# Ant's path is constructed by randomly choosing hops.
# Initially, the probabilities are uniformly distributed.
choices =       [c1, c2, ..., cN]
probabilities = [p1, p2, ..., pN]
# After normalization:
[p1, p2, ..., pN] = 1/N

# After an iteration, hops in the top performer's
# path (e.g., c1, c2) receive a probability boost.
choices =       [c1,     c2,     ..., cN]
probabilities = [p1 + x, p2 + x, ..., pN]
# After normalization:
[p1, p2, ..., pN] = [p1 + x, p2 + x, ..., pN]/sum(P)

# Since the first path was chosen randomly,
# the boost shouldn't be excessive.
# A simple model with pheromone deposit and 
# evaporation will do:
deposit = AntHeuristicParams.PHERONOME_DEPOSIT
rate = AntHeuristicParams.PHERONOME_EVAPORATION_RATE
x = deposit + (1 - rate)*current_pheromone 

# Using deposit = 1.0 and evaporation rate = 0.247:
# The boost for hops in the top performer's path:
x = 1.0 + (1 - 0.247)*1.0 = 1.753
# The boost for other hops:
x = (1 - 0.247)*1.0 = 0.753

# These numbers will translate into probabilities below.

# In addition to keeping history of previous choices, 
# path selection is also guided by the energy and time 
# it takes to travel a path. As part of the heuristic, 
# both components depend on the Manhattan distance
# between nodes in the hardware connectivity graph:
e_route = AntHeuristicParams.ENERGY_ROUTE_ONE_BYTE
e_link = AntHeuristicParams.ENERGY_LINK_ONE_BYTE
energy_per_byte = (dist + 1)*e_route + dist*e_link
n_bytes = dag.edges[edge]['weight']
energy_per_transfer = n_bytes*energy_per_byte
tau = 1/energy_per_transfer

t_compute = dag.nodes[node]['weight']
t_communicate = dag.edges[edge]['weight']*dist
time_total = t_compute + t_communicate
phi = 1/time_total 

# Weights alpha and beta adjust the importance of 
# energy and time components respectively:
p = (tau**alpha)*(phi**beta)

# Example calculation with dist=3, n_bytes=1024:
# (plugging in 1 femtojoule per byte for communication
# and a 128-bit bus @ 200MHz for communication):
n_bytes = 1024
dist = 3
e_route = 1
e_link = 1
energy_per_byte = (3 + 1)*1 + 3*1 = 7
energy_per_transfer = 1024*7 = 7168
tau = 1/7168 = 0.000139509
t_compute = 290
t_communicate = 320*3 = 960
time_total = 290 + 960 = 1250
phi = 1/1250 = 0.0008
p = (0.000139509**0.2)*(0.0008**0.2) = 0.0407

# After adding pheromone bias:
# Top performer edges:
p = 0.0407 + 1.753 ≈ 1.7937
# Others:
p = 0.0407 + 0.753 ≈ 0.7937

# The final probabilities after the first iteration 
# (example for a 4x4 mesh / 240 edges and
# a 19-edge graph from the above):
sum_all = 1.7937*19 + 0.7937*221 ≈ 209.49
prob_top = 1.7937 / 209.49 ≈ 0.856%
prob_other = 0.7937 / 209.49 ≈ 0.379%

# In other words, the edges in the top performer's
# path are only about half a percent likelier to be 
# chosen in the next iteration (0.856-0.379=0.477%).

# Sanity check:
19*0.856% + 221*0.379% ≈ 100%

# The algorithm simply iterates from here.