CP or DP? Why Not Both: A Case Study in the Partial Shop Scheduling Problem
For researchers in combinatorial optimization, this work demonstrates a viable integration of DP and CP, though the performance is not state-of-the-art for the specific problem.
The paper proposes a hybrid approach combining Dynamic Programming (DP) and Constraint Programming (CP) for the Partial Shop Scheduling Problem, using DP as the search framework and CP for constraint propagation. The method is flexible and supports anytime strategies and Large Neighborhood Search, but is not competitive with state-of-the-art pure CP solvers.
Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined effectively and elegantly, with DP serving as the primary search framework and CP used as a subroutine to leverage global constraint propagation. This paper presents such an approach for the Partial Shop Scheduling Problem (PSSP), for which a pure DP method has previously been proposed, and efficient CP filtering algorithms are available. The PSSP is a general scheduling problem where each job consists of a set of operations with arbitrary precedence constraints. The approach is flexible enough to accommodate anytime DP strategies, such as anytime column search, whereas the original DP algorithm operated in a strictly layer-wise manner. Moreover, the flexibility of the CP modeling makes it straightforward to incorporate arbitrary precedence constraints. As a result, the model naturally handles any precedence graph and even enables the design of a Large Neighborhood Search (LNS) scheme, in which the DP model is reused, and partial-order schedules are imposed across restarts to improve the incumbent solution. While not competitive with state-of-the-art pure CP solvers for this specific problem, our primary contribution is demonstrating the viability of this hybrid integration.