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。我们的研究目标是扩大这类问题的集合，这些问题可以得到实际和满意的解决。为了实现这一目标，我们将使用以下三种方法：1)研究使用问题的密切相关松弛来开发新的、有效的方法，这些方法提供的解保证在最优解的满意百分比范围内。2)利用问题的底层组合结构，为改进特定问题的隐式枚举方案提供必要的工具。3)研究构建和应用组合优化模型在其他计算机科学领域的应用。

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.Our research objective is to enlarge the set of such problems which can be practically and satisfactorily solved.  To achieve this objective we will use the following three approaches:1)  Investigate using closely-related relaxations of a problem to develop new, efficient methods which provide solutions which are guaranteed to lie within a satisfactory percentage of the optimal solution.2)  Exploit the underlying combintorial structure of a problem to provide the necessary tools for improved problem-specific implicit enumeration schemes for certain problems of interest.3)  Investigate constructing and applying combinatorial optimization models for applications arising in other areas of computer science.