Redução de dimensionalidade em problemas com muitos objetivos: uma aplicação em composição algorítmica

Abstract

In a real-world environment, it is usually necessary to consider many objectives in an optimization problem. This work describes an approach based on Harmony Trees for the treatment of a many-objective problem. The technique of Harmony Trees is then applied to a algorithmic composition problem for tonal music. The technique of Harmony Trees is gives a visual representation of conflict existent between solutions for a problem. With the amount of harmony and conflict between objectives as well as the position of those features it is possible to infer the potential of reducibility for the objectives, visualize the relation between those objectives, and make the decision making process easier. From an analysis of metrics which can be employed for the evaluation of melodies, we survey the literature to create many objectives to be considered simultaneously for a problem of generating melodies. In this case, we present metrics that consider pitch, tonality, rhythm, and patterns. Some metrics are based on psychology while others are based on musical rules. By transforming those metrics into concrete objectives, Harmony Trees are used to explain the relation between the objectives with practical solutions.