proc One_City_2_Opt_ND(tour: var Tour_Array;
basePos: Tour_Index;
neighbor: Neighbor_Matrix;
position: var City_Position_In_Tour;
numberOfNeigbors: int;
DontLook: var DLB_Array): bool =
var
improved: bool
pos_Y2, i, j: Tour_Index
X1, X2, Y1, Y2: City_Number
improved = false
block two_loops:
for direction in [forward, backward]:
if direction == forward:
i = basePos
X1 = tour[i]
X2 = tour[(i+1) mod N]
else:
i = (N + basePos - 1) mod N
X2 = tour[i]
X1 = tour[(i+1) mod N] # == tour[basePos]
for neighbor_number in 0 .. numberOfNeigbors-1:
Y1 = neighbor[X1][neighbor_number]
if direction == forward:
j = position[Y1]
Y2 = tour[(j+1) mod N]
else:
j = (N + position[Y1] - 1) mod N # pos[Y1] == j+1
Y2 = tour[j]
if (X2 == Y1) or (Y2 == X1):
continue
if Gain_From_2_Opt(X1, X2, Y1, Y2) > 0:
Set_DLB_off(DontLook, [X1, X2, Y1, Y2])
Make_2_Opt_Move(tour, i, j, position)
improved = true
break two_loops
result = improved
proc LS_2_Opt_ND(tour: var Tour_Array;
neighbor: Neighbor_Matrix;
neighborListLen: int = N-1) =
## Optimizes the given tour using 2-opt with neighbor lists
## and dDon't Look Bits (DLB)
var
locallyOptimal: bool = false
improved: bool
DontLook: DLB_Array
baseCity: City_Number
position: City_Position_In_Tour
let numberOfNeigbors = min(neighborListLen, len(neighbor[0]))
position = Create_Position_In_Tour(tour)
Set_DLB_off(DontLook, tour)
while not locallyOptimal:
locallyOptimal = true
for basePos in 0 .. N-1:
baseCity = tour[basePos]
if isDLB_on(DontLook, baseCity):
continue
improved = One_City_2_Opt_ND(tour, basePos, neighbor, position,
numberOfNeigbors, DontLook)
if not improved:
Set_DLB_on(DontLook, baseCity)
else:
locallyOptimal = false
Hello,
ReplyDeleteI am currently working on my Master's Thesis and this site has helped me a lot. To the best of my knowledge, I have not been able to find so much information about local heuristic search methods for TSP as there is here. In addition, everything is written very clearly and precise. I implemented 2-OPT with DLB and neighbours list as shown in this article and it runs perfect (although I had to debug and change some lines depending on how you treat cities, etc).
Again, thank you very much for your efforts to put up a site like this. May I ask if you work in a Spanish University?
Thank you,
Esteban
I'm glad to hear that, Esteban. No, I don't live nor work in Spain.
ReplyDeleteGreetings,
W.K.