我正在尝试实现 D*-Lite 寻路算法,如 Koenig 和 Likhachev 在2002 年针对 Boost::Graph 的文章中所述。我想我已经很好地掌握了它背后的基本思想和理论,但是当Pred
和Succ
集合更新时我在理解上遇到了问题。
我猜它发生在Move to sstart
step in 中Main
,但是第一次调用ComputeShortestPath
将毫无意义?并且该Succ
集合是否应该同时插入Pred
?那么Pred
并且Succ
可以实现为双向链表吗?
我在下面插入了算法的伪代码。和集合分别是前任和后继Pred
。, ,和是不同的成本和权重。是要访问的顶点的优先级队列。Succ
g
h
rhs
c
U
procedure CalculateKey(s)
{01’} return [min(g(s), rhs(s)) + h(sstart, s) + km; min(g(s), rhs(s))];
procedure Initialize()
{02’} U = ∅;
{03’} km = 0;
{04’} for all s ∈ S rhs(s) = g(s) = ∞;
{05’} rhs(sgoal) = 0;
{06’} U.Insert(sgoal, CalculateKey(sgoal));
procedure UpdateVertex(u)
{07’} if (u ≠ sgoal) rhs(u) = min s'∈Succ(u)(c(u, s') + g(s'));
{08’} if (u ∈ U) U.Remove(u);
{09’} if (g(u) ≠ rhs(u)) U.Insert(u, CalculateKey(u));
procedure ComputeShortestPath()
{10’} while (U.TopKey() < CalculateKey(sstart) OR rhs(sstart) ≠ g(sstart))
{11’} kold = U.TopKey();
{12’} u = U.Pop();
{13’} if (kold ˙<CalculateKey(u))
{14’} U.Insert(u, CalculateKey(u));
{15’} else if (g(u) > rhs(u))
{16’} g(u) = rhs(u);
{17’} for all s ∈ Pred(u) UpdateVertex(s);
{18’} else
{19’} g(u) = ∞;
{20’} for all s ∈ Pred(u) ∪ {u} UpdateVertex(s);
procedure Main()
{21’} slast = sstart;
{22’} Initialize();
{23’} ComputeShortestPath();
{24’} while (sstart ≠ sgoal)
{25’} /* if (g(sstart) = ∞) then there is no known path */
{26’} sstart = argmin s'∈Succ(sstart)(c(sstart, s') + g(s'));
{27’} Move to sstart;
{28’} Scan graph for changed edge costs;
{29’} if any edge costs changed
{30’} km = km + h(slast, sstart);
{31’} slast = sstart;
{32’} for all directed edges (u, v) with changed edge costs
{33’} Update the edge cost c(u, v);
{34’} UpdateVertex(u);
{35’} ComputeShortestPath();