Modeling Structural Tones Extraction as a Combinatorial Optimization Problem

This study investigates the automated extraction of “structural tones” that represent the core features of a melody. Traditional approaches often rely on music theory rules or manual judgment, which makes it difficult to achieve both accuracy and automation. To address this challenge, we formulate structural tones extraction as a combinatorial optimization problem and propose methods based on Simulated Annealing (SA) and the Genetic Algorithm (GA) for solving it. We design a dual-objective cost function that evaluates both melodic similarity and note reduction. The experimental results show that the Genetic Algorithm (GA) exhibits a significant advantage in overall cost, and our method effectively extracts concise and representative structural tones from the music. By comparing the performance of SA and GA, we not only verify the applicability of these two heuristic algorithms in melody simplification but also provide a practical optimization framework for applications in music information retrieval and computer-assisted composition.