Algorithm 1: An algorithm of MADDPG with the $ϵ$-greedy policy for AGVs.

for $j=1$ to max-episode do

Initialization of the parameters

for $t=1$ to M do

for $i=1$ to N do

n = random number

if $n<ϵ$ then

execute any action(a)

else

execute the action which maximizes $Q_t(a)$ with $1-ϵ$

end if

$a_i={\mu }_{\theta i}(o_i)+N_t$

$a=(a_i,\dots ,a_N)$

$r_i=k_{i1}\times D_{position}+k_{i2}\times C_v\times v\times cos(\omega )+k_{i3}\times C_e\times (E_{target}-E_i)+k_{i4}\times C_{AGV}+k_{i5}\times C_{obstacles}$

end for

for agent $i=1$ to N do

$y^j=r_i^j+\gamma Q^{\mu }{}_i^{\prime }(x_j^{\prime },a_1^{\prime },\dots a_N^{\prime })$

$\mathcal{L}({\theta }_i)=\frac{1}{s}{\sum }_j{(y^j-Q_i^{\mu }(x^j,a_1^j,\dots ,a_N^j))}^2$

${\nabla }_{{\theta }_i}J\simeq \frac{1}{s}{\sum }_j{\theta }_i{\mu }_i(o_i^j)a_i{Q}_i^{\mu }(x^j,a_1^j,\dots ,a_i,\dots ,a_N^j)|a_i={\mu }_i(o_i^j)$

end for

for $i=1$ to N do

${\theta }_i^{\prime }<-\tau {\theta }_i+(1-\tau ){\theta }_i^{\prime }$

end for

end for

end for