1
Int. Journ. of Unconventional Computing, Vol. 1, pp. 00?00 ? 2005 Old City Publishing, Inc.
Reprints available directly from the publisher Published by license under the OCP Science imprint,
Photocopying permitted by license only a member of the Old City Publishing Group
Conceptual Frameworks for
Artificial Immune Systems
SUSAN STEPNEY
1
, ROBERT E. SMITH
2
, JONATHAN TIMMIS
3
,
ANDY M. TYRRELL
4
, MARK J. NEAL
5
AND ANDREW N. W. HONE
6
1
Dept. Computer Science, University of York, YO10 5DD, UK
2
The Intelligent Computer Systems Centre, University of the West of England, Bristol,
BS16 1QY, UK
3
Computing Laboratory, University of Kent, Canterbury, CT2 7NF, UK
4
Dept. Electronics, University of York, YO10 5DD, UK
5
Dept. Computer Science, University of Wales Aberystwyth, SY23 2AX, UK
6
Institute of Mathematics, Statistics and Actuarial Science, University of Kent,
Canterbury, CT2 7NF, UK
Received 16 December 2004; Accepted 4 February 2005
We propose that bio-inspired algorithms are best developed and analysed
in the context of a multidisciplinary conceptual framework that provides
for sophisticated biological models and well-founded analytical principles,
and we outline such a framework here, in the context of Artificial Immune
System (AIS) network models, and we discuss mathematical techniques
for analysing the state dynamics of AIS. We further propose ways to
unify several domains into a common meta-framework, in the context
of AIS population models. We finally discuss a case study, and hint at
the possibility of a novel instantiation of such a meta-framework, thereby
allowing the building of a specific computational framework that is
inspired by biology, but not restricted to any one particular biological
domain.
1. INTRODUCTION
The idea of biological inspiration for computing is as old as computing
itself. It is implicit in the writings of von Neumann and Turing, despite
2 STEPNEY, et al.
the fact that these two fathers of computing are now more associated
with the standard, distinctly non-biological computational models.
Computation is rife with bio-inspired models (neural nets, evolution-
ary algorithms, artificial immune systems, swarm algorithms, ant colony
algorithms, L-systems, . . .). However, many of these models are naive
with respect to biology. Even though these models can work extremely
well, their naivety often blocks understanding, development, and analysis
of the computations, as well as possible feedback into biology.
2. A CONCEPTUAL FRAMEWORK
The next steps in bio-inspired computation should be to develop
more sophisticated biological models as sources of computational inspi-
ration, and to use a conceptual framework to develop and analyse the
computational metaphors and algorithms.
We propose that bio-inspired algorithms are best developed and
analysed in the context of a multidisciplinary conceptual framework that
provides for sophisticated biological models and well-founded analytical
principles.
Figure 1 illustrates a possible structure for such a conceptual frame-
work. Here probes (observations and experiments) are used to provide
a (partial and noisy) view of the complex biological system. From this
limited view, we build and validate simplifying abstract representations,
models, of the biology. From these biological models we build and
validate analytical computational frameworks. Validation may use
FIGURE 1
An outline conceptual framework for a bio-inspired computational domain.
3CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
mathematical analysis, benchmark problems, and engineering demon-
strators. These frameworks provide principles for designing and analy-
sing bio-inspired algorithms applicable to non-biological problems,
possibly tailored to a range of problem domains, and contain as much or
as little biological realism as appropriate. The concept flow also supports
the design of algorithms specifically tailored to modelling the original
biological domain, permits influencing and validating the structure
of the biological models, and can help suggest ideas of further experi-
ments to probe the biological system. This is necessarily an interdisci-
plinary process, requiring collaboration between (at least) biologists,
mathematicians, and computer scientists to build a complete framework.
An important observation is that none of the representation and
modelling steps outlined above is unbiased. There are many possible
probes, and many possible representations of the same systems even
given the same probes, and they all provide different insights. In particu-
lar, models derived specifically for the goals of biological simulation may
provide insights that are distinct from those that serve computational
goals.
It is very seldom that the modelling steps used in these distinct
activities are examined for common properties, and comparative biases.
In many instances not all of the representational steps outlined above
are taken. In particular, bio-inspired computational algorithms usually
proceed directly from a (naive) biological model to an algorithm,
with little analytical framing of the representation?s properties. Such
?reasoning by metaphor? is a troubling aspect of these algorithms.
Without the application of suitable analysis techniques to the simplified
representations of biological systems, algorithms derived from these
representations rely only on the (often weak) analogy to the biological
system to support their use. We feel that it is important to recognise
the distinct levels of the modelling process outlined above, to avoid
naive assumptions.
