The minimum initial marking problem of Petri nets (
MIM) is defined as follows: “Given a Petri net and a firing count vector
X, find an initial marking
M0, with the minimum total token number, for which there is a sequence δ of transitions such that each transition
t appears exactly
X(
t) times in δ, the first transition is enabled at
M0 and the rest can be fired one by one subsequently.” In a production system like factory automation, economical distribution of initial resources, from which a schedule of job-processings is executable, can be formulated as
MIM.
AAD is known to produce best solutions among existing algorithms. Although solutions by
AMIM+ is worse than those by
AAD, it is known that
AMIM+ is very fast. This paper proposes new heuristic algorithms
AADO and
AMDLO, improved versions of existing algorithms
AAD and
AMIM+, respectively. Sharpness of solutions or short CPU time is the main target of
AADO or
AMDLO, respectively. It is shown, based on computing experiment, that the average total number of tokens in initial markings by
AADO is about 5.15% less than that by
AAD, and the average CPU time by
AADO is about 17.3% of that by
AAD.
AMDLO produces solutions that are slightly worse than those by
AAD, while they are about 10.4% better than those by
AMIM+. Although CPU time of
AMDLO is about 180 times that of
AMIM+, it is still fast: average CPU time of
AMDLO is about 2.33% of that of
AAD. Generally it is observed that solutions get worse as the sizes of input instances increase, and this is the case with
AAD and
AMIM+. This undesirable tendency is greatly improved in
AADO and
AMDLO.
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