Discrete disordered systems: extremes, algorithms, and optimization.

优化是对极值的研究——以一种或另一种形式，它在理论和应用科学探究中无处不在。在组合优化中，人们可能希望最小化访问一组固定城市时所走的总距离（旅行推销员问题），或者最小化确保从一个城市开车到任何另一个城市所需的沥青总里程（最小生成树问题）。在整数规划中，人们希望用最少的单元数来满足需求；也许是城市交通系统中需要的公共汽车数量，或者是完全覆盖城市所需的手机信号塔数量。举一个更有机的例子，考虑一下河流系统的轨迹，它在通往海洋的途中迂回曲折，绕过障碍物。河流的路线不是欧几里得最短路径，但它是最优的，至少在局部，它近似地最小化了水从源头到海洋的轨迹所消耗的能量。

Optimization is the study of extreme values – in one form or another, it is ubiquitous in both theoretical and applied scientific inquiry. In combinatorial optimization one might wish to minimize the total distance travelled when visiting a fixed set of cities (the travelling salesman problem) or the total miles of asphalt required to ensure one can drive from one city to any other (the minimum spanning tree problem). In integer programming one wishes to satisfy demand using a minimum number of units; perhaps, the number of busses needed in an urban transit system, or the number of cell towers required for full coverage of a city. For a more organic example, consider the trajectories of river systems, which twist and turn around obstacles en route to the ocean. A river's route is not a Euclidean shortest path, but it is optimal in that, at least locally, it approximately minimizes the energy expended by the water in its trajectory from source to sea.