Page 101 - Read Online

Page 8 of 19 Mai et al. Intell Robot 2023;3(4):466-84 I http://dx.doi.org/10.20517/ir.2023.37

Equation (15):
 −

 

   0_ < 0

  0 =

− 0 (15)
 0_
 0_ + ≥ 0
  2

 

 0 = 0.7


where isthecurrentnumberofiterations, isthemaximumnumberofiterations, and 0_ istheoriginal
value of 0.
4.2 Dynamically adjusted pheromone update strategy
In traditional ACO algorithms applied to path planning, there is a risk that if the pheromone level on a particu-
larpathbecomesexcessivelyhigh, itcanleadtoahigherprobabilityofsubsequentantschoosingthatpath. This
can constrain exploring other potentially more feasible paths, causing the algorithm to stagnate prematurely.
We have introduced improvements to the pheromone update strategy to address this concern. Specifically, we
now update the pheromone solely on the path traversed by the optimal ant in the current iteration. Addition-
ally, we enforce maximum and minimum limits on the pheromone values to prevent them from becoming
overly dominant or negligible, as shown in Equations (16)-(18):
( + 1) = (1 − ) ( ) + Δ ( ) (16)

Δ ( ) = (17)
(1 − ) +

 ˜
 ( + 1) ≥

 
( + 1) = ˜ ( + 1) < ˜ ( + 1) < (18)



 ˜
 ( + 1) ≤

Among them, Δ represents the change in pheromone concentration between two nodes under the current

optimal path, is the pheromone evaporation parameter, which determines the pheromone attenuation ratio
at the current point after each update, represents the weight of the global optimal fitness value as the basis
for pheromone update, is the pheromone constant. represents the fitness value corresponding to
the current path, and represents the global optimal fitness value. represents the maximum
pheromone concentration, represents the minimum pheromone concentration, and ( + 1) is the
pheromone concentration at the + 1 iteration.

In order to ensure that ants have more opportunities to explore new paths at the beginning of the iteration and
optimize the optimal path in the later stages of the iteration, the probability decreases proportionally as the
number of iterations increases. We set the attenuation ratio, represented as , to 0.9, as shown in Equation
(19):
{
( ) ( , 100) ≠ 0
( + 1) = (19)
( ) ∗ ( , 100) = 0
∈ [0, 1] represents the weight of the global optimal fitness value as the basis for pheromone update.

4.3 Path evaluation function
The heuristic function is crucial in determining the search path, and its strengths and weaknesses directly in-
fluence the algorithm’s convergence speed during iterations. Due to the traditional heuristic function having
fewer constraints, the blind search phenomenon will occur in the early search for ants. Therefore, the algo-
rithm exhibits slow convergence and requires many iterations to reach a solution. Considering the distinctive
application environment of UAVs, this paper introduces an evaluation function grounded in distance, height,