Exploiting the Combinatorial Structures Found in Constraint Programming Models as Multivariate Distributions

许多经济部门依赖于我们解决复杂组合问题的能力，以便以最好的方式计划、组织或安排他们的活动。例如：根据护士的个人技能和偏好安排护士的时间，使其能够满足预计的病人护理需求，并将病人分配给护士，以实现工作量的平衡；或者规划森林道路网络的建设，以便采伐和运输木材，设计采伐地点和工厂之间的卡车路线，并为卡车和装载机建立同步时间表。在实现这一目标的计算机化方法中，约束规划使用一种暴露其大部分结构的形式化方法来表示问题。这项研究建议以更深入的方式使用这种结构，以提高我们解决组合问题的能力。实现这一总体目标的任何进展都可以适用于这些部门，因此可以对我们的生产力和福祉产生重大影响。

Many sectors of the economy rely on our ability to solve complex combinatorial problems in order to plan, organize, or schedule their activities in the best way possible. For example: scheduling nurses in a hospital according to their individual skills and preferences so that they cover the forecast demand in patient care, and assigning patients to them so as to achieve a balanced workload; or planning the construction of a forest road network in order to harvest and then transport the lumber, designing truck routes between harvesting sites and mills, and building synchronized schedules for trucks and loaders. Among the computerized methods to accomplish this, Constraint Programming represents the problem using a formalism that exposes much of its structure. This research proposes to use that structure in a deeper way in order to improve our ability to solve combinatorial problems. Any progress towards that general goal can apply to each of these sectors and therefore can have a significant impact on our productivity and well being.