One example that can be described in terms of such a framework,
at least partially, is Holland?s original adaptive system theories [26,20],
founded on a simplified binary-encoded representation of genetics, and
analytical principles of building blocks, k-armed bandit theories, the
schema theorem, and implicit parallelism. Evolutionary computation
theory has developed and deepened in the wake of this work, and it
continues to influence the prescription of genetic algorithms. We propose
4 STEPNEY, et al.
that other bio-inspired computational domains, including Artificial
Immune Systems, should be put on a similarly sound footing.
3. INSTANTIATING THE FRAMEWORK FOR AIS
The natural immune system is a complex biological system essential
for survival. It involves a variety of interacting cellular and molecular
elements that control either micro- or macro-system dynamics. The effec-
tiveness of the system is due to a set of synergetic, and sometimes com-
petitive, internal strategies to cope with chronic and/or rare pathogenic
challenges (antigens). Such strategies remodel over time as the organism
develops, matures, and then ages (immuno-senescence). The strategies of
the immune system are based on task distribution to obtain distributed
solutions to problems (different cells are able to carry out complementary
tasks) and solutions to distributed problems (similar cells carrying out the
same task in a physically distributed system). Thus, cellular interactions
can be envisaged as parallel and distributed processes among cells with
different dynamical behaviour, and the resulting immune responses
appear to be emergent properties of self-organising processes. Theories
abound in immunology pertaining to how the immune system remembers
antigenic encounters (maintenance of memory cells, use of immune
networks), and how the immune system differentiates between self and
non-self molecules (negative selection, self-assertion, danger theory).
We can explicitly exploit the conceptual framework, in order to
develop, analyse and validate sophisticated novel bio-inspired computa-
tional schemes, including those inspired by complex processes within
the natural immune system. This work needs to be done; here we outline
a suggested route.
3.1 A first step: Interdisciplinary research
AIS is a relatively new and emerging bio-inspired area and progress
has been made from naively exploiting mechanisms of the immune
system. Computer security systems have been developed, anti-virus
software has been created, optimisation and data mining tools have
been created that are performing as well as the current state of the art
in those areas.
The original AIS were developed with an interdisciplinary slant.
For example, Bersini [2?4] pays clear attention to the development
of immune network models, and then applies these models to a control
5CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
problem characterised by a discrete state vector in a state space R
L
.
Bersini?s proposal relaxes the conventional control strategies, which
attempt to drive the process under control to a specific zone of the state
space; he instead argues that the metadynamics of the immune network
is akin to a meta-control whose aim is to keep the concentration of the
antibodies in a certain range of viability so as to continuously preserve
the identity of the system.
There are other examples of interdisciplinary work, such as the
development of immune gene libraries and ultimately a bone marrow
algorithm employed in AIS [25], and the development of the negative
selection algorithm and the first application to computer security [16].
However, in more recent years, work on AIS has drifted away from
the more biologically-appealing models and attention to biological
detail, with a focus on more engineering-oriented approach. This has led
to systems that are examples of ?reasoning by metaphor?. These include
simple models of clonal selection and immune networks [12,13,60,42],
and negative selection algorithms [6,22,59]. We suggest that even such
an engineering-oriented approach may benefit from closer interaction
with biologists, and from a more principled mechanism for the extrac-
tion, articulation, and application of the underlying computational
metaphor.
Freitas & Timmis [17] outline the need to take into account the
application domain when developing AIS. The conceptual framework
proposal here complements that position: once we have a well-developed
conceptual framework, we can specialise it for various application
domains in a justifiable way.
3.2 Adopting the conceptual framework for AIS
de Castro & Timmis [10] propose a structure for engineering AIS. The
basis is a representation to create abstract models of immune organs,
cells, and molecules, together with a set of affinity functions to quantify
the interactions of these ?artificial elements?, and a set of general-purpose
algorithms to govern the dynamics of the AIS.
The structure can be modelled as a layered approach (figure 2). To
build a system, one typically requires an application domain or target
function. From this basis, a representation of the system?s components
is chosen. This representation is domain and problem dependent: the
representation of network traffic, say, may well be different from that
of a real time embedded system. The representation-specific affinity
measures quantify the interactions of the elements of the system. There
6 STEPNEY, et al.
are many possible affinity measures, such as Hamming or Euclidean
distances. The final layer involves the use of algorithms, such as negative
and positive selection, clonal selection, the bone marrow algorithm, and
immune network algorithms, which govern the behaviour (dynamics)
of the system. Each algorithm has its own particular range of uses.
