Binary Differential Evolution

The ability of differential evolution (DE) to perform well in continuous-valued search spaces is well documented. The arithmetic reproduction operator used by differential evolution is simple, however, the manner in which the operator is defined, makes it practically impossible to effectively apply the standard DE to other problem spaces. An interesting and unique mapping method is examined which will enable the DE algorithm to operate within binary space. Using angle modulation, a bit string can be generated using a trigonometric generating function. The DE is used to evolve the coefficients to the trigonometric function, thereby allowing a mapping from continuous-space to binary-space. Instead of evolving the higher-dimensional binary solution directly, angle modulation is used together with DE to reduce the complexity of the problem into a 4-dimensional continuous-valued problem. Experimental results indicate the effectiveness of the technique and the viability for the DE to operate in binary space.