Evolutionary rhythm composition with trajectory-based fitness evaluation

Evaluating creativity in musical genetic algorithms (GAs) requires a balance between objective and subjective fitness measures. This research investigates the use of userdefined compositional rules for composition of rhythmic pieces of any length. Complete pieces of music can be created according to personal definitions of creativity without direct human involvement in the evolutionary process. Musical GAs are grouped by their methods of fitness evaluation and the scope of the music they attempt to create. The fitness method can be objective (Dostal 2005) (Horowitz 1994) (Papadopoulos and Wiggins 1998), subjective (Biles 1994), or hybrid (Birchfield 2003) (Jacob 1995) (Todd and Werner 1999) (Tokui and Iba 2000) evaluators. Regardless of the fitness methods used, the majority of musical GAs deal with simplified representations of the search domain by either focusing on generation of rhythmic fragments (Dostal 2005) (Horowitz 1994) (Tokui and Iba 2000) or brief melodic phrases for use in solos or later combination with other phrases (Biles 1994) (Jacob 1995) (Papadopoulos and Wiggins 1998) (Todd and Werner 1999). Few projects have attempted to evolve complete compositional structures with many musical elements (Birchfield 2003). This research is a continuation of work done in the evolution of complete pieces using hybrid fitness evaluation. While previous research on musical GAs has explored the range of possible fitness measures from the subjective (Biles 1994) to the objective (Papadopoulos and Wiggins 1998), most research shows that a hybrid of these extremes provides the best results (Burton and Vladimirova 1999). Subjective fitness evaluation depends on some form of human input to assign fitness values to genetic individuals during the evolutionary process. Human evaluation reduces the complexity of the GA by removing the need to algorithmically parameterize the user's musical preferences. Initial results from subjective evaluation frequently match evaluator preferences, but many generations of repetitive analysis tends to lead to skewed measurements from evaluator fatigue. In general, human evaluation is recognized as a major performance bottleneck (Burton and Vladimirova 1999). Objective fitness measures parameterize subjective quality into objective rules which allow the GA to operate creatively without human input (Burton and Vladimirova 1999). Papadopolous and Wiggins, and Horowitz before them, use collections of rules to limit the search domain to palatable results. The rhythmic elements of these GAs' individuals are evaluated based on length of silences between notes, where notes fall in relation to the downbeat, beat density, and beat repetition (Papadopoulos and Wiggins 1998) (Horowitz 1994). Dostal's GA (2005) depends on an external source of previously composed music for objective evaluation. GAs with objective fitness measures require all objective rules to be statically defined before evaluation can begin. The quality of the resulting individuals depends greatly on which and how many rules are defined. Too few rules will lead to noise while too many rules will result in overly simplistic music. An overabundance of rules can also result in prohibitive computational complexity (Birchfield 2003). Although a wide variety of hybrids exist, two classes of which are the most prominent: trained and evolutionary evaluators. In the case of trained evaluators, an additional machine learning tool, such as a neural network or another GA, is trained to model the user's preferences either through a preprocessing stage with previously selected music (Jacob 1995) or during the evolutionary process itself (Tokui and Iba 2000). Eventually, the learning tools replace the human evaluator thereby automating the evolutionary process. The human must still provide active feedback for a minimum period of time to get the best results. The creativity allowed by the learned rules always depends in part on the initial training set (Jacob 1995). Evolutionary evaluators use an initial set of rules which are passed into the GA either as part of the population or as their own population. Birchfield (2003) encodes fitness rules in a multi-level structural representation such that each structural level contains the rules for the level below. The appropriate initial rules defined by the user allow the system to evolve its own fitness rules along with the population of results. Todd and Werner (1999) employ coevolution of a male and a female population in which the females select males according to the quality of the male songs. As with Birchfield's system, the initial conditions provided for the female selector population determines the eventual success (Todd and Werner 1999). To isolate the effectiveness of the fitness methods from potential problems caused by an exponentially complex search domain, this research focuses solely on the generation of rhythmic music. An “individual” in a population is a two-dimensional matrix or pattern with a