474 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 9, NO. 5, OCTOBER 2005
A Tutorial for Competent Memetic Algorithms:
Model, Taxonomy, and Design Issues
Natalio Krasnogor and Jim Smith
Abstract—The combination of evolutionary algorithms with
local search was named “memetic algorithms” (MAs) (Moscato,
1989). These methods are inspired by models of natural systems
that combine the evolutionary adaptation of a population with
individual learning within the lifetimes of its members. Addition-
ally, MAs are inspired by Richard Dawkin’s concept of a meme,
which represents a unit of cultural evolution that can exhibit local
refinement (Dawkins, 1976). In the case of MA’s, “memes” refer
to the strategies (e.g., local refinement, perturbation, or construc-
tive methods, etc.) that are employed to improve individuals. In
this paper, we review some works on the application of MAs to
well-known combinatorial optimization problems, and place them
in a framework defined by a general syntactic model. This model
provides us with a classification scheme based on a computable
index
, which facilitates algorithmic comparisons and suggests
areas for future research. Also, by having an abstract model for
this class of metaheuristics, it is possible to explore their design
space and better understand their behavior from a theoretical
standpoint. We illustrate the theoretical and practical relevance of
this model and taxonomy for MAs in the context of a discussion
of important design issues that must be addressed to produce
effective and efficient MAs.
Index Terms—Design issues, evolutionary global–local search
hybrids, memetic algorithms (MAs), model, taxonomy.
I. INTRODUCTION
E
VOLUTIONARY ALGORITHMS (EAs) are a class of
search and optimization techniques that work on a prin-
ciple inspired by nature: Darwinian Evolution. The concept of
natural selection is captured in EAs. Specifically, solutions to a
given problem are codified in so-called chromosomes. The evo-
lution of chromosomes due to the action of crossover, mutation,
and natural selection are simulated through computer code.
It is now well established that pure EAs are not well suited
to fine tuning search in complex combinatorial spaces and that
hybridization with other techniques can greatly improve the ef-
ficiency of search [3]–[6]. The combination of EAs with local
search (LS) was named “memetic algorithms” (MAs) in [1].
MAs are extensions of EAs that apply separate processes to
refine individuals, for example, improving their fitness by hill-
climbing.
Manuscript received July 15, 2003; revised January 27, 2005.
N. Krasnogor is with School of Computer Science and Information
Technology, University of Nottingham, Nottingham NG7 2RD, U.K. (e-mail:
natalio.krasnogor@nottingham.ac.uk).
J. Smith is with the Faculty of Computing, Engineering and Mathematical
Sciences, University of the West of England, Bristol, BS16 1QY England, U.K.
(e-mail: james.smith@uwe.ac.uk).
Digital Object Identifier 10.1109/TEVC.2005.850260
These methods are inspired by models of adaptation in natural
systems that combine the evolutionary adaptation of a popula-
tion with individual learning within the lifetimes of its members.
The choice of name is inspired by Richard Dawkins’ concept of
a meme, which represents a unit of cultural evolution that can
exhibit local refinement [2]. In the context of heuristic optimiza-
tion, a meme is taken to represent a learning or development
strategy. Thus, a memetic model of adaptation exhibits the plas-
ticity of individuals that a strictly genetic model fails to capture.
In the literature, MAs have also been named hybrid genetic
algorithms (GAs) (e.g., [7]–[9]), genetic local searchers (e.g.,
[10]), Lamarckian GAs (e.g., [11]), and Baldwinian GAs (e.g.,
[12]), etc. As noted above, they typically combine local search
heuristics with the EAs’ operators, but combinations with con-
structive heuristics or exact methods may also be considered
within this class of algorithms. We adopt the name of MAs
for this metaheuristic, because we think it encompasses all the
major concepts involved by the other ones, and for better or
worse has become the de facto standard, e.g., [13]–[15].
EAs and MAs have been applied in a number of different
areas, for example, operational research and optimization, auto-
matic programming, and machine and robot learning. They have
also been used to study and optimize of models of economies,
immune systems, ecologies, population genetics, and social sys-
tems, and the interaction between evolution and learning, to
name but a few applications.
