1. International Congress Series 1291 (2006) 1&9~ 17':.
ELSEVIER
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Genetic algorithm with modified reproduction
strategy based on self-organizing map and
usable schema
Ryosuke Kubota a. *, Keiichi Horio b' Takeshi Yamakawa b
a
b
Gradua1e School ~~( Complllcr Science and 5sh>ms Engineering. Kyuslw lnstiwtr (~l Ter1molog_l-;
]~4 1/ihikino. Wakamatsu~ku. Kitakyush11, Fukrmk.1. 80/o:~0/9(,, Japan
Graduate School of L{fe Science and 5)·stems f:'ngim:ering, Kyushu lnHitute of Technology. Japan
Abstract In this paper, v.:e propose a new updating method considerin g usab ility of each element of
inputs and apply it to the reproduction of the GA to achieve more effective search than the traditional
reproduction. In the proposed updating method, the order of updating elements is decided by
ave-raging the corresponding elements multiplied by fitn~ss values of the chromosomes. To verify the
effectiveness of the proposed updating method, the GA with the modi lied reproduction is applied to
0 -- 1 knapsack problem. © 2006 Published by Elsevier B.V
Ke_vword~ ·
Genetic a lgorithms; Self-organizing map; Binary: Genetic diversity: Updating rule : Order of inverting
dcm~nts
I. Introduction
Genetic algori thm (GA) is a search algorithm based o n the mechan ics of natural
selection and natural genetics [I]. Searching in GA is achieved by iterating reproduction,
crossover and mutation strategies. In these strategies, the reproduction strategy is the most
imponan t for decid ing the searching points of the next generation. However. tradi tional
reprod uction operators may lose a genetic diversity of population in an early stage,
because they cannot generate new chromosomes which are d ifferent from the present
chromosomes. A decrease of the genetic diversity leads to ineffect iveness of searchi ng [2].
• Corresponding author. T~l.: +81 93 695 6!23; fax: +Sl 93 695 6133.
E-mail address: kubota-I")'Osuk..;!,~ cdu.brain.k~l.lk..;h.:"h.'.jp (R. Kubota).
0531-5131 / :tj 2006 Published by Elsevier B.V.
Jui: 10.1016/j ICS.200o.OH02

2. '
170
R. Kubota er u/. / lntemational Cm1grcss Series 119/ (2006) /69--- 172
To cope with this problem, we have proposed the reproduction strategy by utilizing an
approximation ability of a binaty version of se l f~o rganizing map (BSOM) [3] to maintain
the genetic di versity of the population 1"41. This BSOM-based reproduction can generate
many kinds of chromosomes with high 1ltness values. However, an order of updatin g
elements of a binary weight vector in the reproduction based on the previous BSOM [4)
influences the searchi ng pcrfonnancc of the GA.
In tillS paper, we propose a modified BSOM-bascd reproduction strategy with new
updating method ofbina1y weight vectors consideting usability of each element to achieve
more effective search than the traditional BSOM-based reproduction.
2, Genetic algorithm with reproduction strategy based on binary self-organizing map
Fig. 1 shows the outline of the GA with the BSOM-based reproduction, where the
elements of the input and weight vectors are represented by binmy numbers. The
chromosomes of the present generation are used as the input vectors of the BSOM, and the
weight vectors after team ing are employed as the chromosomes of the next generation. In
other words, the new chromosomes are reproduced by learning the BSOM. In the updating
phase of the BSOM, the updating of weight vectors is realized by adjusting elements
which are randomly selected in the weight vectors, when the corresponding elements of
the input and the weight vector are different. The number of adjusting elements CL(t) is a
leaming rate and decided by coefticients with respect to fitness values of the input and
weight vectors as following equation:
(1)
where, l J, N,t;,j:._.,,, and d represent Gauss ' notation. the parameter characterized by the
number of clements, fitness values of input and weight vector before updating, and
Eucl idean distance bel:veen the best matching unit and the unit to be updated, respectively.
h(d,(,) represents the neighbourhood fiJnction and is defined by following Gaussian
function:
(2)
The same procedure was also employed in the traditional BSOM-based reproduction (4).
This updating can generate new chromosomes with high fitness values. Moreover, their
genetic diversity is preserved. Thus. BSOM-based reproduction operator can achiev e the
V("It!ht
v~-,,,,.. sr~t·~
{ChrnnK"iHJil'~ ,lk'1" Rt"p. }
C••mpctitiwl.;~yer
Fig. I. Outline of GA Vith BSOl·1-based reproduction.

