Table Of ContentEvolution of Ideas: A Novel Memetic Algorithm
Based on Semantic Networks
Atılım Gu¨nes¸ Baydin∗† Ramon Lo´pez de Ma´ntaras∗
†Departament d’Enginyeria de la Informacio´ i de les Comunicacions ∗Artificial Intelligence Research Institute, IIIA-CSIC
Universitat Auto`noma de Barcelona Campus Universitat Auto`noma de Barcelona
08193 Bellaterra, Spain 08193 Bellaterra, Spain
Email: [email protected] Email: [email protected]
2 Abstract—This paper presents a new type of evolutionary each generation is followed by a local search, or learning,
1 algorithm (EA) based on the concept of “meme”, where the performed by each candidate solution. For this reason, this
0 individuals forming the population are represented by semantic
approach has been often referred to under different names
2 networks and the fitness measure is defined as a function of the
besides MA, such as “hybrid EAs” or “Lamarckian EAs”. To
represented knowledge. Our work can be classified as a novel
n memeticalgorithm(MA),giventhat(1)itistheunitsofculture, date,MAshavebeensuccessfullyappliedtoawidevarietyof
a or information, that are undergoing variation, transmission, problem domains such as NP-hard optimization problems [7],
J
and selection, very close to the original sense of memetics as [8], engineering [9], machine learning [10], [11], and robotics
7 it was introduced by Dawkins; and (2) this is different from [12].
1 existing MA, where the idea of memetics has been utilized as a
The aim of this study is to propose a computational model
means of local refinement by individual learning after classical
] global sampling of EA. The individual pieces of information are comprising a meme pool subject to variation and selection
E representedassimplesemanticnetworksthataredirectedgraphs that will be able to evolve pieces of knowledge under a given
N of concepts and binary relations, going through variation by memeticfitnessmeasure,parallelingtheexistinguseofEAin
memetic versions of operators such as crossover and mutation,
solving optimization problems. While this approach is based
. which utilize knowledge from commonsense knowledge bases.
s onmemetics,itisunliketheexistingsenseofthewordincur-
c In evaluating this introductory work, as an interesting fitness
[ measure, we focus on using the structure mapping theory of rentMA(asanhybridizationoflocalsearchintoEA).Rather,
analogicalreasoningfrompsychologytoevolvepiecesofinforma- itisintendedasanewtoolfocusedexclusivelyonthememetic
2 tionthatareanalogoustoagivenbaseinformation.Considering evolutionofknowledgeitself,whichcanfinduseinfieldssuch
v other possible fitness measures, the proposed representation and
as knowledge-based systems, reasoning, and computational
6 algorithmcanserveasacomputationaltoolformodelingmemetic
creativity. As the basis of our approach, we introduce a solu-
0 theories of knowledge, such as evolutionary epistemology and
7 cultural selection theory. tion representation based on semantic networks [13]. These
2 are a simple type of formal representation for ontologies,
. I. INTRODUCTION formed by graphs where vertices correspond to concepts and
1
The idea that a simple progression of variation, natural edges correspond to directed relations (Fig. 1). To operate on
0
2 selection, and heredity can account for the great complexity thesestructures,weadaptvariationoperatorssuchascrossover
1 and apparent design observed in living beings has eventually and mutation to manipulate concepts and relations, utilizing
: led to the formulation of Universal Darwinism, generalizing the commonsense knowledge bases of ConceptNet [14] and
v
the mechanisms and extending the domain of this process WordNet [15]. From the perspective of representation and
i
X to systems outside biology, including economics, psychology, genetic operators, our approach is partly similar to the use of
r physics, and even culture [1], [2]. Within this larger frame- treestructuresingeneticprogramming[16]andtheapproaches
a work, the concept of meme introduced by Dawkins as an ofgeneticnetworkprogramming[17],[18],paralleldistributed
evolving unit of culture—or information, idea, or belief— genetic programming [19], and evolutionary graph generation
analogous to a gene [3], hosted, altered, and reproduced in [20].
individuals’ minds, forms the basis of the field of memetics1. In this paper, we present three main contributions:
Within the discipline of evolutionary computation, the
• Using semantic networks for encoding individual mem-
recently maturing field of memetic algorithms (MA) has
otypes, where graphs formed by concepts and relations
experienced increasing interest as a successful method for
represent units of evolving knowledge.
solving many hard optimization problems [4], [5], [6]. The
• Introducing operations for evolutionary variation, such
existing formulation of MA is essentially a hybrid approach,
as mutation and crossover, that are adapted to work on
combining classical evolutionary algorithms (EA) with local
semantic networks.
search, where the population-based global sampling of EA in
• Introducing a memetic fitness measure for evolutionary
selection to evaluate our implementation, based on the
1Quoting Dawkins [3]: “Examples of memes are tunes, ideas, catch-
structure mapping theory from psychology.
phrases, clothes fashions, ways of making pots or of building arches. Just
asgenespropagatethemselvesinthegenepoolbyleapingfrombodytobody
Following an overview of our approach, the paper presents
via sperms or eggs, so memes propagate themselves in the meme pool by
leapingfrombraintobrain...” implementationdetailsoftheproposedalgorithminSectionII.
