Heuristic algorithms for the marking construction problem of Petri nets

Abstract

The marking construction problem (MCP) of Petri nets is defined as follows: "Given a Petri net N, an initial marking M i and a target marking M t , construct a marking that is closest to M t among those which can be reached from M i by firing transitions." MCP includes the well-known marking reachability problem of Petri nets. MCP is known to be NP-hard, and we propose two schemas of heuristic algorithms: (i) not using any algorithm for the maximum legal firing sequence problem (MAX LFS) or (ii) using an algorithm for MAX LFS. This paper proposes two algorithms: MCA for (i) and MC feideq a for (ii), and compares their capability based on computing experiments.

Modeling, Reachability and Controllability of Bounded Petri Nets Based on Semi‐Tensor Product of Matrices

“…See for a comprehensive introduction. While for BPNSs, various approaches of verifying marking reachability problem have been proposed, such as reachability graph , optimization approach , hierarchical reachability graph , heuristic approaches , genetic algorithm , process algebra .…”

Lean reachability tree for Petri net analysis

“…For a bounded net the difficulty of reachability analysis only lies in so-called state explosion [3]. The existing exact methods [5] are less efficient even for the problem of medium scale, while the more efficient heuristics [6], [7] and intelligent algorithms [8] can only achieve approximate solutions. For unbounded nets, the problem becomes more complicated and more difficult to address since their state spaces are not fixed but infinitely grow.…”