Figure 3 – GTA Objective function evolution for the sixteen
benchmarking functions
For comparison purposes, the same functions were tested once using PSO,
with a higher value, namely 3,000, for the maximum number of allowed
iterations, but with the same number of cyclists (particles), 500. Table
2 shows the results obtained. The global minimum was achieved only in
three cases: Paraboloid, Shaffer f6 and Salomon. Moreover, a higher
number of evaluations were necessary to achieve these results. In
addition, it can be observed that in most cases there was no
convergence, even with a higher number of iterations, reaching the
maximum number of evaluations possible. The extremely high dimension of
the problems, with most of them depending on 20,000 decision variables,
is the major contributor for this behavior. Many more iterations and
many more particles could have been used to reach (perhaps) an optimal
solution; however, the increase in the computational effort would had
been huge (or unaffordable).