Applying Methods from Combinatorial Optimization in Solving Real World Problems

许多重要的实际问题本质上是组合的。这类问题的一些例子包括可靠通信网络的设计、印刷电路板的快速生产、调度问题和路由问题。众所周知，许多此类问题属于“NP-hard”一类，这有力地证明了这些问题极难解决，而且不太可能存在找到最优（即最佳）解决方案的有效技术。缺乏解决这类问题的有效方法是非常重要的，因为存在大规模的、现实世界的实例需要解决。幸运的是，在实践中，这些问题的解通常是令人满意的，即使不是最优解，至少保证在最优解的某个令人满意的百分比范围内。

Many practically important problems are combinatorial in nature. Some examples of such problems include the design of reliable communication networks, fast printed circuit board production, scheduling problems and routing problems. Many such problems are known to belong to a class called "NP-hard", which is strong evidence that these problems are extremely difficult to solve, and that it is unlikely that efficient techniques for finding the optimal (i.e. the best) solution exist. The lack of efficient methods for such problems is of real importance as there exist large scale, real world instances requiring solutions. Fortunately, in practice, it is often satisfactory to obtain solutions for these problems which, if not optimal, are at least guaranteed to lie within a certain satisfactory percentage of the optimal solution.