normalizes solution vectors and then discretize these normalized vectors to form a bitstring. Empirical results are provided to illustrate the efficiency of both methods in comparison with particle swarm optimizers.