Table 1 Table of notations

A

Geographical area

te

Type of the point

G

Instance of CPP model

sn

Sequentially number of point

\(V_{Ai}\)

A-Type point

\(V_{Ni}\)

N-Type point

NR

NFZ rectangle

\(P_i\)

Planned path

coord(x, y)

Coordinate of point

\(SP_i\)

Sub-path consisting of partial points of the path

\(LS_i\)

line segment

VAS

Set of A-Type points

VNS

Set of N-Type points

NFZS

Set of line segments to define NFZs

\(\nu\)

UAV speed

\(\psi\)

UAV rotation rate

\(\beta\)

Total distance of a path

\(\varphi\)

Total turning angles of a path

\(\Xi\)

Total energy consumption of a path

\(\tau\)

Total completion time of a path

S

The solution archive

n

Number of solutions in solution Archive

m

Number of variables in solution vector

\(s_i\)

The i-th solution int solution archive

\(s_i^j\)

Value of the j-th variable in the i-th solution

\(\omega _i\)

selection weight of the i-th vector in the archive

\(\eta\)

The size of search solution archiving area

C

The self-adaptive parameter archive

Cmax

Array of parameter maximum values

Cmin

Array of parameter minimum values

a

Number of parameters in parameter Archive

b

Number of parameters in parameter vector

\(c_i\)

The i-th parameter vector int archive

\(c_i^j\)

the j-th parameter in the i-th parameter vector

\(\mu\)

the mean value of Gaussian function

\(\sigma\)

the mean square error of Gaussian function

\(d_{ij}^l\)

distance from vertex i to j in the l-th iteration

\(\xi\)

The convergence speed of parameter archive

\(\theta\)

The size of search parameter archiving area

\(\lambda\)

Energy consumption per meter of length

\(\gamma\)

Energy consumption per degree of turn angle

q

Number of ants for each thread

TdNum

Number of parallel threads

Itmax

Maximum number of iterations

Itmax2

Maximum iteration number of finding no better solution

PM

Sub-paths matrix between any two points in VAS after avoiding NFZs