Optimized pseudo code for D*Lite

Question

I'm looking at the optimized version of the DLite:

procedure CalculateKey(s)
{01”} return [min(g(s), rhs(s)) + h(s_start, 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(s_goal) = 0;
{06”} U.Insert(s_goal, [h(s_start, s_goal); 0]);

procedure UpdateVertex(u)
{07”} if (g(u) != rhs(u) AND u ∈ U) U.Update(u,CalculateKey(u));
{08”} else if (g(u) != rhs(u) AND u /∈ U) U.Insert(u,CalculateKey(u));
{09”} else if (g(u) = rhs(u) AND u ∈ U) U.Remove(u);

procedure ComputeShortestPath()
{10”} while (U.TopKey() < CalculateKey(s_start) OR rhs(s_start) > g(s_start))
{11”} u = U.Top();
{12”} k_old = U.TopKey();
{13”} k_new = CalculateKey(u));
{14”} if(k_old < k_new)
{15”}   U.Update(u, k_new);
{16”} else if (g(u) > rhs(u))
{17”}   g(u) = rhs(u);
{18”}   U.Remove(u);
{19”}   for all s ∈ Pred(u)
{20”}   if (s != s_goal) rhs(s) = min(rhs(s), c(s, u) + g(u));
{21”}   UpdateVertex(s);
{22”} else
{23”}   g_old = g(u);
{24”}   g(u) = ∞;
{25”}   for all s ∈ Pred(u) ∪ {u}
{26”}   if (rhs(s) = c(s, u) + g_old)
{27”}     if (s != s_goal) rhs(s) = min s'∈Succ(s)(c(s, s') + g(s'));
{28”}   UpdateVertex(s);

procedure Main()
{29”} s_last = s_start;
{30”} Initialize();
{31”} ComputeShortestPath();
{32”} while (s_start != s_goal)
{33”} /* if (g(s_start) = ∞) then there is no known path */
{34”}   s_start = argmin s'∈Succ(s_start)(c(s_start, s') + g(s'));
{35”}   Move to s_start;
{36”}   Scan graph for changed edge costs;
{37”}   if any edge costs changed
{38”}     km = km + h(s_last, s_start);
{39”}     s_last = s_start;
{40”}     for all directed edges (u, v) with changed edge costs
{41”}       c_old = c(u, v);
{42”}       Update the edge cost c(u, v);
{43”}       if (c_old > c(u, v))
{44”}         if (u != s_goal) rhs(u) = min(rhs(u), c(u, v) + g(v));
{45”}       else if (rhs(u) = c_old + g(v))
{46”}         if (u != s_goal) rhs(u) = min s'∈Succ(u)(c(u, s') + g(s'));
{47”}       UpdateVertex(u);
{48”}     ComputeShortestPath()

I can't guess why at line 44 and 46 is evaluated the same condition (if u ~= s_goal). Wouldn't be possible to evaluate this before entering in the the if/if else that appear in line 43 and 45? Could it be :

if  (u != s_goal)
if (c_old=c(u,v))
  rhs(u)=min(rhs(u),c(u,v)+g(v));
elseif (rhs(u)=c_old + g(v))
  rhs(u)=min_s'(c(u,s')+g(s'))

would it be wrong?

Regards

score 0 · Accepted Answer · answered Apr 12 '12 at 13:26

0

That looks as though it would work, but if u is s_goal only rarely, then you've added one test to almost every iteration where rhs does not need updating to save a couple instructions overall in space and time.

answered Apr 12 '12 at 13:26

oldboy

514
3
4

I think I understand your point, you mean that since the `(if (u != s_goal))` condition is true in the majority of time is supposed to be nested in another if condition that has lower "probability" to be true, in this way there's the highest percentage of probability to skip its evaluation? – Ned112 Apr 13 '12 at 00:04

Optimized pseudo code for D*Lite

1 Answers1