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

许多实际重要的优化问题本质上都是组合优化问题。一些例子包括可靠通信网络的最低成本设计、快速印刷电路板生产、遗传进化树的构建以及各种调度和布线问题的优化。不幸的是，这类问题可能属于一种称为“NP-Hard”的类别，这被认为是它们极难解决的有力证据，而且我们极不可能找到保证在所有情况下都实用和有效的解决它们的技术。缺乏有效的方法来解决这类问题是非常重要的，因为存在需要解决的大规模现实世界实例。幸运的是，在实践中，通常获得这些问题的解就足够了，即使不是最优的，至少可以保证在最优(最佳)解的某个令人满意的百分比内，而在许多情况下，最优(最佳)解是更可行的任务。

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.