Shortest Path Simplex Algorithm with a Multiple Pivot Rule: a Comparative Study

This paper introduces a new shortest path simplex pivot rule choosing a subset of non-basic arcs to simultaneously enter into the basis. The term multiple pivot for this operation is used. From this concept, a generic shortest path simplex algorithm with multiple pivots is described. In addition, a simplex multiple pivot rule is provided to design a shortest path simplex algorithm requiring O(n) multiple pivots and running in O(nm) time. Finally, the results of an experimental analysis performed to study the computational effort of a shortest path simplex algorithm using this pivot rule are reported. This experiment reveals the efficiency of the rule when it is compared with other known efficient shortest path simplex algorithms in the literature.