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

Computational Intelligence - August 2013 - Cover1
Computational Intelligence - August 2013 - Cover2
Computational Intelligence - August 2013 - 1
Computational Intelligence - August 2013 - 2
Computational Intelligence - August 2013 - 3
Computational Intelligence - August 2013 - 4
Computational Intelligence - August 2013 - 5
Computational Intelligence - August 2013 - 6
Computational Intelligence - August 2013 - 7
Computational Intelligence - August 2013 - 8
Computational Intelligence - August 2013 - 9
Computational Intelligence - August 2013 - 10
Computational Intelligence - August 2013 - 11
Computational Intelligence - August 2013 - 12
Computational Intelligence - August 2013 - 13
Computational Intelligence - August 2013 - 14
Computational Intelligence - August 2013 - 15
Computational Intelligence - August 2013 - 16
Computational Intelligence - August 2013 - 17
Computational Intelligence - August 2013 - 18
Computational Intelligence - August 2013 - 19
Computational Intelligence - August 2013 - 20
Computational Intelligence - August 2013 - 21
Computational Intelligence - August 2013 - 22
Computational Intelligence - August 2013 - 23
Computational Intelligence - August 2013 - 24
Computational Intelligence - August 2013 - 25
Computational Intelligence - August 2013 - 26
Computational Intelligence - August 2013 - 27
Computational Intelligence - August 2013 - 28
Computational Intelligence - August 2013 - 29
Computational Intelligence - August 2013 - 30
Computational Intelligence - August 2013 - 31
Computational Intelligence - August 2013 - 32
Computational Intelligence - August 2013 - 33
Computational Intelligence - August 2013 - 34
Computational Intelligence - August 2013 - 35
Computational Intelligence - August 2013 - 36
Computational Intelligence - August 2013 - 37
Computational Intelligence - August 2013 - 38
Computational Intelligence - August 2013 - 39
Computational Intelligence - August 2013 - 40
Computational Intelligence - August 2013 - 41
Computational Intelligence - August 2013 - 42
Computational Intelligence - August 2013 - 43
Computational Intelligence - August 2013 - 44
Computational Intelligence - August 2013 - 45
Computational Intelligence - August 2013 - 46
Computational Intelligence - August 2013 - 47
Computational Intelligence - August 2013 - 48
Computational Intelligence - August 2013 - 49
Computational Intelligence - August 2013 - 50
Computational Intelligence - August 2013 - 51
Computational Intelligence - August 2013 - 52
Computational Intelligence - August 2013 - 53
Computational Intelligence - August 2013 - 54
Computational Intelligence - August 2013 - 55
Computational Intelligence - August 2013 - 56
Computational Intelligence - August 2013 - 57
Computational Intelligence - August 2013 - 58
Computational Intelligence - August 2013 - 59
Computational Intelligence - August 2013 - 60
Computational Intelligence - August 2013 - 61
Computational Intelligence - August 2013 - 62
Computational Intelligence - August 2013 - 63
Computational Intelligence - August 2013 - 64
Computational Intelligence - August 2013 - 65
Computational Intelligence - August 2013 - 66
Computational Intelligence - August 2013 - 67
Computational Intelligence - August 2013 - 68
Computational Intelligence - August 2013 - 69
Computational Intelligence - August 2013 - 70
Computational Intelligence - August 2013 - 71
Computational Intelligence - August 2013 - 72
Computational Intelligence - August 2013 - 73
Computational Intelligence - August 2013 - 74
Computational Intelligence - August 2013 - 75
Computational Intelligence - August 2013 - 76
Computational Intelligence - August 2013 - 77
Computational Intelligence - August 2013 - 78
Computational Intelligence - August 2013 - 79
Computational Intelligence - August 2013 - 80
Computational Intelligence - August 2013 - 81
Computational Intelligence - August 2013 - 82
Computational Intelligence - August 2013 - 83
Computational Intelligence - August 2013 - 84
Computational Intelligence - August 2013 - 85
Computational Intelligence - August 2013 - 86
Computational Intelligence - August 2013 - 87
Computational Intelligence - August 2013 - 88
Computational Intelligence - August 2013 - Cover3
Computational Intelligence - August 2013 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202311
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202308
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202305
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202302
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202211
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202208
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202205
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202202
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202111
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202108
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202105
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202102
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202011
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202008
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202005
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202002
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201911
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201908
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201905
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201902
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201811
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201808
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201805
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201802
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter12
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall12
https://www.nxtbookmedia.com