Petri Net Induced Heuristic Search for Resource Constrained Scheduling

2026-05-15

AI Summary

This study addresses the Resource-Constrained Project Scheduling Problem (RCPSP) by proposing a modeling approach based on timed Petri nets, wherein scheduling decisions are represented as transitions in the state space triggered by relative delay tokens. Building upon this formulation, the authors design an admissible A* heuristic that integrates critical path information with resource-constrained lower bounds to enable efficient optimal search. Experimental results on the PSPLIB benchmark suite demonstrate that the proposed method outperforms state-of-the-art mixed-integer programming solvers such as SCIP and CBC in both solution success rate and computational time. Furthermore, the findings reveal a complementary performance relationship between heuristic search and mixed-integer programming approaches across varying problem scales.

Abstract

We formulate the Resource-Constrained Project Scheduling Problem (RCPSP) as optimal search over the reachability graph of a Timed Transition Petri Net with Resources, using relative-delay tokens so that scheduling decisions correspond to transition firings in the induced state space. We solve the resulting problem with $A^*$ guided by a heuristic that combines Critical Path and resource-based lower bounds, and prove that it is consistent under our token-based time semantics. Experiments on the PSPLIB benchmarks show that the approach outperforms strong exact Mixed-Integer Linear Programming (MIP) baselines (SCIP, CBC) in both success rate and solve time. Per-instance analysis shows that heuristic search and MIP degrade along independent axes, resource tightness for $A^*$ and formulation size for MIP, with resource strength mediating which solver benefits from scale.

Problem

• Resource-Constrained Project Scheduling
• Petri Net
• Heuristic Search
• A* Algorithm
• Scheduling

Innovation

• Petri Net
• Heuristic Search
• Resource-Constrained Scheduling
• A* Algorithm
• Consistent Heuristic