From an optimization point of view, MAs have been shown
to be both more efficient (i.e., requiring orders of magnitude
fewer evaluations to find optima) and more effective (i.e., iden-
tifying higher quality solutions) than traditional EAs for some
problem domains. As a result, MAs are gaining wide accep-
tance, in particular, in well-known combinatorial optimization
problems where large instances have been solved to optimality
and where other metaheuristics have failed to produce compa-
rable results (see for example [16] for a comparison of MAs
against other approaches for the quadratic assignment problem).
II. G
OALS,AIMS, AND
METHODS
Despite the impressive results achieved by some MA prac-
titioners, the process of designing effective and efficient MAs
currently remains fairly ad hoc and is frequently hidden behind
problem-specific details. This paper aims to begin the process
of placing MA design on a sounder footing. In order to do this,
we begin by providing some examples of MAs successfully ap-
plied to well-known combinatorial optimization problems, and
draw out those differences which specifically arise from the hy-
bridization of the underlying EA, as opposed to being design
choices within the EA itself. These studies are exemplars, in the
1089-778X/$20.00 © 2005 IEEE
KRASNOGOR AND SMITH: TUTORIAL FOR COMPETENT MEMETIC ALGORITHMS: MODEL, TAXONOMY, AND DESIGN ISSUES 475
sense that they represent a wide range of applications and algo-
rithmic options for a MA.
The first goal is to define a syntactic model which enables
a better understanding of the interplay between the different
component parts of an MA. A syntactic model is devoid of
the semantic intricacies of each application domain and hence
exposes the bare bones of this metaheuristic to scrutiny. This
model should be able to represent the many different parts that
compose an MA, determine their roles and interrelations.
With such a model, we can construct a taxonomy of MAs, the
second goal of this paper. This taxonomy is of practical and the-
oretical relevance. It will allow for more sensible and fair com-
parisons of approaches and experimental designs. At the same
time, it will provide a conceptual framework to deal with more
difficult questions about the general behavior of MAs. More-
over, it will suggest directions of innovation in the design and
development of MAs.
Finally, by having a syntactic model and a taxonomy, the
process of more clearly identifying which of the many compo-
nents (and interactions) of these complex algorithms relate to
which of these design issues should be facilitated.
The rest of this paper is organized as follows. In Section III,
we motivate our definition of the class of metaheuristics under
consideration, and give examples of the type of design issues
that have motivated this study. This is followed in Section IV by
a review of some applications of MAs to well-known problems
in combinatorial optimization and bioinformatics. Section V
presents a syntax-only model for MAs and a taxonomy of
possible architectures for these metaheuristics is given in Sec-
tion VI. In Section VII, we return to the discussion of design
issues, showing how some of these can be aided by the insights
given by our model. Finally, we conclude with a discussion and
conclusions in Section VIII.
III. B
ACKGROUND
A. Defining the Subject of Study
In order to be able to define a syntactic model and taxonomy,
we must first clarify what we mean by an MA. It has been argued
that the success of MAs is due to the tradeoff between the ex-
ploration abilities of the EA, and the exploitation abilities of the
local search used. The well-known results of MAs over multi-
start local search (MSLS) [17] and greedy randomized adaptive
search procedure (GRASP) [8] suggest that, by transferring in-
formation between different runs of the local search (by means
of genetic operators) the MA is capable of performing a much
more efficient search. In this light, MAs have been frequently
described as genetic local search which might be thought as the
following process [18]:
In each generation of GA, apply the LS operator to all
solutions in the offspring population, before applying the
selection operator.
Although many MAs indeed use this formula this is a somewhat
restrictive view of MAs, and we will show in the following sec-
tions that many other ways have been used to hybridize EAs
with LS with impressive results.
In [19], the authors present an algebraic formalization of
MAs. In their approach, an MA is a very special case of GA
where just one period of local search is performed. As we will
show in the following sections, MAs are used in a plethora
of alternative ways and not just in the way the formalism
introduced in [19] suggests.
It has recently been argued by Moscato that the class of MAs
should be extended to contain not only “EA-based MAs,” but
effectively include any population-based approach based on
a “k-merger” operator to combine information from solutions
[13], creating a class of algorithms called the polynomial
merger algorithm (PMA). However, PMA ignores mutation
and selection as important components of the evolutionary
metaheuristic. Rather, it focuses exclusively on recombination,
or it is more general form, the “k-merger” operator. Therefore,
we do not use this definition here, as we feel that it is both
restrictive (in that it precludes the possibility of EAs which do
not use recombination), and also so broad that it encompasses
such a wide range of algorithms as to make analysis difficult.
