# Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
## 4 Simulation Studies
Generally, the proposed algorithm performs excellently on the tested instances, especially on large problems. The algorithm is able to find a better solution length for problems gr431 and ali535 than the optimum solution length retrieved from the TSP library. For comparison with other metaheuristic algorithms, its performance on the berlin52, kroA100, ali535, U1060, and U1432 problems was compared to GA and PSO. The comparison results shown \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**FN** & **DIM** & **Average** & **STD** & **Best** & **SRT** & **SP** \\ \hline \multirow{3}{*}{Sphere} & 3 & \(2.0542\times 10^{-32}\) & \(6.4473\times 10^{-32}\) & \(2.0461\times 10^{-44}\) & \(10/10\) & 290 \\  & 5 & \(1.9122\times 10^{-33}\) & \(5.500\times 10^{-33}\) & \(2.6131\times 10^{-41}\) & \(10/10\) & 260 \\  & 10 & \(6.2708\times 10^{-33}\) & \(1.7927\times 10^{-33}\) & \(1.6542\times 10^{-42}\) & \(10/10\) & 360 \\ \hline \multirow{3}{*}{Rosenbrock} & 3 & \(4.1337\) & \(5.0670\) & \(8.3202\times 10^{-1}\) & \(0/10\) & - \\  & 5 & \(6.3453\times 10^{2}\) & \(8.4359\times 10^{2}\) & \(4.000\) & \(0/10\) & - \\  & 10 & \(2.0175\times 10^{5}\) & \(1.1898\times 10^{5}\) & \(9.000\) & \(0/10\) & - \\ \hline \multirow{3}{*}{[PERSON]} & 3 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 310 \\  & 5 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 270 \\  & 10 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 210 \\ \hline \multirow{3}{*}{[PERSON]} & 3 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 260 \\  & 5 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 290 \\  & 10 & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(10/10\) & 380 \\ \hline \hline \end{tabular} FN, Function; DIM, Dimension; STD, Standard Deviation of the mean; SRT, Success Ratio; SP, Success Performance; \"-\" indicates that SP cannot be computed because there is no successful run.  
\end{table} 
Table 7: Simulation results of the improved CSO (ICSO). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Benchmarks** & **Dimensions** & **BCSO** & **ICSO [19]** & **CSO [5]** \\ \hline \multirow{3}{*}{Sphere} & 3 & \(\mathbf{0.0000}\) & \(2.0542\times 10^{-32}\) & \(2.6752\times 10^{-5}\) \\  & 5 & \(\mathbf{0.0000}\) & \(1.9122\times 10^{-33}\) & \(2.997\times 10^{-5}\) \\  & 10 & \(\mathbf{0.0000}\) & \(6.2708\times 10^{-33}\) & \(2.4621\times 10^{-5}\) \\ \hline \multirow{3}{*}{Rosenbrock} & 3 & \(\mathbf{1.3\times 10^{-6}}\) & \(4.1337\) & \(2.8385\times 10^{7}\) \\  & 5 & \(\mathbf{4.4\times 10^{-5}}\) & \(6.3453\times 10^{2}\) & \(1.9639\times 10^{8}\) \\  & 10 & \(\mathbf{0.0000}\) & \(2.0175\times 10^{2}\) & \(1.4063\times 10^{9}\) \\ \hline \multirow{3}{*}{Griewangk} & 3 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(8.0108\times 10^{-1}\) \\  & 5 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(6.4033\times 10^{-1}\) \\  & 10 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(5.8016\times 10^{-1}\) \\ \hline \multirow{3}{*}{Rastrigin} & 3 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(1.9667\times 10^{3}\) \\  & 5 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(5.3334\times 10^{2}\) \\ \cline{1-1}  & 10 & \(\mathbf{0.0000}\) & \(\mathbf{0.0000}\) & \(1.4396\times 10^{2}\) \\ \hline \multicolumn{3}{l}{No. of Good Optima} & 12 & 6 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the mean global best of BCSO, ICSO and original CSO. Figure 3: Graph illustrating one of the experiments on the ali535 instance of TSP (containing 535 cities) solved by the proposed BCSO algorithm. The graph depicts the city location, total distance and best solution found. Figure 2: Graph illustrating one of the experiments on the gr431 instance of TSP (containing 431 cities) solved by the proposed BCSO algorithm. The graph depicts the city location, total distance and best solution found.