3. R. Kubv r.1
l'l a /. / fnrcm arional
Iii
Cvngrcss Saies I '!91 (2006) / 69 172
effective search . llowevcr. the order of updating elements of binaty weight vector
innuences a search ing performance of the GA. Therefore, the order of updating elements
in the updating phase must be considered to realize more effective search than the
traditional BSOM reproduction.
3. Proposed updating method based on usable schema
In this paper, we propose a new updating method considerin g the order of updating
elements and apply it to the BSOM-based reproduction. In the proposed updating method,
the order of updating elements is decided by a usability of the schema. The usable schema
is proper for one element which may contribu te to the high fitness value in a set of the
input vectors. Specifically. the usability of ith element is decided by S; as following
equation:
0~5,~1.
(3)
where K represents th~ number ot' input vectors. In Eq. (3), S; represents the propo11ion of
the binary values in a column of the input vectors which have high fitness values. Note
that the usability is higher, when S; is closer to "o·· or''!''. On the contrary. the usability is
lower. when S, is closer to ''0.5''. In the proposed updating, each element of weight vector
is adjusted to input vector based on th~ order of the usability. when elements of input and
weight vectors are di ffercnt.
4. Simulation results
In order to verifY the effecti veness of the BSOM-based reproduction employing the
proposed updating method, it is applied to the 0-1 knapsack problem (one of the primaty
combinatorial optimization problem). The searc hing performance of the BSOM-based
reproduction employing the proposed updating method is compared with Roulette Wheel
Selection (RWS) and that employing the previous updating method. In this simulation ,
population size, crossover probability and mutation probability are 25. 0.3 and 0.0 I,
respectively. These methods ar~ compared trom the view points of the number of
generations, and CPU time until the quasi-optimal solution is acquired. Tabk l shows the
simu lation results. Ten nms are executed and the average value is calculated to suppress
dependencies on all stochastic effects. These results show that the GA with the BSOM-
Tahtc I
Number of ge-nerat ion and CP U rime
Number of subjects
Methods
Number of generations
CPU time (s)
~0
RWS
1~80
0.76
0.63
Prt: vious [4
Proposed
50
RWS
Previous 14)
Proposed
3 18
164
7089
107
76
0.44
2.R4
0.62
0.42

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R. Kuhota et ,,,_ / lntemational Congrt'S.' S(;:rie,· I !Y 1 (2 006) /6 9 172
based reproduction operator employing the proposed updating method can realize the
faster searc h in smaller number of generations comparing with that employing the
traditional reproduction operators.
5. Conclusion
[n thi s paper, we proposed the new updating method of weight vectors to achieve the
more effective search of the GA employing BSOM-based reproduction comparing with
that employin g the traditional BSOM. The ineffective searching using the traditional
updating method is attributed to the problem which the elements to be updated arc selected
randomly. ln the proposed updating method. the order of updating elements is considered.
The order is decided by the usability which is defined by averaging the corresponding
elements multiplied by fitness values of the input vectors. The GA employing the BSOMbased reproducti on with the proposed updating method can achieve the more effective
search comparing with that employing the traditional and the previous BSOM-based
reproductions. The etTectiveness and validity of proposed updating method were shown by
solving the combinatorial optimization problem.
Acknowledgements
This work was partially supported be the :? 1st Century COE Program in Kyushu
Institute of Technology, entitled "'World of Brain CompLlting Interwoven o ut of Animals
and Robots,"' and was also supported by the Ministry of Education, Science. Sports and
Culture, Grant-in-Aid for Scientific Research (A), 2002. 14205038.
References
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g e n e ti~;.·
algorithm perfom1<mce in dynamic l!n vironment.s, Ad,·anced in Infom1ation Systl!ms LeciUre N ote in
Compurcr Science 2457 (200c) 3 !4 - 323.
[3 ] T. Ko honen. Self-organization :md Associat ive Memory. 1984.
[~ ] R. Kubota. K. Horio. T. Yamak:lva. Binary SOM Bastd on Significance of L
nputs anJ its Applicatum to
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