The marking construction problem (
MCP) of Petri nets is defined as follows: “Given a Petri net
N, an initial marking
Mi and a target marking
Mt, construct a marking that is closest to
Mt among those which can be reached from
Mi 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 (
MAXLFS) or (ii) using an algorithm for
MAXLFS. Moreover, this paper proposes four pseudo-polynomial time algorithms:
MCG and
MCA for (i), and
MCHFk and
MC_feideq_a for (ii), where
MCA (
MC_feideq_a, respectively) is an improved version of
MCG (
MCHFk). Their performance is evaluated through results of computing experiment.
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