MILP-Based Lick Sequencing for 12-Bar Blues Guitar Solos: An Empirical Scalability Study

This study examines the computational scaling of mixed-integer linear programming (MILP) for 12-bar blues guitar-solo generation. A Python/PuLP implementation uses CBC to select and order licks under duration, turnaround, repetition, pause, and connectivity constraints. Transitions receive deterministic rule-based scores. The 7 baseline configurations contain 100 sampled instances each, yielding 693 proven-optimal completions, 6 timeouts, and 1 error. Among completed runs, larger candidate sets have lower mean and median transition scores and higher optimization times. Standard errors, bootstrap confidence intervals, distributional diagnostics, and nonparametric comparisons characterize these results. A paired sensitivity study uses 100 candidate instances per pool to vary repetition and pause limits. Relaxing the repetition limit substantially reduces transition scores across all pools, while runtime decreases in Moderate and increases in Fast. Relaxing the pause limit produces smaller score improvements. The released implementation exports MusicXML outputs and records the information needed to reproduce sampled instance.