IsA(bird,animal)2) describing a subsumption hierarchy that
think
city is true by definition; in assertional networks, the relations
CapableOf describeinstantiationsandassertionsthatarecontingentlytrue
AtLocation
(e.g. AtLocation(human,city)) [13]. In this study we com-
human
Desires bine the two approaches for increased expressivity (Fig. 1).
Desires
As such, semantic networks provide a simple yet powerful
IsA learn
meanstorepresentthe“memes”ofDawkinsasdatastructures
eat
cake UsedFor Causes read that are algorithmically manipulatable, allowing a procedural
animal implementation of memetic evolution.
CreatedBy
Desires IsA There are several existing algorithms using graph-based
representations for the encoding of candidate solutions in EA
bird
bake [21]. The most notable work among these is genetic program-
CapableOf
ming (GP) [16], where candidate solutions are pieces of com-
puterprogramrepresentedinatreehierarchy,whichisactually
fly
a specific type of graph structure [21]. In parallel distributed
genetic programming (PDGP) [19], the restrictions of the tree
Fig.1. Asemanticnetworkwith11conceptsand11relations. structureofGPisrelaxedbyallowingmultipleoutputsfroma
node,whichallowsahighdegreeofparallelismintheevolved
programs. In evolutionary graph generation (EGG) [20] the
We evaluate the method with experiments presented in Sec- focus is on evolving graphs with applications in electronic
tion III and conclude the paper and discuss future work in circuitdesign.Geneticnetworkprogramming(GNP)[17],[18]
Section IV. introduces compact networks with conditional branching and
action nodes; and similarly, neural programming (NP) [22]
II. ANEWTYPEOFMEMETICALGORITHM
combines GP with artificial neural networks for the discovery
Our algorithm proceeds similar to conventional EA, with of network structures via evolution.
a relatively small set of parameters. We implement semantic Theuseofagraph-basedrepresentationmakesthedesignof
networks as linked-list data structures of concept and relation variationoperatorsspecifictographsnecessary.Inworkssuch
objects.Thedescriptionsofrepresentation,memeticvariation, as GNP, this is facilitated by using a string-based encoding of
fitness evaluation, and selection steps are presented in the nodenames,types,andconnectivity,permittingoperatorsvery
following sections. The parameters affecting each step of the close to their counterparts in conventional EA; and in PDGP,
algorithm (Algorithm 1) are given in Table I. the operations are simplified by making nodes occupy points
in a fixed-size two-dimensional grid. What is common with
Algorithm 1 The proposed memetic algorithm GP related algorithms is that the output of each node in the
1: procedure MEMETICALGORITHM graph can constitute an input to another node. In comparison,
2: P(t=0)← INITIALIZE(Popsize,Cmax,Rmin,T) the range of connections that can form a semantic network
3: repeat of a given set of concepts is limited by commonsense knowl-
4: φ(t)← EVALUATEFITNESSES(P(t)) edge, i.e. the relations have to make sense to be useful (e.g.
5: S(t)← SELECTION(P(t),φ(t),Ssize,Sprob) IsA(bird,animal) is meaningful while Causes(bird,table)
6: V(t)← VARIATION(S(t),Pc,Pm,T) is not). To address this issue, we introduce new crossover
7: P(t+1)←V(t) and mutation operations for memetic variation, making use
8: t←t+1 of commonsense reasoning [23], [14] and adapted to work on
9: until stop criterion semantic networks.
10: end procedure
B. Commonsense Knowledge Bases
Commonsense reasoning refers to the type of reasoning
A. Representation: Semantic Networks as Memes involved in everyday human thinking, based on commonsense
The algorithm is centered on the use of semantic networks knowledge that an ordinary person is expected to know, or
[13]forencodingevolvingmemotypes.Asemanticnetworkis “the knowledgeof how theworld works” [23]. Commonsense
a graphic notation for the representation of knowledge in the knowledge bases such as the ConceptNet3 project of MIT
form of sets of vertices representing concepts, interconnected Media Lab [14] and Cyc4 maintained by Cycorp company
by edges representing relations (Fig. 1). This type of graph aresetuptoassembleandclassifycommonsenseinformation.
representation has found use in many subfields of artificial The lexical database WordNet5 maintained by the Cognitive
intelligence, including natural language processing, machine Science Laboratory at Princeton University also has charac-
translation, and information retrieval. Constructs resembling
semantic networks have long been in use also in other fields 2HereweadoptthenotationIsA(bird,animal)tomeanthattheconcepts
such as philosophy and linguistics. birdandanimalareconnectedbythedirectedrelationIsA,i.e.“birdisan
animal.”
