Applying Methods from Combinatorial Optimization in Solving Large-Scale Real World Problems

许多实际上重要的优化问题是组合的性质。一些例子包括可靠通信网络的最小成本设计，快速印刷电路板生产，遗传进化树的构建以及各种调度和路由问题的优化。不幸的是，可能这样的问题属于一类所谓的“NP难”，这被认为是强有力的证据，他们是非常难以解决的，这是极不可能的，我们将找到解决这些问题的技术，保证是实用和有效的在所有情况下。由于存在需要解决方案的大规模、真实的世界实例，因此缺乏针对这些问题的有效方法是非常重要的。幸运的是，在实践中，通常足以获得这些问题的解决方案，如果不是最佳的，至少保证位于最佳（最佳）解决方案的某个满意百分比内，这在许多情况下是更可行的任务。

Many practically important optimization problems are combinatorial in nature. Some examples include the minimum cost design of reliable communication networks, fast printed circuit board production, the building of genetic evolutionary trees as well as the optimization of various scheduling and routing problems. Unfortunately, may such problems belong to a class called "NP-hard", which is considered strong evidence that they are extremely difficult to solve, and that it is highly unlikely that we will find techniques for solving them that are guarantee to be practical and efficient in all cases. The lack of efficient methods for such problems is of significant importance as there exist large-scale, real world instances requiring solutions. Fortunately, in practice, it is often sufficient to obtain solutions for these problems which, if not optimal, are at least guaranteed to lie within a certain satisfactory percentage of the optimal (best) solution, which in many cases is much more viable task.