As the limits of “what is” and “what is not” an MA are
stretched, it becomes more and more difficult to assess the
benefit of each particular component of the metaheuristic in
search or optimization. A priori formalizations such as [13]
and [19] inevitably leave out many demonstrably successful
MAs and can seriously limit analysis and generalization of the
(already complex) behavior of MAs. Our intention is to provide
an a posteriori model of MAs, using algorithms as data; that
is, applications of MAs that have been proven successful. It
will be designed in such a way to encompass those algorithms.
Thus, we use a commonly accepted definition, which may be
summarized as [20]:
An MA is an EA that includes one or more local search
phases within its evolutionary cycle.
While this definition clearly limits the scope of our study, it
does not curtail the range of algorithms that can fit this scope.
As with any formal model and taxonomy, ours will have its own
“outsiders,” but hopefully they will be less numerous than those
left aside by [13] and [19]. The extension of our model to other
population-based metaheuristics is being considered in a sepa-
rate paper.
Finally, we should note that we have restricted the survey part
of this paper to MAs approaches for single-objective combina-
torial optimization problems (as opposed to multiobjective or
numerical optimization problems). This is not because MAs are
unsuited to these domains—they have been very successfully
applied to the fields of multiobjective optimization (see, e.g.,
[21]–[24], an extensive bibliography can be found in [25]),
and numerical optimization (see, e.g., [26]–[32]). Rather, the
reason for this omission is partly practical, to do with the space
this large field would demand. It is also partly because we wish
to introduce our ideas in the context of the simple algorithm
, where it is straightforward to
define a neighborhood, improvement, and the concept of local
optimality. When we consider multiobjective problems, the
whole concept of optimality becomes clouded by the trade-
offs between objectives, and dominance relations are usually
preferred. Similarly, in the case of numerical optimization, the
concept of local optimality is clouded by the difficulty, in the
absence of derivative information, of knowing when a solution
is truly locally optimal, as opposed to say, a point, a very small
476 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 9, NO. 5, OCTOBER 2005
distance away. Nevertheless, it is worth stressing that the issues
cloud the exposition, rather than invalidate the concept of
“schedulers” which leads to our syntactic model and taxonomy,
and the subsequent design guidelines which can equally well
be applied in these more complex domains.
B. Design Issues for MAs
Having provided a fairly broad-brush definition of the class
of metaheuristics that we are concerned with, it is still vital to
note that the design of “competent” [33] MAs raises a number
of important issues which must be addressed by the practitioner.
Perhaps the foremost of these issues may be stated as:
“What is the best tradeoff between local search and the
global search provided by evolution?”
This leads naturally to questions such as the following.
•
Where and when should local search be applied within the
evolutionary cycle?
•
Which individuals in the population should be improved
by local search, and how should they be chosen?
•
How much computational effort should be allocated to
each local search?
•
How can the genetic operators best be integrated with
local search in order to achieve a synergistic effect?
As we will see in the following sections, there are a host
of possible answers to these questions, and it is important to
use both empirical experience and theoretical reasoning in the
search for answers. The aim of our syntactic model is to pro-
vide a sound basis for understanding and comparing the effects
of different schemes. The use of a formal model aids in this by
making some of the design choices more explicit, and by pro-
viding a means of comparing the existing MA literature with the
(far broader) body of research into EAs.
Similarly, while theoretical understanding of the interplay be-
tween local and global search is much less developed than that
of “pure” EAs, it is possible to look in that literature for tools
and concepts that may aid in the design of competent MAs, for
example:
•
Is a Baldwinian or Lamarckian model of improvement to
be preferred?
•
What fitness landscape(s) does the population of the MA
operate on?
•
What local optima are the MAs operating with?
•
How can we engineer MAs that efficiently traverse large
neutral plateaus and avoid deep local optima?
IV. S
OME EXAMPLE APPLICATIONS OF
MAS
IN OPTIMIZATION AND SEARCH
In this section, we will briefly comment on the use of MAs
on different combinatorial optimization problems and adaptive
landscapes. Applications to traveling salesman problem (TSP),
quadratic assignment problem (QAP), binary quadratic pro-
gramming (BQP), minimum graph coloring (MGC), and protein
structure prediction problem (PSP) will be reviewed.
This section does not pretend to be an exhaustive bibliog-
raphy survey, but rather a gallery of well-known applications
of MAs from which some architectural and design conclusions
might be drawn. In [34], a comprehensive bibliography can be
found.
