Information Technology Reference
In-Depth Information
The parameter setting of AIS-LP is:
-
population cardinality: 10;
-
number of clones: 5;
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number of inner iterations: 5;
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convergence criterion: the search ends if the objective function value does
not improve for more than ten external generations.
Results are averaged on 10 independent runs to take into account the statistical
variation of performances due to the stochastic nature of the algorithm.
6
Discussion
In Fig. 5 MILP and AIS-LP are compared with respect to the computational
time (in seconds) to converge to the optimal value on a Pentium IV 2.8 GHz.
These data are displayed versus dimension of problem, represented by the value
of
N
intervals
.
Fig. 5 shows two important properties. Firstly, there is a crossover between
the two curves of MILP and AIS-LP. This fact leads to the consideration that the
computational time of MILP approach becomes impracticable for large instances,
i.e. for fine discretization and/or long period managements.
Secondly, by analyzing each curve, it is possible to find that MILP has an
exponential dependence of the computational time on the cardinality of the
problem, while AIS-LP has a quadratic rule. The previous considerations are
confirmed by the analysis of Fig. 6 which shows the number of LP problems
solved by the two techniques. In this case the number of LP problem is linearly
dependent on the cardinality of the problem. It is also worth noting that the
solutions found by AIS-LP and MILP models share the same objective function
Fig. 5.
Computational time of the two procedures vs number of time intervals. AIS-LP
computational time has a quadratic dependence on the cardinality of the problem.