This layered structure is not complete from the conceptual framework
perspective. For example, we propose that AIS algorithms (in some
cases) may benefit from asking questions such as: what is ?self?, or
?danger?. In addition, AIS algorithms in their current form can be classi-
fied as population based or network based [10]. In the following sections,
we adopt this classification, and propose how one might undergo a
development of an AIS algorithms adopting the conceptual framework
above.
3.3 Population based AIS algorithms
Three common algorithms in AIS, those of positive, negative, and
clonal selection, are all based on populations of agents trained to
recognise certain aspects of interest (see [10] for an overview). There
are similarities between the algorithms: positive and negative selection,
for example, are merely two sides of the same coin. There are also differ-
ences: positive and negative selection involve essentially random genera-
tion of candidate recognisers, whilst clonal selection uses a form of
reinforcement based on selection and mutation of the best recognisers.
We defer discussion of these models to the meta-frameworks of
section 5, and population based models in general.
3.4 Network based AIS algorithms
Jerne?s original immune network theory [30] suggests an immune
system with a dynamic behaviour even in the absence of non-self
FIGURE 2
A structure for AIS, from [10].
7CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
antigens. This differs from the biological basis of the clonal and negative
selection algorithms, as it suggests that B-cells are capable of recognising
each other.
Theoretical immunologists have been interested in creating models
of immune networks in order to introduce new ways of explaining how
the immune systems works [52,14]. Researchers have translated some
of these ideas into the computing domain, in applications such as
optimisation and control [2,4]. This work has also inspired the develop-
ment of machine learning network models with applications mainly in
data analysis [60,13].
However, as we stated earlier, the later work has somewhat deviated
from the biological model, being adapted to a particular problem. In
addition, Jerne?s immune network theory itself is controversial, and
not widely accepted by immunologists. This has an impact on the AIS
algorithm: if the biology is not correct, then one must re-examine the
algorithm to understand what is really going on; this would hopefully
shed light on the more complex nature of the immune systems, and the
networks that are clearly present therein.
The first step to achieving this understanding would be to probe
the biological system from the perspective of interpreting the system as a
network of interaction, cooperation and competition amongst molecules,
cells, organs, and tissues. The results could then be used to formulate
a suitable mapping between biological properties and framework compo-
nents. These components could then be used as the basis for the topology
and dynamics of new biological models, in addition to re-examining
existing models such as [53,55]. The new models would allow a greater
understanding of the operation of such systems to be developed in an
artificial context.
Within the context of these new immune network models, one could
examine, for example, Matzinger?s danger theory [37], context of
response [31,36], memory mechanisms [58], general alarm response
or stress response [50], self/non-self recognition [39], and Varela?s
self-assertion [64]. Additionally, the constructive role of noise in biologi-
cal systems, which is an intrinsic feature of such systems, could also be
examined [18].
From these biological models, suitable new computational metaphors
and analytical frameworks could be created, to include appropriate rep-
resentations for components, methods of assessing interactions between
components, and processes to act on components. The frameworks
8 STEPNEY, et al.
should also provide features that allow biological models to be repre-
sented and manipulated in a number of ways, and should permit the
analysis and identification of generic properties. An instantiation of
a framework should permit the capture of properties relevant to the
application being developed. In an iterative process, the framework algo-
rithms should be implemented and tested in order to test and develop
the biological metaphors prior to their implementation and experimental
exercises on the intended platform.
Taking this fuller view of immune networks may yield AIS algorithms
that truly mimic the qualities of the diversity of immune network memory
mechanisms, and may inform us as to the scalability of immune net-
works, their ability to cope more effectively with noise, their open nature,
and the level of interaction both within the network and external to the
network. Biology would benefit from the resulting sophisticated models,
too.
3.5 Self, or danger?
Some researchers have begun taking a more interdisciplinary slant
again. For example, Aicklen et al. [1] describe an ambitious interdiscipli-
nary project investigating novel ideas from immunology such as danger
theory [37], with application to computer security. Those authors pro-
pose to observe the biological system by undertaking new experiments to
identify key signals involved in cell death, and identify the functions of
such signals and how these affect immune cells. The aim is to shed light
on how the immune system distinguishes self from non-self, in order to
build effective immune-inspired computer security systems that no longer
rely on the need to define a priori the self of the system. Although those
authors make no reference to adopting a framework approach such as
outlined above, we believe that taking such an approach would to help
to ensure not only biologically-plausible algorithms, but effective and
general solutions.
