This paper addresses exact approaches to multi-agent collective construction problem which tasks a group of cooperative agents to build a given structure in a blocksworld under the gravity constraint. We propose a generalization of the existing exact model based on mixed integer linear programming by accommodating varying agent action durations. We refer to the model as a fraction-time model. The generalization by introducing action duration enables one to create a more realistic model for various domains. It provides a significant reduction of plan execution duration at the cost of increased computational time, which rises steeply the closer the model gets to the exact real-world action duration. We also propose a makespan estimation function for the fraction-time model. This can be used to estimate the construction time reduction size for the purpose of cost-benefit analysis. The fraction-time model and the makespan estimation function have been evaluated in a series of experiments using a set of benchmark structures. The results show a significant reduction of plan execution duration for non-constant duration actions due to decreasing synchronization overhead at the end of each action. According to the results, the makespan estimation function provides a reasonably accurate estimate of the makespan.

翻译：本文研究多智能体集体构造问题的精确解法，该问题要求一组协作智能体在重力约束下于积木世界中构建指定结构。我们提出基于混合整数线性规划的现有精确模型的泛化方法，通过容纳不同的智能体动作持续时间。我们称此模型为分时模型。引入动作持续时间的泛化能够为不同领域创建更现实的模型。该模型以增加计算时间为代价显著缩短计划执行时长，且当模型越接近真实世界动作持续时间时，计算时间增长越陡峭。我们还提出了分时模型的完工时间估计函数，可用于估算建设时长缩减幅度以进行成本效益分析。通过一系列基准结构实验评估，结果表明：由于降低了每个动作结束时的同步开销，非恒定持续时间动作的计划执行时长显著缩短。实验结果证明，完工时间估计函数能提供较为准确的完工时间估算值。