A∗-based construction of decision diagrams for a prize-collecting scheduling problem

New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

“…The former method dominated the latter in providing quality solutions for instances with less than 100 jobs, while the opposite was more often true for instances with 100 to 300 jobs. To our knowledge, the state-of-the art algorithm for the PC-JSOCMSR is presented in Horn et al (2021a). It relies on relaxed and restricted MDDs build with a TDC procedure that uses a A* search principle and cost-based filtering procedures to remove arcs in the MDDs.…”

“…As mentioned by Horn et al (2021a), the PC-JSOCMSR is a resource-constrained project scheduling problem (RCPSP) with fixed time lags between some of the tasks and the objective of minimizing a weighted sum of tardy jobs. To understand this, each job j P J is split into three tasks with the adequate precedence constraints.…”

“…It has application in particle therapy scheduling (Maschler and Raidl, 2020) and in pre-runtime scheduling of avionic systems. We refer to the work Horn et al (2021a) for details about these real-world applications (see §3.3 of the previously cited work).…”

Improving the filtering of Branch-And-Bound MDD solver (extended)

“…More recently, Horn et al explored an idea in [25] which closely relates to RUB. They use "fast-to-compute dual bounds" as an admissible heuristic to guide the compilation of MDDs in an A* fashion for the prize-collecting TSP.…”

“…It prunes portions of the state space during the MDD construction, similarly to when RUB is applied. Our approach differs from that of [25] in that we attempt to incorporate problem specific knowledge in a framework that is otherwise fully generic. More precisely, it is perceived here as a problem-specific pruning that exploits the combinatorial structure implied by the state variables.…”