4. MATHEMATICAL ANALYSIS OF AIS
The adaptive immune system is able to recognise a vast number of
different pathogens. The recognition of potentially harmful foreign
invaders is a necessary (but not sufficient [62]) condition for the immune
response to be activated. The robustness of the immune response relies on
9CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
the diversity of the lymphocyte repertoire. This diversity is achieved in
two ways. Firstly, new cells are generated at random (although they may
be selectively deleted later). Secondly, the number of lymphocytes is huge:
the total number of lymphocytes in a mouse is of the order of 10
8
, with
approximately 10
7
different types of receptors, while in the human body
there are of the order of 10
12
lymphocytes [54]. These two aspects ensure
the completeness of the repertoire, in the sense that essentially all possible
pathogens that might be encountered will be recognised.
The importance of the size of the lymphocyte repertoire has not
yet been addressed for the development of AIS algorithms. Many AIS
algorithms, including CLONALG [10], the B-Cell Algorithm (BCA)
[29,33,32] and MISA [65], are based purely on mutation and selection
mechanisms for randomly generated clones (clonal selection), and these
algorithms use very small populations of artificial immune cells. The
main reason is probably straightforward: very large cell networks are
computationally too expensive to implement. However, the emergent
properties of complex systems can depend crucially on system size [24].
Lymphocytes interact and respond to one another in a highly com-
plicated and nonlinear fashion: a small difference in the input to the
system can produce a large (and complicated) change in the output.
Nonlinearity is a key feature of complex systems that display emergent
phenomena [56,57]. AIS algorithms that are inspired by the network of
interactions in the adaptive immune system include the Resource-limited
Artificial Immune Network (RAIN) [41], AINE [35] and aINET [11].
In the next subsections, we show how the theory of Markov chains can
be used to understand the stochastic nature and convergence properties
of AIS, and explain how nonlinear effects in network models may be
analysed.
4.1 Optimisation problems and Markov chains
Many AIS algorithms are based purely on clonal selection mecha-
nisms, without any interaction between the different members of the
cell populations. Such algorithms are purely stochastic, in the following
sense: given the state of the cell population at time t, the subsequent state
at time t + 1 is a random variable. In many cases, the changing behaviour
of the population with the time t (which varies in discrete steps) is natu-
rally described in terms of a Markov chain (see [8,23] for background
material).
10 STEPNEY, et al.
Convergence is a highly desirable property for optimisation problems
(although not necessarily so for other kinds of problem, such as ones
to do with openness). The convergence of MISA [65], a multi-objective
optimisation algorithm, has been proved via an associated Markov
chain, under the assumption of an elitist selection mechanism. Many AIS
algorithms have been tested on optimisation problems, because such
problems are ubiquitous in applications to optimal control [34] and the
calculus of variations [19,28,27]. Furthermore, AIS apparently perform
well in tackling extremely hard biological optimisation problems,
including protein folding [9,45].
We represent the state of our system by a variable X. The aim of the
algorithm is to find the state value X that optimises (for example,
minimises) the function F(X). We can represent the state at time t by a
random variable X
t
, and optimise by making many iterations in time.
To be completely concrete, we illustrate this idea with the example of
BCA [33,29,28,32] as an optimisation algorithm, inspired by the notion
of contiguous hypermutation in B-cell clones. For BCA, the different
cells in the population do not interact, so we can focus on the dynamics of
one individual cell, and define the state X
t
to be the value of the bit string
corresponding to this cell. At each time t, a set of clones is taken from the
cell, hypermutation is applied to the clones, and if for some clone C
t
it
happens that F(C
t
) < F(X
t
) then the next state value is X
t + 1
= C
t
, otherwise
the original cell is kept and X
t + 1
= X
t
(see [33] for details). At each stage
there is a definite probability for transition to a new state (bit string)
value for X
t + 1
, and BCA is purely elitist in the sense that only mutations
that result in improvement are kept (the value of F(X
t
) is non-increasing
with t).
To describe the evolution of a cell in BCA in terms of a Markov chain,
we label the possible states (bit strings) by an index j running from 1 to N,
where N is the number of possible states, and we implicitly identify state
values with their labels. We model the value of the bit string at time t by
the probability distribution vector v
t
= (v
t,1
, v
t,2
...v
t,N
), with jth compo-
nent v
t,j
= P(X
t
= j): the probability of being in state j at time t. The initial
value is given by v
0
.
