Note—Response to “A Note on ‘The Formulation of the M-Salesman Traveling Salesman Problem’”

Abstract

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Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems

“…SmTSP and many of its variants continued being modeled using integer programming. Most of these formulations were based on transformations to TSP [11][12][13][14][15][16][17][18][19], and only a few were direct [20,21]. Some variants included the case where at most m salespersons are in the solution; some refer to such variant as the SmTSP with fixed charges [13], and others as variable SmTSP [22].…”

“…The main attribute of the proposed IPs is adding vertices to the input graph, which has become a common practice [5,[10][11][12]. The added vertices are usually of two types: exact copies of an actual depot (part of the input) or dummy depots.…”

A Discussion on the physics of the solar atmosphere - Solar flares

“…(1) The (cool) optical (Ha) flare, apparent from its emission lines in the visible spectrum. The parameters of the optical flare have been described by Svestka (1976), particularly note worthy is the very small effective thickness, being of the order of tens of kilometres.…”