An important characteristic of a semantic network is
3http://conceptnet.media.mit.edu
whether it is definitional or assertional: in definitional 4http://www.cyc.com
networks the emphasis is on taxonomic relations (e.g. 5http://wordnet.princeton.edu
teristics of a commonsense knowledge base, via synonym, generation (i.e. P +P = 1). We also employ elitism, by
c m
hypernym6, and hyponym7 relations [15]. replacing a randomly picked offspring in the next generation
In our implementation we make use of ConceptNet version with the individual with the current best fitness.
4 and WordNet version 3 to obtain and process commonsense
E. Memetic Variation Operators
knowledge, where ConceptNet contributes around 560,000
definitional and assertional relations involving 320,000 con- In contrast with existing graph-structured evolutionary ap-
cepts and WordNet contributes definitional relations involving proaches such as GP, PDGP, and GNP that we have discussed
around 117,000 synsets8, as of the writing of this article. in Section II-A, our representation does not permit arbitrary
The hypernym and hyponym relations among noun synsets connections between different nodes and requires variation
in WordNet provide a reliable collection of IsA relations. In operators that should be based on information provided by
contrast, the variety of assertions in ConceptNet, contributed commonsense knowledge bases.
by volunteers across the world, makes it more prone to noise. This means that any variation operation on the individuals
We address this by ignoring all assertions with a reliability should: (1) preserve the structure within boundaries set by
score (determined by contributors’ voting) below a set mini- commonsense knowledge; and (2) ensure that even vertices
mum R (Table I). and edges randomly introduced into a semantic network con-
min
nect to existing ones through meaningful relations.
C. Initialization
Here we present commonsense crossover and mutation
At the start of a run, the population of size Pop operators specific to semantic networks.
size
is initialized with individuals created by random semantic 1) Commonsense Crossover: In classical EA, features rep-
networkgeneration(Algorithm1).Thisisachievedbystarting resenting individuals are commonly encoded as linear strings
from a network comprising only one concept randomly and the crossover operation simulating genetic recombination
picked from commonsense knowledge bases and running is simply defined as a cutting and merging of this one dimen-
a semantic network expansion algorithm that (1) randomly sionalobjectfromtwoparents;andingraph-basedapproaches
picks a concept in the given network (e.g. human); (2) suchasGP,subgraphscanbefreelyexchangedbetweenparent
compiles a list of relations—from commonsense knowledge graphs [24], [16], [21]. Here, as mentioned, the requirement
bases—that the picked concept can be involved in (e.g. thatasemanticnetworkhastomakesenseimposessignificant
{CapableOf(human,think),Desires(human,eat),···}) constraints on the nature of recombination.
(3) appends to the network a relation randomly picked from We introduce two types of commonsense crossover that
this list, together with the other involved concept; and (4) are tried in sequence by the variation algorithm. The first
repeats this until a given number of concepts has been type attempts a sub-graph interchange between two selected
appended or a set timeout T has been reached (covering parents similar to common crossover in standard GP; and
situations where there are not enough relations). Figure 1 where this is not feasible due to the commonsense structure
presents a random semantic network created this way. Note of relations forming the parents, the second type falls back to
that even if grown in a random manner, the network itself is a combination of both parents into a new offspring.
totally meaningful because it is a combination of information Type I (subgraph crossover): A pair of concepts, one
from commonsense knowledge bases. from each parent, that are interchangeable9 are selected
Theinitializationalgorithmdependsupontheparametersof as crossover concepts, picked randomly out of all possible
C , the maximum number of initial concepts, and R , such pairs. For instance, in Figure 2, bird and airplane
max min
the minimum ConceptNet relation score (Table I). are interchangeable, since they can replace each other in
the relations CapableOf(·,fly) and AtLocation(·,air).
D. Selection
In each parent, a subgraph is formed, containing: (1)
After the assignment of a fitness value to each individual the crossover concept; (2) the set of all relations, and
in the current generation (Section II-F), all individuals in the associated concepts, that are not common with the other
population are replaced with offspring generated by variation crossover concept (In Figure 2 (a), HasA(bird,feather)
operators applied on parents. The parents are probabilistically and AtLocation(bird,forest); and in (b)
selected from the population according to their fitness, with HasA(airplane,propeller), MadeOf(airplane,metal),
reselection allowed. While individuals with a higher fitness and UsedFor(airplane,travel)); and (3) the set of all
have a better chance of being selected, even individuals with relations and concepts connected to these (In Figure 2 (a)
low fitness have a chance to produce offspring, however PartOf(feather,wing) and PartOf(tree,forest); and in
small. In our experiments we employ tournament selection (b) MadeOf(propeller,metal)), excluding the ones that are
(Section III). also one of those common with the other crossover concept
In each cycle of the algorithm, crossover is applied to par- (the concept fly in Figure 2 (a), because of the relation
entsselectedfromthepopulationuntilPop ×P offspring CapableOf(·,fly)). This, in effect, forms a subgraph of
size c
are created (Table I). Mutation is applied to Pop ×P information specific to the crossover concept, which is
size m
selected individuals, supplying the remaining part of the next insertable into the other parent. Any relations between the
subgraph and the rest of the network not going through the
6YisahypernymofXifeveryXisa(kindof)Y(IsA(dog,canine)).
