Improved Heuristic Algorithms for Minimizing Initial Markings of Petri Nets

The minimum initial marking problem MIM of Petri nets is described 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." This paper proposes two heuristic algorithms AAD and AMIM+ and shows the following (1) and (2) through experimental results: (1) AAD is more capable than any other known algorithm; (2) AMIM+ can produce M0, with a small number of tokens, even if other algorithms are too slow to compute M0 as the size of an input instance gets very large.