# Spectrum Allocation Based on an Improved Gravitational Search Algorithm
## 5 Simulation Experiment
### Simulations and Analyzation  
**Experiment 1. ** _In order to validate the performance of the improved algorithms which optimizes the original GSA at different iteration stages, we conduct this experiment firstly. In Figure 2, GSA + CCM indicates an optimized method that initializes the population of GSA with Chebyshev chaotic map, and GSA + PSA is an optimized approach that enhances the local searchability of GSA using PSA. As we can see in Figure 2, in the first 50 iterations, the performance curve of GSA + CCM is close to IGSA but still lower than IGSA. Due to IGSA adopting the encoding and decoding rules to reduce the computing dimension and data redundancy, the convergence rate increases. Whereas GSA + CCM still performs better than GSA + PSA in convergence because initializing population with the chaotic map effectively avoids premature convergence. However, the insufficiency in local search leads to its inferior exploitation ability in the last stage of iteration. Different from GSA + CCM, GSA + PSA vanishes the deficiency of GSA in fine search and achieves good performance. However, it suffers from the premature convergence which causes the convergence speed to be lower than the other algorithms. Compared with the other GSA-based improved algorithms, IGSA not only avoids premature convergence but has sufficient capability in local search._  
**Experiment 2. ** _In this experiment, we evaluate the performance of the IGSA and GSA, PSO, CSGC in terms of overall system performance. From Figure 3, we can see that the overall performance grows with the iteration times, where the number of available channels is \(M=10\), the number of SUIs is \(N=20\)._  
_As shown in Figure 3, the performance of CSGC is far inferior to PSO, GSA and IGSA, and it starts converging until 150 iterations. The PSO is better than CSGC but still lower than GSA and IGSA. Before 35 iterations, the performance of GSA exceeds IGSA in terms of overall system performance. However, due to GSA easily falling into local extremum and prematurely converging, GSA reaches the convergence state with the maximum overall benefits 248 until 90 iterations. Using the chaotic map initializes population causing the convergence speed of IGSA to be lower than GSA at the beginning of the iteration, but it effectively prevents IGSA from trapping in the local optimum. Besides, owing to the PSA process being introduced to IGSA, the fine searchability of IGSA is enhanced in an efficient way. IGSA gets into convergence state when it iterates 75 times with benefit 260. As is shown in Figure 3, IGSA performs better in overall system performance than other algorithms._  
Figure 2: Performance of the GSA-based improved algorithm. **Experiment 3**. : _Figures 4 and 5 show the performance of the four algorithms in terms of the system utility and the system fairness under the condition of fixed spectrum number and increasing SU number, respectively, where the available channel number is fixed on \(M=10\), the number of SUs distributes in \(N=[10,30]\)._  
_Figure 4 shows the trend of the system utility, which is growing with the increasing of SU. From the figure, we can see that the system utility grows with the increasing of SU numbers even though the the number of available channels is fixed. The growth speed of PSO and CSGC are inferior to GSA and IGSA. The curve of IGSA is always higher than others, which means that IGSA not only can escape the local extremum in a timely manner but it can also obtain the close-to-optimal solution quickly._  
_Figure 5 shows the trend of the system fairness, which is growing with the increasing of SU. As we can see, the fairness of SUs access to spectrum declines with the increasing of SU numbers while the available channel number is fixed. Because more SUs will cause more conflicts. Nevertheless, the descent rate of the IGSA is the slowest, and the CSGC  
**Experiment 4**.