7YisahyponymofXifeveryYisa(kindof)X. 9Wedefinetwoconceptsfromdifferentsemanticnetworksasinterchange-
8Asynset isasetofsynonymsthatareinterchangeablewithoutchanging ableifbothcanreplacetheotherinall,orpart,oftherelationstheotheris
thetruthvalueofanypropositionsinwhichtheyareembedded. involvedin,queriedfromcommonsenseknowledgebases.
crossover concept are severed (e.g. UsedFor(wing,fly) in as the number of nodes or edges, shortest path length, or the
Figure 2 (a)). The two offspring are formed by exchanging clustering coefficient [26].
these subgraphs between the parent networks (Figure 2 (c) Another interesting possibility is to make the inclusion
and (d)). of certain concepts a requirement, allowing the discovery of
Type II (graph merging crossover): A concept from each memes formed around a given set of seed concepts. This can
parent that is attachable10 to the other parent is selected as be also achieved through starting the initialization procedure
a crossover concept. The two parents are merged into an described in Section II-C with the given concepts.
offspring by attaching a concept in one parent to another A direct and very interesting application of our approach
conceptintheotherparent,pickedrandomlyoutofallpossible would be to devise experiments with realistically formed
attachments (CreatedBy(art,human) in Figure 3. Another fitness functions modeling selectionist theories of knowledge,
possibilityisDesires(human,joy).).Thesecondoffspringis which remain untested until this time. One such theory is
formed randomly the same way. In the case that no attachable the evolutionary epistemology of Campbell [2], describing
concepts are found, the parents are merged as two separate the development of human knowledge and creativity through
clusters within the same semantic network. selectionist principles such as blind variation and selective
2) Commonsense Mutation: We introduce several types of retention (BSVR).
commonsense mutation operators that modify a parent by
means of information from commonsense knowledge bases.
III. EXPERIMENTSANDRESULTS
For each mutation to be performed, the type is picked at
random with uniform probability. If the selected type of
To evaluate our approach, we first introduce a fitness
mutation is not feasible due to the commonsense structure of
measure based on structure mapping. The rest of this section
the parent, another type is again picked. In the case that a set
then summarizes our choice of parameters and results from
timeout of T trials has been reached without any operation,
experiments.
the parent is returned as it is.
Type I (concept attachment): A new concept randomly
A. Analogy with a Given Semantic Network
picked from the set of concepts attachable to the parent is
attached through a new relation to one of existing concepts
As a simple and interesting memetic fitness function, we
(Figure 4 (a) and (b)).
introduceanalogicalsimilaritywithagivensemanticnetwork,
TypeIIa(relationaddition):Anewrelationconnectingtwo
utilizing the Structure Mapping Engine (SME) [27], [28].
existing concepts in the parent is added, possibly connecting
SMEisanalgorithmimplementingthepsychologicalstructure
unconnected clusters within the same network (Figure 4 (c)
mapping theory of Gentner [25], often cited as the most
and (d)).
influential work on modeling analogy-making [29]. Using the
Type IIb (relation deletion): A randomly picked relation in analogicalmatchingscorefromSMEasafitnessmeasure,our
the parent is deleted, possibly leaving unconnected clusters algorithm can evolve collections of information, or memes,
within the same network (Figure 4 (e) and (f)). that are analogous to a given one.
Type IIIa (concept addition): A randomly picked new con-
SME is based on the idea that an analogy is a one-to-one
cept is added to the parent as a new cluster (Figure 4 (g) and
mappingfromonedomain(thebase)intoanother(thetarget),
(h)).
whichcorrespond,inourfitnessmeasure,tothesemanticnet-
Type IIIb (concept deletion): A randomly picked concept is
work supplied at the start and the individual networks whose
deletedwithalltherelationsitisinvolvedin,possiblyleaving
fitnessesareevaluatedbythefunction.Themappingisguided
unconnected clusters within the same network (Figure 4 (i)
by the structure of relations between concepts in the two
and (j)).
domains, ignoring the semantics of the concepts themselves;
Type IV (concept replacement): A concept in the parent,
and is based on the systematicity principle, where connected
randomly picked from the set of those with at least one inter-
knowledge is preferred over independent facts and is assigned
changeableconcept,isreplacedwithoneofitsinterchangeable
a higher matching score. A commonly used example is the
concepts,againrandomlypicked.Anyrelationsleftunsatisfied
analogy between the Solar System and the Rutherford–Bohr
by the new concept are deleted (Figure 4 (k) and (l)).
