# A Compact Cat Swarm Optimization Algorithm Based on Small Sample Probability Model
## 4 Experimental Results and Analysis  
With reference to the literature [4, 20], the SSPCCSO would be tested on 47 benchmark functions, which include those where their coordinates had been transformed and their shifted [21]. The composition test functions [22] are also introduced; all of the benchmark functions are listed in the Appendix A.  
SSPCCSO is a compact optimization algorithm based on small size samplings. Firstly, we select rcGA, cDE and cPSO as the compared algorithms. As SSPCCSO is also a member of evolutionary algorithms, traditional DE [23], PSO [24] and CSO [9] should be considered. From the perspective of saving memory, ISPO [25] is an indispensable object; it should be one of the objects of comparison with SSPCCSO.  
All of the experiments were carried out on a personal computer with MATLAB language, which is equipped with Pentium (R) dual core E6600 CPU, 3.06 GHz and 2.96 gb RAM. The operation system is set at windows XP platform. Each comparison algorithm will select a set of parameters through which the best results can be obtained. With reference to the literature [4, 26], all of the parameters for each compared algorithm are listed in Table 1. For all of the real population-based algorithms, the population size is 60, for all of the virtual population-based algorithms, the population size is 300. To achieve a truly fair comparison for all of the compared algorithms, all of the algorithms involved in the comparison were evaluated by taking the average value after running for over 30 times. In all of the tables, each value represents the corresponding mean value and the standard deviation value calculated for each comparison algorithm within 30 times, and \"+\", \"-\" and \"=\" have the same implication as in the literature [2].  
The remains of this section are described as below: first, a comparison for memory usage is listed in Table 2. Then, the comparisons for the memory-saving algorithms are presented. Next to this, the comparisons between the population-based algorithms and SSPCCSO will be shown; the analyses of the results for SSPCCSO are summarized in the final section.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Parameters** & **Literature** & **Algorithm** & **Parameters** & **Literature** \\ \hline rcGA & \(N_{p}=300\) & [1] & DE & \(N_{p}=60,F=0.5,Cr=0.9\) & [23] \\ \hline cDE & \(N_{p}=300,F=0.5\) & [2] & PSO & \(\phi_{1}=-0.2,\phi_{2}=-0.07,\phi_{3}=3.74\) & [24] \\  & \(Cr=0.3\) & [2] & \(\gamma_{1}=\gamma_{2}=1,N_{p}=60\) & & \\ \hline cPSO & \(\phi_{1}=-0.2,\phi_{2}=-0.07,\phi_{3}=3.74\) & [3] & ISPO & \(A=1,P=10,B=2,S_{f}=4\) & [25] \\  & \(\gamma_{1}=\gamma_{2}=1,N_{p}=300\) & & & \(H=30,\epsilon\epsilon=1.0\times 10^{-5}\) & [25] \\ \hline CSO & \(N_{p}=60,c1=c2=2\) & [10] & SSPCCSO & \(w=-0.4,c1=2,c2=-0.07\) & \\  & \(W=0.9\) & [10] & SSPCCSO & \(N_{p}=300\) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Selected parameters list for all compared algorithms in this projection.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Components** & **Memory Slots** \\ \hline ISPO & Single individual, 1 global best & 2 \\ \hline rcGA & One individual, persistent elitism, 1 sampling & 4 \\ \hline cDE & 3 sampling, 1 global best & 4 \\ \hline cPSO & 1 sampling, 5 persistent variables & 5 \\ \hline SSPCCSO & The same to cPSO & 5 \\ \hline PSO & Population-based, history and current individuals & 2N\({}_{\text{P}}\) \\ \hline DE & Population-based, current individuals only & Np \\ \hline CSO & Population-based, history and current individuals & 2N\({}_{\text{P}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Running memory space for all compared algorithms.