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.

本文提出了一个自适应大邻域搜索（ALNS）框架来解决多天音乐排练问题（MMRP），其中具有不同播放器集和持续时间的音乐作品按预定义的排练天数进行排列，从而使出勤的总天数并且将所有玩家经历的等待时间降到最低。MMRP的两个变体，即不带建立时间的MMRP（MMRP-0）和带建立时间的MMRP（MMRP-1），是基于能力车辆路径问题（CVRP）和音乐排练问题的数学公式进行探索的（MRP）。在120个生成的实例和78个基准实例上的大量计算结果表明，ALNS可以提供​​比精确方法和文献中的基准启发法等价或更好的解决方案，因此效率非常高，用更少的计算时间。我们还发现，ALNS在大型和复杂的MMRP设置中往往表现更好，因为它在120个生成的实例中有34个优于时间受限的CPLEX，并成功地为8个大型基准实例找到了4个新的最著名的解决方案。