Endocrine-Immune Network and Its Application for Optimization - Intelligent Computing for Sustainable Energy and Environment - page 155

4.2 Comparing with Cob-aiNet[C] and Copt-aiNet

In this subsection, we compared the EINET-TSP with the two recent competitive
immune network algorithms for combinatorial optimization such as cob-aiNet
[C] [12] and copt-aiNet [8]. These four instances, namely att48, eil75, kroC100
and ch150, were extracted from the TSPLIB.
The quality of the best route found by EINET-TSP for each problem was
compared with the best results obtained by cob-aiNet[C] and copt-aiNet from
the literature [8, 12]. From Table 1 it is possible to see that both cob-aiNet[C]
and copt-aiNet were able to find the optimal route for all the problems studied
here, except ch150. However, even for ch150 the best solutions found by both
algorithms are very close to the optimal one. When comparing, EINET-TSP
were able to solve all the four problems studied here, which indicates that the
technique is effectively capable of dealing with such problem.

Tabl e 1. Best Results Obtained by Each Algorithm

Opt cob-aiNet[C] cob-aiNet[C] EINET-TSP

att48 10628 10628 10628 10628

eil76 538 538 538 538

kroC100 20749 20749 20749 20749

ch150 6528 6529 6531 6528

Table 2 shows the mean and standard deviation of results obtained by cob-
aiNet[C] and our EINET-TSP, evaluated over the 10 runs for each problem,
together with their difference (in percentage) from the global optima. As it
is possible to see, EINET-TSP is capable of obtaining a set of solutions for
each problem with costs very close to the optimal routes. Compared with cob-
aiNet[C], our algorithm EINET-TSP has lower average percent difference or
better accuracy solutions than cob-aiNet[C].

Tabl e 2. Mean and Standard Deviation, Over 10 Runs, and Difference (in %) of These
Mean Values From the OTIMA

cob-aiNet EINET

Average Percentage Average Percentage

(std,dev.) fromOpt (std,dev.) fromOpt

att48 1074593.6 1.1% 1066327.3 0.3%

eil76 555.146.4 3.2% 5402.0 0.3%

kroC100 21418498.0 3.2% 20856106.2 0.5%

ch150 6747.896.2 3.4% 670786.8 2.7%