# An Artificial Plant Community Algorithm for Collision-Free Multi-Robot Aggregation
## 6 Benchmark Data and Experiments
### Performance Comparison
\begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Method**} & \multicolumn{5}{c}{**Number of Tasks**} \\  & & \(T_{max}=1\) & \(T_{max}=3\) & \(T_{max}=5\) & \(T_{max}=7\) & \(T_{max}=9\) & \(T_{max}=11\) & \(T_{max}=13\) & \(T_{max}=15\) \\ \hline APC & Makespan \(k_{T}^{make}\) & **0.144** & **0.276** & 0.357 & **0.391** & 0.413 & **0.425** & 0.432 & **0.443** & **0.360** \\  & Total collision time \(k_{T}^{coll}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & **0.286** & 0.294 & 0.302 & 0.317 & **0.324** & 0.329 & 0.336 & **0.355** & **0.318** \\  & Total travel distance \(D_{T}^{travel}\) & 0.158 & **0.169** & 0.179 & 0.188 & **0.197** & **0.205** & 0.211 & **0.219** & **0.191** \\  & Solution time (s) & 518 & 519 & 523 & 532 & 546 & 543 & 556 & 565 & 537.8 \\ GWO & Makespan \(k_{T}^{make}\) & **0.144** & 0.289 & 0.363 & 0.400 & 0.426 & 0.432 & 0.447 & 0.448 & 0.369 \\  & Total collision time \(k_{T}^{coll}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & 0.000 \\  & Total energy consumption \(e_{T}^{total}\) & 0.291 & 0.295 & 0.313 & 0.325 & 0.327 & 0.336 & **0.335** & 0.359 & 0.323 \\  & Total travel distance \(D_{T}^{travel}\) & 0.161 & 0.173 & 0.182 & 0.191 & 0.204 & 0.217 & 0.219 & **0.224** & 0.196 \\  & Solution time (s) & 505 & **508** & 512 & 536 & **533** & 540 & 548 & 564 & 530.8 \\ GA & Makespan \(k_{T}^{real}\) & 0.149 & 0.283 & 0.368 & 0.404 & 0.422 & 0.431 & 0.440 & 0.444 & 0.368 \\  & Total collision time \(k_{T}^{real}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & 0.000 \\  & Total energy consumption \(e_{T}^{total}\) & **0.286** & 0.305 & 0.310 & 0.334 & 0.340 & 0.341 & 0.349 & 0.367 & 0.329 \\  & Total travel distance \(D_{T}^{travel}\) & 0.162 & 0.171 & 0.178 & **0.187** & **0.197** & 0.206 & 0.214 & 0.225 & 0.193 \\  & Solution time (s) & 517 & 509 & **510** & 525 & 534 & 551 & **544** & 587 & 530.9 \\ PSO & Makespan \(k_{T}^{real}\) & 0.146 & 0.282 & 0.365 & 0.408 & 0.423 & 0.434 & 0.439 & 0.452 & 0.369 \\  & Total collision time \(k_{T}^{real}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & 0.000 \\  & Total energy consumption \(e_{T}^{total}\) & 0.293 & **0.293** & 0.318 & 0.320 & 0.329 & **0.327** & 0.348 & 0.361 & 0.324 \\  & Total travel distance \(D_{T}^{travel}\) & **0.157** & 0.174 & **0.177** & 0.193 & 0.206 & 0.210 & 0.217 & 0.228 & 0.195 \\  & Solution time (s) & 506 & 517 & 521 & 523 & 537 & 552 & 555 & 563 & 534.3 \\ ACO & Makespan \(k_{T}^{real}\) & 0.150 & 0.287 & 0.371 & 0.418 & **0.412** & 0.436 & 0.445 & 0.454 & 0.372 \\  & Total collision time \(k_{T}^{real}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & 0.000 \\  & Total energy consumption \(e_{T}^{total}\) & 0.294 & 0.308 & 0.311 & 0.326 & 0.335 & 0.339 & 0.341 & 0.372 & 0.328 \\  & Total travel distance \(D_{T}^{travel}\) & 0.159 & 0.170 & 0.188 & 0.192 & 0.205 & 0.216 & 0.221 & 0.229 & 0.198 \\  & Solution time (s) & **504** & 512 & 513 & **521** & 536 & **599** & 552 & 558 & **529.4** \\ DL & Makespan \(k_{T}^{real}\) & 0.148 & 0.287 & **0.355** & 0.396 & 0.419 & 0.438 & **0.431** & **0.443** & 0.365 \\  & Total collision time \(k_{T}^{real}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & 0.000 \\  & Total energy consumption \(e_{T}^{total}\) & 0.292 & 0.306 & **0.299** & **0.314** & 0.325 & 0.333 & 0.342 & 0.357 & 0.321 \\  & Total travel distance \(D_{T}^{travel}\) & **0.157** & 0.173 & 0.186 & 0.195 & 0.203 & 0.211 & **0.210** & 0.230 & 0.196 \\  & Solution time (s) & 1952 & 2078 & 2191 & 2114 & 2227 & 2239 & 2383 & 2476 & 2207.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of algorithms under varying numbers of tasks. Table 7 shows the comparison results of benchmark tests using the six heuristic algorithms with different numbers of tasks. The first line of Table 7 presents the total number of tasks, with nine scenarios in total, including the mean value.