An adaptive large neighborhood search for the multiple-day music rehearsal problems

Abstract

This paper presents an Adaptive Large Neighborhood Search (ALNS) framework to solve the Multiple-Day Music Rehearsal Problem (MMRP), where music pieces with different player sets and durations are arranged in a predefined number of rehearsal days so that the total days of attendance and waiting times experienced by all players are minimized. Two variants of the MMRP, namely the MMRP without setup times (MMRP-0) and the MMRP with setup times (MMRP-1), are herein explored based on mathematical formulations of the Capacitated Vehicle Routing Problem (CVRP) and the Music Rehearsal Problem (MRP). Extensive computational results on 120 generated instances and 78 benchmark instances indicate that the ALNS is greatly efficient as it can provide equivalent or better solutions than the exact method and a benchmark heuristic from the literature, with much less computational time. We also find that the ALNS tends to perform better in large and complicated MMRP settings, considering that it outperforms the time-restricted CPLEX in 34 out of 120 generated instances and successfully finds 4 new best-known solutions to 8 large benchmark instances.