For the definition of the problems, the notation in [35] will
be used. The reader interested in the complexity and approx-
imability results of those problems is referred to the previous
reference. The pseudocode used to illustrate the different algo-
rithms is shown as used by the respective authors, with only
some minor changes made for the sake of clarity.
In [36], a “standard” local search algorithm is defined in terms
of a local search problem. Because this standard algorithm is
implicit in many MAs, we repeat it here.
Begin
produce a starting solution
to problem instance ;
Repeat Until (locally optimal) Do
using
and generate the next
neighbor
;
If (
is better than ) Then
;
Fi
Od
End.
Algorithm captures the in-
tuitive notion of searching a neighborhood as a means of
identifying a better solution. It does not specify tie-breaking
policies, neighborhood structure, etc.
This algorithm uses a “greedy” rather than a “steepest” policy,
i.e., it accepts the first better neighbor that it finds. In general,
a given solution might have several better neighbors, and the
rule that assigns one of the (potentially many) better neigh-
bors to a solution is called a pivot rule. The selection of the
pivot rule or rules to use in a given instantiation of the stan-
dard local search algorithm has tremendous impact on the com-
plexity of the search and potentially in the quality of the solu-
tions explored.
Note also that the algorithm above implies that local search
continues until a local optima is found. This may take a long
time, and in the continuous domain proof of local optimality
may be decidedly nontrivial. Many of the local search proce-
dures embedded within the MAs in the literature are not stan-
dard in this sense, that is, they usually perform a shorter “trun-
cated” local search.
A. MAs for the TSP
The TSP is one of the most studied combinatorial optimiza-
tion problems. It is defined by the following.
Traveling Salesman Problem
Instance: A set
of cities, and for each pair of cities
, a distance .
Solution: A tour of
, i.e.,
a permutation
.
Measure: The length of the tour, i.e.,
.
Aim: minimum length tour
.
KRASNOGOR AND SMITH: TUTORIAL FOR COMPETENT MEMETIC ALGORITHMS: MODEL, TAXONOMY, AND DESIGN ISSUES 477
In [37], a short review on early MAs for the TSP is presented,
where an MA was defined by the following skeleton code.
Begin
/
, , /
For
To Do
Iterative_Improvement
;
Od
stop_criterion:= false
While (
stop_criterion) Do
;
For
To Do
/
Mate /
;
/
Recombine /
;
Iterative_Improvement
;
;
Od
/
Select /
;
evaluate stop_criterion
Od
End.
Here, we can regard as a
particular instantiation of
, and
appropriate code should be used to initialize the population,
mate solutions, and select the next generation. Note that the
mutation stage was replaced by the local search procedure.
Also, a
selection strategy was applied. The use of
local search and the absence of mutation is a clear difference
between
and standard EAs.
In [37], early works on the application of MAs to the TSP
were commented on. Those works used different instantiations
of the above skeleton to produce near-optimal solution for small
instances of the problem. Although the results were not defin-
itive, they were very encouraging, and many of the following
applications of MAs to the TSP (and also to other NPO prob-
lems) were inspired by those early works.
In [38], the MA
is
used which has several nonstandard features. For details, the
reader is referred to [13] and [38]. We are interested here
in remarking the two important differences with the MA
shown previously. In this MA,
the local search procedure is used after the application of each of
the genetic operators and not only once in every iteration of the
EA. These two metaheuristics differ also in that in the last case
a clear distinction is made between mutations and local search.
In [38], the local search used is based on the powerful guided
local search (GLS) metaheuristic [39]. This algorithm was com-
pared against MSLS, GLS, and a second MA, where the local
search engine was the same basic move used by GLS without
the guiding strategy. In this paper, results were presented from
experiments using instances taken from TSPLIB [40] and
fractal instances [41]. In no case was the MSLS able to achieve
an optimal tour unlike the other three approaches. Out of 31
instances tested, the
solved 24 to optimality, MSLS 0, MA with simple local search
10, and GLS 16. It is interesting to note that the paper was not
intended as a “better than” paper but rather as a pedagogical
paper, where the MAs were exposed as a new metaheuristic in
optimization.
