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3.3. Differential evolution
Similar to the genetic algorithm, the differential evolutionary algo-
rithm is also a global optimization algorithm consisting of mutation,
crossover and selection operation (
Storn and Price
,
1997
). However,
different from the genetic algorithm, the mutation vector in differential
evolution is generated by the difference vector of the parent generation.
Besides, it intersects with the individual vector of the parent generation
to generate a new individual vector and directly selects with the indi-
vidual of the parent generation. Therefore, the differential evolution
algorithm is expected to be more effective than the genetic algorithm
in path planning.
To improve the performance of differential evolution algorithm in
AUV application, usually the cost function of the algorithm is modi-
fied in consideration of the kinematic constraints of the AUV model
shown in Section
2
. For example, in order to adapt to the complex
environments of AUV path planning,
Zhang et al.
(
2014
) proposed an
adaptive differential evolutionary algorithm. In their method, the cost
function with penalty method takes the curvature constraint caused by
AUV model, path length and energy consumption into account, which
was used to adjust the algorithm’s parameters adaptively according
to the position and size of the obstacles.
Li et al.
(
2014a
) applied
the differential evolution algorithm to the obstacle avoidance task of
AUV. They first classified the obstacles and constructed an avoidance
function with the differential evolution algorithm. They verified the
proposed method by conducting experiments with single and multiple
obstacles on a simulation platform. In addition,
Mahmoud et al.
(
2018
)
used a differential evolution algorithm to optimize the control points of
B-spline generation, which enables AUV to effectively deal with various
obstacles in three-dimensional space. In their method, the penalty
method defined in the cost function takes into account the kinematic
constraints of the AUV on surge, sway, yaw and pitch components, as
well as the constraints on the depth maneuver. In their experiments,
the AUV path planning based on differential evolution algorithm can
make full use of the expected current to deal with the unexpected
current interference. However, the parent individuals generated by the
algorithm are not optimized and the computational efficiency is low.
3.4. Particle swarm optimization
Particle swarm optimization is an evolutionary computing tech-
nique based on random population (
Eberhart and Kennedy
,
1995
),
which is derived from the study of birds’ foraging behavior. When birds
are looking for food, they do not know the specific location of food,
but only know their current locations and the distance from food. Their
search strategy is to find the bird closest to food and walk with it (
Patle
et al.
,
2019
). The flow chart of a particle swarm optimization algorithm
is shown in
Fig. 5
. In
Fig. 5
, ‘‘Pbest’’ is called the individual extremum,
which means the optimal solution found by a particle, and ‘‘Gbest’’
means the optimal solution in the whole particle swarm, namely the
global extremum. The whole process of the particle swarm optimization
algorithm is to use information of the current position X and velocity
V of particles, ‘‘Pbest’’ and ‘‘Gbest’’ to iterate until an optimal solution
is found.
Particle swarm optimization and its most important variant — quan-
tum particle swarm optimization (
Sun et al.
,
2004
) have been widely
applied in various path planning tasks of AUV. For example,
Yang
and Zhang
(
2009
) proposed an adapted inertia-weight particle swarm
optimization algorithm, in which the update of each particle changes
with the evolution of the population. The proposed method considers
the speed and direction of the current in the fitness function of the
algorithm, which not only completes the obstacle avoidance for AUV,
but also enables AUV to work in the presence of strong currents.
Tang
et al.
(
2010
) applied the particle swarm optimization algorithm to
path planning of AUV in 3D environments. In their method, the 3D
space is sliced for dimension reduction, and a path effective function is
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