model of the atom [25], where sun and planet in the first
domain are analogous to nucleus and electron in the second
F. Fitness Measure
domain. The labels and structure of relations in the two
Since the evolving individuals in our approach represent domains (e.g. {Attracts(sun,planet), Orbits(planet,sun),
pieces of knowledge, or memes, the fitness measure for evo- ···} and {Attracts(nucleus, electron), Orbits(electron,
lutionary selection is defined as a function of the represented nucleus), ···}) define and constrain the possible mappings
knowledge.InSectionIIIwedefineamemeticfitnessmeasure
between concepts in the two domains that can be formed by
based on the structure mapping theory from psychology [25],
SME.
to evaluate our approach. The simple fitness function used
We make use of our own implementation of SME based
in this introductory study can be extended to take graph-
on the original description by Falkenhainer [27] and adapt it
theoretical properties of semantic networks into account, such
tothesimpleconcept–relationstructureofsemanticnetworks,
by mapping the predicate calculus constructs of entities into
10We define a distinct concept as attachable to a semantic network if at
concepts, relations to relations, attributes to IsA relations,
leastonecommonsenserelationconnectingtheconcepttoanyoftheconcepts
inthenetworkcanbediscoveredfromcommonsenseknowledgebases. and excluding functions.
(a) Parent1 (b) Parent2
lift
Causes
metal
fly wing
MadeOf
travel
MadeOf propeller PartOf
UsedFor HasA CapableOf feather
airplane
air bird HasA
AtLocation
AtLocation PartOf AtLocation
CapableOf oxygen
forest
air fly
CapableOf kite PartOf tree
(c) Offspring1 (d) Offspring2
Fig.2. CommonsensecrossovertypeI(subgraphcrossover),centeredontheconceptsofbirdforparent1andairplaneforparent2.
notes
PartOf
music joy
UsedFor Causes
art
Causes violin IsA
Causes
human planet
IsA joy HasA AtLocation art
brain
notesPartOf music Causes IsA earth IsA CreatedBy IsA HawsAoman
human
HasA
UsedFor
AtLocation HasA
violin woman planet IsA earth brain
(a) Parent1 (b) Parent2 (c) Offspring
Fig.3. CommonsensecrossovertypeII(graphmergingcrossover),mergingbytherelationCreatedBy(art,human).Ifnoconceptsattachablethrough
commonsenserelationsareencountered,theoffspringisformedbymergingtheparentnetworksastwoseparateclusterswithinthesamesemanticnetwork.
B. Results population of Pop =200 individuals to tournament selec-
size
tion with tournament size S = 8 and winning probability
In this introductory study, we adopt values for crossover size
S =0.8.
and mutation probabilities similar to earlier studies in graph- prob
based EA [24], [16] (Table I). We use a crossover probability Using this parameter set, we present the results from two
ofP =0.85,andasomewhat-above-averagemutationrateof runsofexperiment:evolvedanalogiesforanetworkdescribing
c
P = 0.15, accounting for the high tendency of mutation some basic astronomical knowledge are shown in Figure 5
m
postulated in memetic literature11. We employ tournament and for a network of familial relations in Figure 6. We show
selection, meaning that for each selection, a “tournament” is in Figure 7 (a) the progress of the best and average fitness
held among a few randomly chosen individuals, and the more in the population during the run that produced the results in
fit individual of each successive pair is the winner according Figure 5. The best and average size of semantic networks
to a winning probability. In our experiments, we subject a formingtheindividualsareshowninFigure7(b).Weobserve
that evolution asymptotically reaches a fitness plateau after
11SeeGil-White[30]forareviewanddiscussionofmutationinmemetics. about 40 generations. This coincides roughly with the point
home dessert
dessert
eat home
AtLocation
eat IsA
UsedFor Desires AtLocation UsedFor Desires person IsA IsA
cheesecake
person dessert CapableOf IsA cheesecake IsA
dessert walk cake cake
(a) MutationtypeI(before) (b) MutationtypeI(after) (c) MutationtypeIIa(before) (d) MutationtypeIIa(after)
sweet
sweet
eat
dessert HasProperty HasProperty eat
dessert UsedFor dessert UsedFor
dessert
IsA
IsA
IsA IsA IsA IsA cheesecake IsA cheesecake IsA person
cheesecake
cheesecake IsA IsA IsA
cake cake cake cake
(e) MutationtypeIIb(before) (f) MutationtypeIIb(after) (g) MutationtypeIIIa(before) (h) MutationtypeIIIa(after)
eat
sweet
sweet UsedFor home university
eat
HasProperty
dessert UsedFor HasProperty dessert
AtLocation AtLocation
eat eat
IsA
cheesecake IsA IsA UsedFor Desires person UsedFor Desires person
dessert CapableOf dessert CapableOf
IsA cake cake walk walk
(i) MutationtypeIIIb(before) (j) MutationtypeIIIb(after) (k) MutationtypeIV(before) (l) MutationtypeIV(after)
Fig.4. Examplesillustratingthetypesofcommonsensemutationusedinthisstudy.