GLS_Based_Memetic_Algorithm
Begin
Initialize population;
For
To sizeOf(population) Do
;
;
Evaluate(individual);
Od
Repeat Until (termination_condition)
Do
For
To #recombinations Do.
selectToMerge a set
;
;
;
Evaluate(offspring);
Add offspring to population;
Od
For
To #mutations Do
selectToMutate an individual in
population;
Mutate(individual);
;
Evaluate(individual);
Add individual to population;
Od
population=SelectPop(population);
If (population has converged) Then
population=RestartPop(population);
Fi
Od
End.
Merz and Freisleben in [42]–[44] show many different com-
binations of local search and genetic search for the TSP [in both
its symmetric (STSP) and asymmetric (ATSP) versions], while
defining purpose-specific crossover and mutation operators. In
[42], the following code was used to conduct the simulations.
STSP-GA
Begin
Initialize pop
with
;
For
To Do
, ;
478 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 9, NO. 5, OCTOBER 2005
Od
Repeat Until (converged) Do
For
To #crossover Do
Select two parents
randomly;
;
Lin-Kernighan-Opt
;
With probability
do
Mutation-STSP
;
Replace an individual of
by ;
Od
Od
End.
In this pseudocode, the authors employ specialized crossover
and mutation operators for the TSP (and a similar algorithm
for the ATSP). As in previous examples, the initial popu-
lation is a set of local optima, in this case, with respect to
. In this case, the LK heuristic
is also applied to the results of crossover and mutation. The
authors motivate this, saying:
and let a GA operate on the set of local optima to
determine the global optimum.
However, they also note that this can lead to a disastrous
loss of diversity, which prompts their use of a selection strategy
which is neither a
nor a but a hybrid between
the two, whereby the new offspring replaces the most similar
member of the population, (subject to elitism). As the authors re-
mark, the large step Markov chains and iterated-Lin-Kernighan
techniques are special cases of their algorithm.
In [44], the authors change their optimization scheme to one
similar to
, which has a
more traditional mutation and selection scheme and in [43] they
use the same scheme as
but after finalization
of the GA run, postprocessing by means of local search is per-
formed.
It is important to notice that Merz and Freisleben’s MAs are
perhaps the most successful metaheuristics for TSP and ATSP,
and a predecessor of the schemes described was the winning al-
gorithm of the First International Contest on Evolutionary Op-
timization.
In [45], Nagata and Kobayashi described a powerful MA with
an intelligent crossover, in which the local searcher is embedded
in the genetic operator. The authors of [46] describe a detailed
study of Nagata and Kobayashi’s work, and relate it to the local
searcher used by Merz and Freisleben.
B. MAs for the QAP
The QAP is found in the core of many practical problems such
as facility location, architectural design, VLSI optimization, etc.
Also, the TSP and GP can be recast as special cases of QAP. The
problem is formally defined as the following.
Quadratic Assignment Problem
Instance: A,B matrices of
.
Solution: A permutation
.
Measure: The cost of the permutation, i.e.,
Aim: Minimun cost permutation
.
Because of the nature of QAP, it is difficult to treat with
exact methods, and many heuristics and metaheuristics have
been used to solve it. In this section, we will briefly comment
on the application of MAs to the QAP.
In [9], the following MA described as a “hybrid GA meta-
heuristic” is proposed.
Begin
;
For
To m Do
generate a random permutation
;
Add
to ;
Od
Sort
;
For
To number_of_generations Do
For
To num_offspring_per_
generation Do
select two parents
, from ;
;
Add
to ;
Od
Sort
;
;
Od
Return the best
;
End.
In the code shown above, and are initializa-
tion and improvement heuristics, respectively. In particular, the
authors reports on experiments where
is a tabu search
(TS) heuristic. At the time that paper was written, their MA was
one of the best heuristics available (in terms of solution quality
for standard test instances).
It is interesting to remark that as in
and , the
GA is seeded with a high-quality initial population, which is
the output of an initial local search strategy,
(TS in this
case). Again, we find that the selection strategy, represented
by
,isa strategy as in the previous MAs.
The authors further increase the selection pressure by using a
mating selection strategy. As in
,
no explicit mutation strategy is used: Fleurent and Ferland
regard
and as mutations that are applied with
a probability 1. As in
, the opti-
mization step is applied only to the newly generated individual,
that is, the output of the crossover stage.
In [16], results were reported which are improvements to
those in the paper previously commented, and for other meta-
heuristics for QAP. The sketch of the algorithm used is the
following.