Strong and efficient filtering algorithms for scheduling constraints

调度是确定操作、任务或活动的集合应该以什么顺序执行的过程，以便它们的执行所需的资源不会过载。这些任务通常受到各种约束，并且问题带有优化标准。调度问题通常是NP难的，需要特殊的技术来有效地解决。约束编程（CP）是一种从人工智能中产生的技术，它被证明可以非常有效地解决调度问题。尽管最近取得了进展，但工业问题仍然难以解决。由于计算时间长，求解器在找到最优解之前就停止了，因此返回的次优调度可能会导致机场延误或装配线空闲时间。如果开发出更快的求解器，这些不便就可以避免。约束规划在解决调度问题上的成功来自于它的过滤算法，该算法对调度约束进行推理以修剪搜索空间。这些算法应用几个过滤规则的基础上放松的调度问题。如果调度问题的宽松版本禁止任务在给定时间开始，求解器可以安全地丢弃这些解决方案，并花费时间探索搜索空间的另一部分。通过改进过滤规则使用的松弛，可以过滤搜索空间的更大部分，从而加快求解过程。该计划的长期目标是提高基于约束的调度器的速度，以便在合理的时间内找到大型和复杂的最优调度。这是通过实现三个次级目标来实现的。* 1)基于比现有算法实现更多过滤的更强松弛来设计过滤算法;*2）基于知道客观标准的松弛来设计过滤算法;*3）设计更快的过滤算法。**我们提出了一个研究计划，将充分培养2个新的博士学位。学生，3个新的硕士生，并允许一个实际的博士学位。学生完成论文。此外，该计划还为本科生提供3个实习机会。**一名硕士生和一名博士生将开发更强的弛豫，这将提供更好的搜索空间修剪。一个新的博士还有一个即将毕业的博士学生将研究适应客观标准的过滤规则。最后，两名硕士生将研究更快的算法，以执行现有的过滤规则。

Scheduling is the process of determining in what order a collection of operations, tasks, or activities should be executed so that the resources required for their executions are not overloaded. The tasks are generally subject to a variety of constraints and the problem comes with an optimization criteria. Scheduling problems are generally NP-Hard and require special techniques to be efficiently solved. Constraint Programming (CP) is a technique issued from artificial intelligence that proved itself very efficient to solve scheduling problems.******Despite recent advances, industrial problems remain hard to solve. Due to long computation times, solvers are halted before the optimal solution is found and therefore return sub-optimal schedules that can cause delays in airports or idle times on an assembly line. These inconveniences would be avoided if faster solvers were developed.******The success of constraint programming for solving scheduling problems comes from its filtering algorithms that reason over the scheduling constraints to prune the search space. These algorithms apply several filtering rules based on a relaxation of the scheduling problem. If the relaxed version of the scheduling problem forbids a task to start at a given time, the solver can safely discard these solutions and spend time exploring another part of the search space. By improving the relaxation used by the filtering rules, it is possible to filter larger portions of the search space and therefore to speed up the solving process.******The long-term objective of this program is to increase the speed of constraint-based schedulers to find large and complex optimal schedules in a reasonable time. This is achieved by fulfilling 3 sub-objectives.***1) Designing filtering algorithms based on stronger relaxations that achieve more filtering than existing ones;***2) Designing filtering algorithms based on relaxations that are aware of the objective criterion;***3) Designing faster filtering algorithms.******We propose a research program that will fully train 2 new Ph.D. students, 3 new master students, and allow one actual Ph.D. student to complete his thesis. Moreover, this program offers 3 internships for undergrad students.******One master and one doctoral student will develop stronger relaxations that will offer a better pruning of the search space. One new Ph.D. and one finishing Ph.D. student will work on filtering rules that are adapted to the objective criterion. Finally, two master students will work on faster algorithms that enforce existing filtering rules.**