Parameter-Free Genetic Algorithm Inspired by "Disparity Theory of Evolution" Hidefumi Sawai 1 and Sachio Kizu ~ 1 Kansal Advanced Research Center, CRL, MPT, Kobe, 651-2401 Japan, e-mail:
[email protected] 2 Toshiba R & D Center, Kawasaki, 210 Japan e-malh
[email protected] A b s t r a c t . We propose a novel Genetic Algorithm which we call a Parameter-free Genetic Algorithm (PfGA) inspired by the "disparity theory of evolution". The idea of the theory is based on different mutation rates in double strands of DNA. Furthermore, its idea is extended to a very compact and fast adaptive search algorithm accelerating its evolution based on the variable-size of population taking a dynamic but delicate balance between exploration (i.e., global search) and exploitation (i.e., local search). The PfGA is not only simple and robust, but also does not need to set almost all genetic parameters in advance that need to be set up in other Genetic Algorithms. To verify the effectiveness of the PfGA, we compared its results with those on the first Internatinal Contenst on Evolutionary Optimization at ICEC'96 using some recent function optimization problems. A parallel and distributed PfGA architecture is being investigated as an extension of this work, some preliminary results of which are shown.
1
Introduction
The Genetic Algorithm (GA)[2] is an evolutionary computation paradigm inspired by biological evolution. GAs have been successfully applied to many practical applications such as functional optimization problems, combinatorial optimization problems, and optimal design of parameters in machines[3]. However, the design of genetic parameters in a GA has to be determined by trial and error, making optimization by GA ad hoc. One of the most important research areas in Evolutionary Computation is to adapt genetic parameters and operators in a self-adaptive manner because such adaptation can tune an algorithm during solving a given problem. In [12], a classification of adaptation is developed, which covers different levels (such as environment, population, individual and component) and types (such as static and dynamic ones). However, it is a very time-consuming task to design an optimal evolutionary strategy in an adaptive way because we have to perform the evolutionary algorithm many times by trial and error. To relieve the user of this kind of adaptive parameter-setting problem, we propose a Parameter-free Genetic Algorithm (PfGA)[17][18] [19] where no control parameters for genetic operations need to be set as constants in advance. It merely uses arbitrarily random values or
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leading 3' parental
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5'
strand ~ 3'
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:enzymes
strand
+5'
5' lagging strand
lagging +5' -3
~ ~ copy
strand ~
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Fig. 1. A hypothesis in the disparity theory o.f evolution
probabilities for setting almost all genetic parameters. The PfGA is inspired by the "disparity theory of evolution" which was proposed by Furusawa et a1.[5][6]. The idea is based on the disparity of copy error rates in the leading and lagging strands of DNA when each strand makes its copy. The error rate in the lagging strand is much higher than that of the leading strand. So the error rate accumulates more in the lagging strand than in the leading strands as generations proceed. The offsprings from the leading strands rarely suffer from the copy error (we call it a wild type). On the other hand, the offsprings fl'om the lagging strand accumulate more copy error than the leading strand. Consequently, asymmetry or disparity occurs in the two kinds of offsprings. This leads to diversity in a biological ecosystem. Inspired by the idea of the "disparity theory of evolution," we proposed a Parameter-free Genetic Algorithm (PfGA) where almost none of the genetic parameters, such as initial population size, crossover rate, and mutation rate, need to be set up by a user in advance. All that is needed is a random number generator. The search strategy in the PfGA is based on a dynamic change of subpopulation size extracted from the population which enables an adaptive search to take a delicate balance between global and local search methods. This two kinds of search methods correspond to exploration and exploitation, respectively, and maintain diversity in GAs. 2
Disparity
Theory
of Evolution
As Charles Darwin claimed in the "Origin of Species" in t859[1], a major factor contributing to evolution is mutation, which can be caused by spontaneous misreading of bases during DNA synthesis. Semiconservative replication of double-stranded DNA is an asymmetric process, in which there is a leading and a lagging strand. Furusawa et al. proposed a "disparity theory of evolution"[5] based on a difference in frequency of strand-specific base misreading between the leading and lagging DNA strands (i.e., disparity model). Fig.l shows a hypothesis in the disparity theory of evolution. In the figure, the leading strand is (:opied smoothly, whereas in the lagging strand a copy error can occur because
704 population
"family" O: parent 0:
S
child
better
Case
1
P2 Pl C2 C~ ~ 0 ~
Case
2
0
Case
3
Case
4
0
Fig. 2. Population S, subpopulation S', family S" (left) and selection rules -(right) in Parameter-fi'ee GA plural enzymes are necessary to produce its copy. This disparity or asymmetry in producing each strand occurs because of the different mutation rates in the leading and lagging strands. Thus "diversity" of DNAs is maintained in a population as generations proceed. The disparity model guarantees that the mutation rate of some leading strands is zero or very small. When circumstances change, for example when the original wild type can not survive, selected mutants might adapt tinder the new circumstances as a new wild type. In their study, the disparity model was compared with a parity model in which there was no statistical difference in the fi-equency of base misreading between strands as in the generally accepted model. The disparity model outperformed the parity model in a knapsack optimization problem. They clearly showed that the advantageous situation for the disparity model happened in the cases of a small population, strong pressure, a high mutation rate, sexual reproduction with diploidy, and strong competition. On the other hand, survival conditions for the parity model are a large population, weak selection pressure, a low mutation rate, asexual reproduction with haploidy, and weak competition.J6] 3
Parameter-free
Genetic
Algorithm
The PfGA is inspired by the disparity theory of evolution, described in the previous section. The population of the PfGA is considered as a whole set S of individuals which corresponds to all possible solutions. From this whole set S, a subset S' is introduced. All genetic operations such as selection, crossover, and mutation are conducted for S', thus evolving the subpopulation S'. From the subpopulation S', we introduce a family which contains two parents and two children generated from the two parents (see Fig.2 (left)).
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T a b l e 1. Test functions
F1
F2
SphereModel : n f ( x i ) = ~ i = l ( x , - 1) 2
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