**6. Conclusions**

64 Simulated Annealing – Single and Multiple Objective Problems

**5.5. Performance with harder instances** 

**Table 4.** Definition of benchmark instances A and B.

No. of Cells, *n*

**Figure 7.** Execution time performance comparison between three different methods for CAP.

are more difficult have been studied. Their main characteristics are shown in Table 4.

A 21 2**d**<sup>3</sup> Yes Yes Yes (*cii*=5) B 21 4**d**<sup>3</sup> Yes Yes Yes (*cii*=5)

Our methods are going to be compared with the GA-based approach by Funabiki et al. (Funabiki, 2000). Using the μGA the best assignments we were able to find required 855 and 1713 channels, for problems A and B, respectively, while the method in (Funabiki, 2000) required slightly higher values, 858 and 1724 (results are shown in Table 5). On the other hand, the SQ method requires 855 and 1715 channels, respectively. Thus, in case A –which is a bit simpler than case B- both SQ and GA achieve near optimal results, while in case B –a rather more complex network- SQ requires two more channels than the GA, and 9 less than the NN method. In terms of computation times, the μGA took 11.86 and 23.76 seconds, for problems A and B, respectively; the other GA-based algorithm took about 16.73 and 32.8

To conclude this analysis of the performance of the proposed methods, two more cases that

**d** ACC CCC CSC

NC-based algorithms (GA and SQ) have been proven to fit very well for solving complex NP-complete problems such as the fixed channel allocation problem. Both of them show good convergence properties and reduced computational load. We have solved 18 different benchmark instances with successful results, proving, this way, the accuracy, flexibility and robustness of the proposed methods. Making use of several well-known benchmark instances, their performances have been shown to be superior to those of the existing frequency assignment algorithms in terms of computation time, convergence properties and quality of the solution. Even when compared to one of the best previous approaches −based on a NN-based scheme−, GA and SQ methods have been able to find better solutions to the most complex benchmarks tested.

While both the μGA and SQ offer similar computational load, convergence properties and quality of the solution for simple and moderately-simple benchmark instances, the proposed μGA shows the most reduced computational load when applied to complex problems.
