The ASTSPP has been unattended in the past despite its high practical importance for real-time navigation in digital traffic nets! We are given a graph G with asymmetric arc weights, start point s, target point t, and a subset S ⊆ V(G). The objective is to find a shortest route from s to t in G visiting all nodes of S at least once. The proposed deterministic solution approach relies
(a) on an Advanced Scan of Spanning Trees applied to approximate Steiner trees T⊂ G spanning S, (b) on a Tree Structure Adaption that overcomes “flaws” of T hampering good results and (c) on a Confined Complete Enumeration that rearranges the sequence of the last n≤ 6 stopovers of S, each time a new successor x ∈ S has been found.
The implemented algorithm shows a maximal sample standard deviation q-max ≤ 1,86 % and it remains real-time capable for |S| < 150. It complies with demands for using graphs that must not necessarily be complete (e.g. traffic maps), that have generally asymmetric arc weights, and that have not to comply with the triangle inequality. It satisfies the request to evenhandedly compute near-optimal round trips (s= t) as well general routes (s≠ t) without any special precaution.
Keywords: Asymmetric Steiner Traveling Salesman Path ProblemScheduled
TB3 TSP and its variants
June 10, 2021 11:15 AM
3 - TC Koopmans