Computational Intelligence - August 2013 - 57
XC1,YC1,ZC1
XN,YN,ZN
XH1,YH1,ZH1
XH3,YH3,ZH3
XH2,YH2,ZH2
XH4,YH4,ZH4
XC2,YC2,ZC2
XH5,YH5,ZH5
XH6,YH6,ZH6
XC3,YC3,ZC3
XH7,YH7,ZH7
XH8,YH8,ZH8
XC4,YC4,ZC4
XO1,YO1,ZO1
XO2,YO2,ZO2
XH9,YH9,ZH9
Figure 2 Tree-based representation of non-cyclic molecule.
X TS = " x ; df ^xh = 0, 7!k c k 1 0 , ,
(1)
where c k is an eigenvalue of the Hessian matrix d 2 f ^xh .
Scientists are generally interested on specific transition states
with the following properties:
❏ low-energy, i.e. 6x d X TS f ^ x h < fmax where fmax is some
user-defined threshold.
❏ unique, i.e. 6x, y d X TS ; f ^ x h - f ^ y h ;< f & i ^ x, y h < j
where f and j are the maximum acceptable similarities in
the potential energy and the structural configuration spaces,
respectively.
❏ precise, i.e. df ^ x h < d, d " 0.
III. Molecular Memetic Computing
As an emerging field, memetic computing has gained increasing research attention in the recent few decades with growing
number of successes [28]-[36]. Inspired by Dawkins' notion of
a meme, it was first introduced as the Memetic Algorithm
(MA)-a marriage between population-based global search
and individual-based local search which respectively facilitate
exploration and exploitation of the search space. Not only is
MA capable of escaping local optimum trap, but it also converges rapidly to some optimum with sufficient precision due
to the life-time learning of the individual. To-date, MAs have
been crafted for solving real-world problems in science and
engineering more efficiently [29], [31]-[32], [37]-[45].
In this section, specialized representation and operators for
the evolution of molecular structure will be presented. These
are crucial for efficient discovery of the low-energy transition
states of small non-cyclic molecules using the molecular
memetic computing (MMC) methodology. Specialized fitness
function will also be formulated to enable efficient selection
Figure 3 Initial population of MMC.
Chromosomes Aligned
Figure 4 Covalent-bond-driven crossover.
using the stochastic roulette-wheel procedure. Finally, the valley-adaptive clearing scheme [16] and Berny algorithm [15]
for maintaining diversity and enabling life-time individual
august 2013 | IEEE ComputatIonal IntEllIgEnCE magazInE
57
Table of Contents for the Digital Edition of Computational Intelligence - August 2013
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