Algorithm 1 The procedure of MA*-3DDV-Hop.

Initialization: The number of nodes M, the beacon nodes N, communication radius $R\mathrm{c}$

Input: Parameter settings of MA*-3DDV-Hop and the experimental area; Parameter settings of MA*-3DDV-Hop: see Table 1; Experimental area is 100 × 100 × 100 ${\mathrm{m}}^3$

1: Generate simulated 3D random topology scene;

2: Calculate the hop-count value $Ho{p}_i^j\_pre$ according to the shortest path algorithm;

3: Calculate the hop-count value $Ho{p_i}^j\_A*$ according to the shortest path algorithm again combination with Equations (7) and (8);

4: for k = 1 to M do

5:  for i = 1 to M do

6:   for j = 1 to M do

7:    if h(x) < min(h(x)) then

8:     Min(h(x)) = h(x);

9:     $\mathrm{Min}\left(\mathrm{h}\right(\mathrm{x}\left)\right)\_\mathrm{index}=\mathrm{points}\left(\mathrm{i}\right);$;

10:    end if

11:   end for

12:   F(x) = g(x) + min(h(x));

13:   num = num + 1;

14:  end for

15: end for

16: Calculate the average distance per hop; $H\mathit{op}siz{e}_i\_A*\_M\_A\mathrm{ve}$, according to Equations (9)–(11);

17: Calculate the unknown distances; According to Equation (12);

18: Calculate the coordinate;

19: Calculate the fitness of objective function using Equation (14), fast non-dominated sort, selection, crossover, mutation. Execution NSGA-II algorithm see Table 1;

20: lb = S(i,:)-r;

21: ub = S(i,:)+r;

22: ……….

23: end