In this paper we propose a dual ascent heuristic for solving the linear relaxation of the generalized set partitioning problem with convexity constraints, which often models the master problem of a column generation approach. The generalized set partitioning problem contains at the same time set covering, set packing and set partitioning constraints. The proposed dual ascent heuristic is based on a reformulation and it uses Lagrangian relaxation and subgradient method. It is inspired by the dual ascent procedure already proposed in literature, but it is able to deal with right hand side greater than one, together with under and over coverage. To prove its validity, it has been applied to the minimum sum coloring problem, the multi-activity tour scheduling problem, and some newly generated instances. The reported computational results show the effectiveness of the proposed method.

在本文中，我们提出了一种用于解决具有凸约束的广义集划分问题的线性松弛的对偶启发式算法，该方法通常模拟列生成方法的主要问题。广义集合划分问题同时包含集合覆盖，集合打包和集合划分约束。拟议的双重上升启发法基于重新公式化，并使用拉格朗日松弛法和次梯度法。它受到文献中已经提出的双重上升程序的启发，但是它能够处理大于一的右手边以及覆盖范围不足和覆盖范围过大的问题。为了证明其有效性，已将其应用于最小和着色问题，多活动巡回调度问题以及一些新生成的实例。