Petri Net Induced Heuristic Search for Resource Constrained Scheduling

TL;DR

This paper introduces a Petri net-based heuristic search method for resource-constrained scheduling, outperforming traditional MIP approaches on benchmark problems.

Contribution

It formulates RCPSP as a search over Petri net reachability graphs and develops an A* heuristic combining critical path and resource bounds.

Findings

A* with the new heuristic outperforms MIP baselines in success rate and solve time.

The approach is consistent under token-based time semantics.

Heuristic search and MIP degrade along different problem axes.

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.