The integral simplex using decomposition (ISUD) algorithm was recently developed to solve efficiently set partitioning problems containing a number of variables that can all be enumerated a priori. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution depending on the stopping criterion used. In this paper, we develop an integral column generation (ICG) heuristic that combines ISUD and column generation to solve set partitioning problems with a very large number of variables. Computational experiments on instances of the public transit vehicle and crew scheduling problem and of the airline crew pairing problem involving up to 2000 constraints show that ICG clearly outperforms two popular column generation heuristics (the restricted master heuristic and the diving heuristic). ICG can yield optimal or near-optimal solutions in less than 1 hour of computational time, generating up to 300 integer solutions during the solution process.

中文翻译：

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集合划分问题的整体列生成

最近开发了使用分解的整体单纯形法（ISUD），以解决有效设置的分区问题，该问题包含许多可以先验枚举的变量。该原始算法生成具有降低成本的整数解序列，这取决于所使用的停止准则而导致了最优或接近最优的解。在本文中，我们开发了一种集成列生成（ICG）启发式方法，该方法将ISUD和列生成相结合，以解决具有大量变量的集合分区问题。对涉及多达2000个约束的公交车辆和机组调度问题以及航空公司机组配对问题实例的计算实验表明，ICG明显优于两种流行的列生成启发式算法（受限主启发式算法和潜水启发式算法）。ICG可以在不到1小时的计算时间内产生最佳或接近最佳的解，在解过程中最多生成300个整数解。