TABLEI
wherethesizeofthebestindividualbecomescomparablewith
PARAMETERSUSEDDURINGEXPERIMENTS
thatofthegivenbasesemanticnetwork(Figure5),afterwhich
improvements in the one-to-one analogy become sparser.
Parameter Value
Our experiments demonstrate that the proposed algorithm is
capable of spontaneously creating collections of knowledge Evolution Populationsize(Popsize) 200
analogous to the one given in a base semantic network, with Crossoverprobability(Pc) 0.85
very good performance. In most cases, our implementation Mutationprobability(Pm) 0.15
was able to reach extensive analogies within 50 generations Semanticnetworks Max.initialconcepts(Cmax) 5
and reasonable computational time. Min.relationscore(Rmin) 2.0
Timeout(T) 10
IV. CONCLUSIONANDFUTUREWORK
Selection Type Tournament
In summary, we have presented a novel evolutionary algo- Tournamentsize(Ssize) 8
rithmthatemployssemanticnetworksasevolvingindividuals, Tournamentwinprob.(Sprob) 0.8
paralleling the evolutionary model of cultural variation and Elitism Employed
selection in the existing field of memetics. This algorithm, to
our knowledge, is the first of its kind. The use of semantic
networks provides a suitable basis to implement the represen-
evaluate the feasibility and performance of our work. Con-
tation and manipulation of memes—in the sense of units of
sidering other possible fitness measures, we hope that our
culture,orknowledge,asitwasputforthbyDawkins[3].We
approach can serve as a computational tool for implementing
have introduced preliminary versions of variation operators
andexperimentingwithdifferenttheoriesofculturalevolution
that work on this representation, utilizing knowledge from
encountered in memetics, such as evolutionary epistemology
commonsense knowledge bases. We have also contributed
and cultural selection theory. The facts that:
a memetic fitness measure based on the structure mapping
theory of Gentner [25] with a firm basis in psychology, to • the algorithm is exclusively on the evolution of knowl-
galaxy home
AtLocation PartOf universe father IsA man AtLocation
solar system IsA dream
human
PartOf CapableOf
HasSubevent
large object AtLocation sleep
IsA
family
IsA
planet HasA mass PartOf woman
IsA MadeOf mother IsA IsA
HasA earth matter HasProperty CapableOf female
moon
HasProperty care
HasProperty
(a) Givensemanticnetwork,11concepts,11relations(basedomain)
spherical
(a) Givensemanticnetwork,10concepts,11relations(basedomain)
music hall
mountain percussion instrument AtLocation
forest play instrument
PartOf IsA IsA
AtLocation tree drum instrument CapableOf HasSubevent
make music
IsA
source of vitamin AtLocation
IsA wind instrument
fruit IsA
IsA HasA IsA
member of orchestra
apple
HasA clarinet
seed
leave
HasProperty CapableOf
HasProperty
green perform glissando
(b) Evolvedindividual,9concepts,9relations(targetdomain) (b) Evolvedindividual,10concepts,9relations(targetdomain)
Fig. 5. Experiment 1: The evolved individual is encountered after 35 Fig. 6. Experiment 2: The evolved individual is encountered after 42
generations, with fitness value 2.8. Concepts and relations of the individual generations, with fitness value 2.7. Concepts and relations of the individual
notinvolvedintheanalogyarenotshownhereforclarity. notinvolvedintheanalogyarenotshownhereforclarity.
edge itself under a fitness measure defined as a function sible analogical mappings between two given domains [29],
of the represented knowledge; while our approach provides a novel technique for the open-
• and that it uses an encoding based on knowledge rep- ended discovery of information analogous to a given domain,
resentation (in the form of semantic networks), utilizing together with the analogical mapping.
memetic operators specifically created for the modifica- For future work following this study, we acknowledge
tion of these several lines of research concerning the design of the al-
gorithm and its possible applications. Regarding the design,
setitapartfromexistingMA,wheretheconceptofmemet-
the research would benefit from exploring different types of
ics has been used as a synonym for an hybridization of local
mutation and crossover [24], [17]. It would be significant to
refinement by individual learning after a classical global EA
ground the design of such operators on existing theories of
sampling.
cultural transmission and modification, discussed in sociolog-
Theproposedalgorithmishighlyrelevantfromtheperspec-
ical theories of knowledge.
tive of computational creativity [31], [32], especially for tasks
Regardingtheapplications,inanupcomingpaperweintend
such as conceptual blending [33] and story generation [34].
to focus on different types of computational creativity that
Webelievethatourapproachcanfitintobothclassificationsof
would be achievable with this model. In the long term, we
creativity discussed by Boden [35]: (1) exploratory creativity,
argue that if a theoretically sound basis for memetic varia-
where the commonsense nature of our memetic operators
tion and inheritance can be put in place, and together with
addresses the criticism about the lack of world knowledge12;
realistic memetic fitness measures, our approach can enable
and (2) transformational creativity, where the potential of
“computational memetic simulations” analogous to those in
evolutionary approaches have already been noted. Within the
computational biology, such as genetic drift or coalescent
field of analogical reasoning, virtually all of existing research
theories.
