## 4 Conclusions  
This paper proposes a two-objective integer linear programming (ILP) model of open-path multi-depot asymmetric traveling salesman problem (OP-MDATSP) for the multi-robot task assignment in an intelligent warehouse. The theoretical bound on the computational time complexity of this model is \(O(n!)\). Then, we transfer the two-objective linear integer programming model to a single-objective model using the linear weight method. We solve this single-objective model on a small-scale problem using the Gurobi solver, and we compare the results with the nearest distance-based single-task assignment method. The values of the minimum sum-of-cost and makespan obtained based on the ILP model are much lower than those of the the nearest-distance-based single-task assignment (STA). After testing eight kinds of different multi-chromosome coding-based genetic algorithms in four small-scale experiments, we find that two genetic algorithms, EGA and NSGA3, perform relatively better. We use them to solve the large-scale problems. The results of the large-scale experiments show that the two genetic algorithms can solve large-scale problems well. This shows that the multi-robot task assignment method proposed in this paper has great practical significance for the intelligent warehouse to reduce its operating cost. In addition, we can adjust the weight coefficients in the objective function of this paper according to the needs of the actual scene.  
For the following work, we will consider the path conflicts between robots during the task assignment of the intelligent warehouse. In addition, this paper only considers task assignment in a static state, where all task points and robot positions are determined. In the future, we will consider some unexpected scenarios, such as the dynamic change of robot state and task point state, to further verify the robustness of our method. In this paper, we assume that the robot's power is infinite and do not consider issues such as charging, which we will study in the following work.  
Conceptualization, formal analysis, methodology, and writing--original draft preparation by [PERSON]; funding acquisition, project administration, supervision, and writing--review and editing by [PERSON]; data curation, investigation, resources, and software by [PERSON]; validation and visualization by [PERSON] All authors have read and agreed to the published version of the manuscript.  
Our project is supported by the Shenzhen Basic Research Program JCYJ20180507183837726 and the National Natural Science Foundation U1813206, 61977019.  
Not applicable.  
We thank anyone who has provided guidance and assistance with this paper. In particular, we thank the reviewers and editors of the paper.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multirow{2}{*}{**Interation**} & \multicolumn{2}{c}{**EGA**} & \multicolumn{2}{c}{**NSGA3**} \\ \cline{3-6}  & & **Best** & **Aveg** & **Best** & **Aveg** \\ \hline \multirow{3}{*}{SOC} & 5000 & 186,274 & 188,044 & 183,507 & 185,334 \\  & 20,000 & 182,712 & 184,076 & 182,074 & 184,494 \\  & \(GaP_{SOC}\) & 1.91\% & 2.11\% & 0.78\% & 0.45\% \\ \hline \multirow{3}{*}{MS} & 5000 & 40,410 & 42,021 & 37,241 & 37,836.2 \\  & 20,000 & 39,552 & 40,455.3 & 37,272 & 37,795.7 \\ \cline{1-1}  & \(GaP_{MS}\) & 2.12\% & 3.73\% & \(-\)0.08\% & 0.11\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Large-scale experiment results by genetic algorithms.