Mathematical Sciences: Theoretical and Algorithmic Studies in Combinatorial Problem-Solving

数学规划关注的是 函数在许多变量中受到边约束。 组合 优化解决了同样的问题，但增加了复杂性 通过纳入不可分割的活动，即，通过 必须采用整数值的变量。 在纯粹的组合 所有的变量都必须是整数。 自成立以来不久， 第二次世界大战后，数学规划思想已经成为 成功地用于制定和解决许多复杂的规划 问题，应用程序涵盖了整个范围， 从定量社会科学到工程科学。 增加的 数字解决数学规划问题的能力 带来了更大的需求， 规划模型。 这项研究旨在扩大 组合问题解决的计算前沿，以及 实现更好的数学理解的组合 优化问题

Mathematical programming is concerned with the optimization of functions in many variables subject to side constraints. Combinatorial optimization addresses the same problem with an additional complication brought about by the inclusion of indivisible activities, i.e., by variables that must assume integer values. In purely combinatorial problems, all variables must be integer. Since its inception shortly after World War II, mathematical programming ideas have been successfully utilized to formulate and to solve many complex planning problems, with applications covering the entire range from the quantitative social sciences to engineering science. The increased ability to numerically solve mathematical programming problems has brought about a greater demand to incorporate indivisible activities into the planning models. This research aims to extend the computational frontiers of combinatorial problem-solving as well as to achieve a better mathematical understanding of combinatorial optimization problems.