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5 CONCLUSIONS
The main contributions of this proposalare the deriva-
tion of formulae for computing the parameters of an
adequate Multivariate Normal Distribution for locat-
ing the optimum, and the introduction of simple an-
nealing schedules for updating the β value.
The derived formulae for computing the search
distribution use the objectivefunctionvalue as a linear
factor for estimating weighted parameters. The lin-
ear weights avoid prematurely collapsing probability
mass around a single solution, preventing premature
convergence. In addition, this fashion of parameter
estimation produces a softer change in the structure
of the covariance matrix between consecutive gener-
ations, in contrast to the exponential weights used in
similar approaches (Yunpeng et al., 2006). The ad-
vantage of using linear weights, even with a fixed β
value, is well documented in (Valdez et al., 2013),
where similar formulae are used for the univariate
case. Our proposal combines the conviniences of the
linear weights with simple annealing schedules to reg-
ulate the exploration of the algorithm.
The advantage of using the linear weights and
the annealing schedules is evidenced by statistical re-
sults presented in Section 4. Furthermore, the results
demonstrate that the BEMNA effectively solves the
Rosenbrock problem, which is not solved by similar
algorithms, (Yunpeng et al., 2006) and (Valdez et al.,
2013); as well as the other problems using an inferior
computational cost.
Future work intends to propose additional en-
hancement techniques to be applied over the current
BEMNA for reducing the population size as well as
the number of function evaluations. Moreover, we
will explore new ways to use this approach in evo-
lutionary computation.
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