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是组合的。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，许多这样的问题属于一类被称为“NP-hard”的问题，这被认为是极难解决的有力证据，而且我们极不可能找到解决这些问题的技术，保证在所有情况下都是实用和有效的。缺乏有效的方法来解决这些问题是非常重要的，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，这些问题的解即使不是最优的，至少保证在最优（最佳）解的一定满意百分比内，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. Our research objective is to enlarge the set of such NP-hard problems arising from applied combinatorial optimization models which can be practically and satisfactorily solved. To achieve this goal we will use the following three approaches: 1) Investigate developing new and improved efficient methods for such problems which provide solutions guaranteed to lie within a satisfactory percentage of the optimal solution. 2) Investigate ways to improve the success rate of current methods which attempt to find an exact optimal solution for such problems. 3) Investigate ways of applying combinatorial optimization models and methods to applications arising in other areas of Computer Science.