A multi-objective differential evolution algorithm for 4-voice compositions

In this paper we explore the use of differential evolution for the musical problem called unfigured bass harmonization: a bass line is given and the composer has to write other 3 voices to have a complete 4-voice piece of music with a 4-note chord for each bass note. Solving such a problem means finding appropriate chords to use for each bass note and also find a placement of the four notes within each chord so that melodic concerns are addressed. Other papers have tackled this problem using evolutionary algorithms. In this paper we show how we can improve on these algorithms using differential evolution. In our algorithm we follow the standard differential evolution strategy but we also use customizations specific to the problem considered. We have implemented in Java our algorithm and we have run several tests to evaluate it. The results show that the differential approach allows us to improve on previous algorithms.