ABSTRACT

In the inverse optimization problem, we modify parameters of the original problem at minimum total cost so as to make a prespecified solution optimal with respect to new parameters. We extend in this paper a class of inverse single facility problems on trees, including inverse balance point, inverse 1-median and inverse 1-center problem, and call it the inverse stable point problem. For the general situation where variables are both edge lengths and vertex weights under an extension of Chebyshev norm and bottleneck Hamming distance, we first derive an algorithm that reduces the corresponding problem to the one under either Chebyshev norm or bottleneck Hamming distance and then develop an approximation approach for the problem. Special cases concerning the problem under this extension with strongly polynomial time algorithms are also discussed.

摘要

在逆优化问题中，我们以最小的总成本修改原始问题的参数，以使预先指定的解决方案对于新参数是最优的。我们在本文中扩展了一类树上的逆单设施问题，包括逆平衡点、逆1-中值和逆1-中心问题，并称其为逆稳定点问题。对于在切比雪夫范数和瓶颈汉明距离的扩展下变量既是边长又是顶点权重的一般情况，我们首先推导出一种算法，将相应问题简化为切比雪夫范数或瓶颈汉明距离下的问题，然后开发一个近似值问题的方法。还讨论了在此扩展下具有强多项式时间算法的问题的特殊情况。