大学课程排课中的分解、重构与潜水
Decomposition, Reformulation, and Diving in University Course Timetabling
摘要：
在许多现实生活中的优化问题中，解决方案中有多个相互作用的组件。例如，不同的组件可以指定对不同种类资源的分配。通常，每个组件与不同的软约束集相关联，因此与软约束违反的不同度量相关联。然后，目标是最小化这些措施的线性组合。本文研究了这样的问题，这可以被认为是多个目标/值限制的子模型的多阶段开发的方法。在这种方法中，只有一个计算上困难的组成部分的问题和相关的子集的目标被认为是在第一。这将产生部分解，在完整问题的搜索空间中定义有趣的邻域。通常，可以选择初始组件，以便在第一阶段执行变量聚合，并且保证接下来要探索的邻域包含可行的解决方案。使用整数规划，就可以很容易地实现生产解决方案，其质量的界限。我们的研究是在2007年国际排课比赛中使用的大学课程排课问题，也被称为乌迪内课程排课问题。在所提出的启发式，一个目标限制的邻域生成器产生的分配期间的事件，与两个周期相关的软约束的违反数量减少。这些被放松到事件到天的分配，这定义了更容易搜索所有四个软约束的社区。所有子问题的可编程公式，并使用CPLEX 11的EQUIPMENT进行评估。分析和讨论了这种方法的更广泛适用性。
英文摘要：
In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
