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Physarum solver, also called the physarum polycephalum inspired algorithm(PPA), is a newly developed bio-inspired algorithm that has an inherent abilityto find the shortest path in a given graph. Recent research has proposedmethods to develop this algorithm further by accelerating the original PPA(OPPA)'s path-finding process. However, when does the PPA ascertain that theshortest path has been found? Is there a point after which the PPA coulddistinguish the shortest path from other paths? By innovatively proposing theconcept of the dominant path (D-Path), the exact moment, named the transitionpoint (T-Point), when the PPA finds the shortest path can be identified. Basedon the D-Path and T-Point, a newly accelerated PPA named OPPA-D using theproposed termination criterion is developed which is superior to all otherbaseline algorithms according to the experiments conducted in this paper. Thevalidity and the superiority of the proposed termination criterion is alsodemonstrated. Furthermore, an evaluation method is proposed to provide newinsights for the comparison of different accelerated OPPAs. The breakthrough ofthis paper lies in using D-path and T-point to terminate the OPPA. The noveltermination criterion reveals the actual performance of this OPPA. This OPPA isthe fastest algorithm, outperforming some so-called accelerated OPPAs.Furthermore, we explain why some existing works inappropriately claim to beaccelerated algorithms is in fact a product of inappropriate terminationcriterion, thus giving rise to the illusion that the method is accelerated.

When does the Physarum Solver Distinguish the Shortest Path from other Paths: the Transition Point and its Applications