We propose a new algorithm for fixed‐charge network flow problems based on ghost image (GI) processes as proposed in Glover (1994) and adapted to fixed‐charge transportation problems in Glover et al. (2005). Our GI algorithm iteratively modifies an idealized representation of the problem embodied in a parametric GI, enabling all steps to be performed with a primal network flow algorithm operating on the parametric GI. Computational testing is carried out on well‐known problems from the literature plus a new set of large‐scale fixed‐charge transportation and transshipment network instances. We also provide comparisons against CPLEX 12.8 and demonstrate that the new GI algorithm with tabu search (TS) is effective on large problem instances, finding solutions with statistically equivalent objective values at least 700 times faster. The attractive outcomes produced by the current GI/TS implementation provide a significant advance in our ability to solve fixed‐cost network problems efficiently and invites its use for larger instances from a variety of application domains.

中文翻译：

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固定费用网络问题的极点禁忌搜索算法

我们在Glover（1994）中提出了一种基于重影（GI）过程的固定费用网络流问题的新算法，并适用于Glover等人的固定费用运输问题。（2005）。我们的GI算法可以迭代地修改参数GI中包含的问题的理想表示形式，从而使所有步骤都可以通过在参数GI上运行的原始网络流算法来执行。针对文献中的已知问题以及一组新的大规模固定收费运输和转运网络实例进行了计算测试。我们还提供了与CPLEX 12.8的比较，并证明了带有禁忌搜索（TS）的新GI算法在大问题实例上有效，找到具有统计等效目标值的解决方案至少快700倍。