has been focused on the discovery and assessment of pos-
ACKNOWLEDGMENT
12QutingBoden[35]:“What’smissing,ascomparedwiththehumanmind,
This work was supported by a JAE-Predoc fellowship from
is the rich store of world knowledge (including cultural knowledge) that’s
ofteninvolved.” CSIC, and the research grants: 2009-SGR-1434 from the
3.0
[10] H. A. Abbass, “A memetic pareto evolutionary approach to artificial
2.5 (cid:232)(cid:232)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232) noenuArarltinfiectiwaloIrnktse,”lliignePncroec(eAeId0i1n)g,ssoerf.tLheec1t4utrheANuosttersailniaCnoJmoipnuttCeronSfceireennccee,
(cid:232)(cid:232) (cid:233)(cid:233) vol.2256. Springer,2001,pp.1–12.
2.0 (cid:232)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:233)(cid:233) [11] M. Mignotte, C. Collet, P. Perez, and P. Bouthemy, “Hybrid genetic
Fitness 1.5 (cid:232)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:233) ooApfntaismlhyasizdisaotwaionndshaManpdaecsshtiaintniestsIinoctnaelalrlmigioemdnaecglee,bravyso,”el.dI2Ea2pE,pEpropTa.cr1ah2n9fso–ar1c4ttih1oe,ns2c0lao0sn0s.ifiPcaattteiornn
(cid:232) (cid:233) [12] N.ChaiyaratanaandA.Zalzala,“Hybridisationofneuralnetworksand
1.0 (cid:232) (cid:233) geneticalgorithmsfortime-optimalcontrol,”inProceedingsofthe1999
(cid:232) (cid:233) Congress on Evolutionary Computation (CEC 99). Washington, DC:
0.5 (cid:233) IEEE,1999,pp.389–396.
(cid:233) [13] J. F. Sowa, Principles of Semantic Networks: Explorations in the
0.0 RepresentationofKnowledge. SanMateo:MogranKaufmann,1991.
0 10 20 30 40 50 [14] C.Havasi,R.Speer,andJ.Alonso,“ConceptNet3:aflexible,multilin-
Generations t gual semantic network for common sense knowledge,” in Proceedings
ofRecentAdvancesinNaturalLanguageProcessing,2007.
(a)
[15] C. Fellbaum, WordNet: An Electronic Lexical Database. MIT Press,
(cid:72)(cid:76)
1998.
20 (cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233)(cid:233) [16] JG..RL.anKzoaz,aG,eMne.tiAc.PKroegarnaem,mMin.gJ.IVS:trReeotuetri,neWH. uMmyadnlo-Cwoemc,peJt.itYivue,Manad-
(cid:233)(cid:233)(cid:233) chineIntelligence. KluwerAcademicPublishers,2003.
(cid:233)
worksize 15 (cid:232)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232)(cid:232) [17] HScrI.oCKsEsaotAvaengrniruiin,aKlgCe.nHoenitrfiaecsrenanwectawe,,oJvr.koHlp.ur,2o.agnrdaSmJp.mriMninguger,ra”,tai2n,0“0PC2ro,omcpeppe.adr1iin2ng6gs3s–oo1fm2t6eh8eg.r4a1psht
Semanticnet 105 (cid:232)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:232)(cid:233)(cid:233) [[1198]] SR3rrie6.t.ih9nMPm–foo3a:lr9bic,G8ue,N,men2eKee0wn.t0itc7HIld.eienraaaersstnwaiiwnongar,kO,”apEpntrivdomogliJurs.aatimHtoionmuna,i.rn“ygACM(goGcrmaGNpprPhua)-wtbaa-atHinsodeindll,i,tves1vo9ole.9lxu91tte,5ino,csnhnia.oornP.ya3uar,aslgilpnlopeg-l.
(cid:232)(cid:232)(cid:233)(cid:233) DistributedGeneticProgramming.
(cid:233)(cid:233)
[20] D. Chen, T. Aoki, N. Homma, T. Terasaki, and T. Higuchi, “Graph-
0 basedevolutionarydesignofarithmeticcircuits,”IEEETransactionson
0 10 20 30 40 50 EvolutionaryComputation,vol.6,no.1,pp.86–100,2002.
Generations t [21] H. A. Montes and J. L. Wyatt, “Graph representation for program
evolution:Anoverview,”UniversityofBirminghamSchoolofComputer
(b)
Science,Tech.Rep.,2004.
