Advancing 4-Part Evolutionary Harmony Through Analysis of Human–Machine Approaches to Teaching–Learning

This work explores the challenges related to the 4-part harmony problem, addressing both the computational complexity of the search space and the benefits of integrating human teaching/learning processes into evolutionary problem-solving approaches. From a computational perspective, we analyze strategies to enhance algorithm efficiency, including parallelization, precomputation of fitness values, directed mutation, and adaptive directed mutation, which collectively reduce the time required to find solutions. Synthetic harmonic models are employed to validate these techniques. Complementing this, we investigate the role of human expertise, emphasizing the synergy between expert teaching and the learning processes of novice students. By examining how human teaching and learning paradigms can inspire innovative problem-solving techniques, we draw on the concept of evolutionary machine teaching, which reduces the search space, applied here to a standard harmonic model. Our findings highlight the potential of integrating computational advancements with methodologies driven by human learning. Specifically, the search space produced by Sharpmony students accounts for less than 1% of the total space. Using this approach, we have achieved a fourfold speedup over previous results of the same quality. Moreover, longer runs of the new approach have provided solutions with an average fitness of less than 1 error, considering the complete set of 50 rules and exceptions.