(cid:72)(cid:76)
[22] A. Teller, “Algorithm evolution with internal reinforcement for signal
Fig. 7. Evolution of (a) fitness and (b) semantic network size during the
understanding,” Ph.D. dissertation, Carnegie Mellon University, Pitts-
course of an experiment with parameters given in Table I. Filled circles
burgh,PA,1998.
representthebestindividualinageneration,whiletheemptycirclesrepresent
[23] E.T.Mueller,CommonsenseReasoning. MorganKaufmann,2006.
populationaverage.Networksizeistakentobethenumberofrelations(edges)
[24] F. B. Pereira, P. Machado, E. Costa, and A. Cardoso, “Graph based
inthesemanticnetwork.
crossover—Acasestudywiththebusybeaverproblem,”inProceedings
of the Genetic and Evolutionary Computation Conference, vol. 2.
MorganKaufmann,1999,pp.1149–1155.
[25] D. Gentner and A. B. Markman, “Structure mapping in analogy and
Generalitat de Catalunya, CSD2007-0022 from MICINN, and
similarity,”AmericanPsychologist,vol.52,pp.45–56,1997.
Next-CBR TIN2009-13692-C03-01 from MICINN. [26] M.SteyversandJ.B.Tenenbaum,“Thelarge-scalestructureofsemantic
networks:statisticalanalysesandamodelofsemanticgrowth,”Cogni-
tiveScience,vol.29,pp.41–78,2005.
REFERENCES
[27] B.Falkenhainer,K.D.Forbus,andD.Gentner,“TheStructure-Mapping
Engine:Algorithmandexamples,”ArtificialIntelligence,vol.41,pp.1–
[1] D.C.Dennett,Darwin’sDangerousIdea:EvolutionandtheMeanings 63,1989.
ofLife. Simon&Schuster,1995. [28] K.D.Forbus,R.W.Ferguson,andD.Gentner,“Incrementalstructure-
[2] M. H. Bickhard and D. T. Campbell, “Variations in variation and mapping,” Proceedings of the Cognitive Science Society, pp. 313–318,
selection:theubiquityofthevariation-and-selective-retentionratchetin 1994.
emergentogranizationalcomplexity,”FoundationsofScience,vol.8,pp. [29] R.M.French,“Thecomputationalmodelingofanalogy-making,”Trends
215–2182,2003. inCognitiveSciences,vol.6,no.5,pp.200–205,2002.
[3] R.Dawkins,TheSelfishGene. OxfordUniversityPress,1989. [30] F. Gil-White, “Let the meme be (a meme): insisting too much on the
[4] P.A.Moscato,“Onevolution,search,optimization,geneticalgorithms genetic analogy will turn it into a straightjacket,” in Culture, Nature,
and martial arts: Towards memetic algorithms,” Caltech Concurrent Memes, T. Botz-Bornstein, Ed. Newcastle upon Tyne: Cambridge
ComputationProgram,Tech.Rep.C3P826,1989. Scholars,2008.
[5] P.A.Moscato,C.Cotta,andA.Mendes,StudiesinFuzzinessandSoft [31] G.A.Wiggins,“Apreliminaryframeworkfordescription,analysisand
Computing–NewOptimizationTechniquesinEngineering. NewYork: comparisonofcreativesystems,”Knowledge-BasedSystems,vol.19,pp.
Springer,2004,ch.MemeticAlgorithms. 449–458,2006.
[6] N. Krasnogor and J. Smith, “A tutorial for competent memetic algo- [32] W.Duch,“Intuition,insight,imaginationandcreativity,”IEEECompu-
rithms: model, taxonomy, and design issues,” IEEE Transactions on tationalIntelligenceMagazine,vol.2,no.3,pp.40–52,2007.
EvolutionaryComputation,vol.9,no.5,pp.474–488,2005. [33] G.Fauconnier,“Generalizedintegrationnetworks,”inNewDirectionsin
[7] T.BuiandB.Moon,“Geneticalgorithmandgraphpartitioning,”IEEE CognitiveLinguistics,V.EvansandS.Pourcel,Eds. JohnBenjamins,
TransactionsonComputers,vol.45,pp.841–855,1996. 2009.
[8] P. Merz, “A comparison of memetic recombination operators for the [34] M.O.Riedl,“Storyplanning:Creativitythroughexploration,retrieval,
traveling salesman problem,” in GECCO 2002: Proceedings of the andanalogicaltransformation,”MindsandMachines,vol.20,no.4,pp.
GeneticandEvolutionaryComputationConference. NewYork:Morgan 1–26,2010.
Kaufmann,2002,pp.472–479. [35] M. A. Boden, “Computer models of creativity,” AI Magazine, vol. 30,
[9] C. Cotta and J. M. Troya, “A comparison of several evolutionary no.3,pp.23–34,2009.
heuristics for the frequency assignment problem,” in Connectionist
ModelsofNeurons,LearningProcesses,andArtificialIntelligence,ser.
LectureNotesinComputerScience,J.MiraandA.Prieto,Eds. Berlin:
Springer,2001,vol.2084,pp.474–481.