The probability of transition between state j and state k is independent
of the time t, and so can be represented by the N ? N transition matrix P,
with entries P
jk
= P(X
t + 1
= k | X
t
= j): the probability of being in state k at
time t + 1, given being in state j at time t. P is a stochastic matrix: all of
11CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
its entries lie between 0 and 1, and the row sums satisfy S
k
P
jk
= 1; that is,
from state j the cell must make a transition somewhere with probability 1.
To work out the probability distribution at time t + 1, we have
PX k PX k X j
ttt
j
N
()( )
++
=
== = =
?11
1
?
(4.1)
====
+
=
?
PX k X jPX j
tt t
j
N
(|)()
1
1
(4.2)
and so
vvP
tk tjjk
j
N
tt+
=
+
==
?1
1
1,,
or vvP
(4.3)
Because the transition matrix P is time-independent, the probability
distribution vector vt can be written immediately in terms of the initial
distribution, as
v
t
= v
0
P
t
(4.4)
It is evident from the form of equation (4.4) that if we wish to under-
stand the long-time behaviour of the algorithm, we need to understand
what happens to the powers of the transition matrix P
t
as t ??. For
BCA it is further possible to prove that where there is a unique optimum
state, it is reached with probability one in the limit t ??;* in the
terminology of Markov chains, a unique optimum is an absorbing state
[23].
There are other instances of biologically-inspired computing being
applied to optimisation problems and the calculus of variations, in
particular the use of genetic algorithms (see references in [29]) and neural
networks [38]. We expect that a similar analysis of stochastic properties
will be relevant to some of these other approaches to biologically-
inspired computing. Moreover, Markov chain techniques could be used
to prove the convergence (or otherwise) of many other existing AIS and
genetic algorithms. A thorough analysis of rates of convergence for
optimisation algorithms would be even more useful, since the limit t ??
cannot be reached in practice.
* Edward Clark (2004) private communication.
12 STEPNEY, et al.
4.2 Nonlinear dynamics
The dynamics of cell populations in the immune system has been
modelled extensively using nonlinear dynamical systems [21,47,54,63].
These models generally involve coupled systems of differential equations,
taking the form
d
dt
z
fz= ()
(4.5)
where the vector z(t) is the state vector at time t; or coupled discrete
(difference) equations
z
t + 1
= g(z
t
) (4.6)
In each case the components of the state vector z typically correspond to
populations of cells or molecules of different species, and in general each
of the components of the vectors f and g are nonlinear functions of their
arguments. (For analytical calculations, it is often simpler to work with
systems of ordinary differential equations; but for computer algorithms
discrete equations are more appropriate).
The main difference between the dynamics of a Markov chain, defined
by equation (4.3), and the dynamical systems here, is that the evolution of
the state X
t
is random and the vector v
t
is a probability distribution,
whereas the state vector z satisfies a purely deterministic evolution: the
state at time t is determined uniquely by the initial state at t = 0.
The original development of AIS algorithms received much inspira-
tion from mathematical models of immune networks (see section 3.4),
such as those in [54], which are based on nonlinear interactions between
cell populations. Therefore, in order to understand the behaviour of AIS
algorithms, it makes sense to apply methods from the theory of nonlinear
dynamical systems [48].
In general, given such a system such as that described by equation
(4.6), one would like to make sense of the time evolution of the state
vector by understanding how it moves in the phase space (the space of all
possible states). One can explore this by iterating the difference equation:
start with an initial value z
0
, then calculate z
1
(a nonlinear function f(z
0
)),
z
2
, z
3
, . . . and so on.
For a general mapping of the form
z
t
?? z
t + 1
= g(z
t
) (4.7)
13CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
it is natural to consider the fixed points, namely the solutions of the
equation z
s
= g(z
s
) that remain fixed by equation (4.7). The initial value
z
0
is said to be in the basin of attraction of the point z
s
if z
t
? z
s
as t ??.
For each fixed point there is a corresponding basin of attraction, and it
is well known [51] that for even simple cases such as Newton-Raphson
iteration, these basins are fractal sets. There are also periodic orbits
which lie outside the basins of attraction. For a high-dimensional
dynamical system the attractors can be more complicated than just
points: they may be ?strange attractors?, which are themselves fractals
[48]. The attractors and periodic orbits correspond to the important
landmarks in the phase space.
AIS networks are based on nonlinear interactions between artificial
cell populations. If an AIS network algorithm is required to perform
some recognition task, or solve a multi-objective optimisation problem,
then the different objectives might be regarded as attractors in a suitable
phase space. Moreover, one would expect that the properties of the
nonlinear mathematical models that have inspired the AIS, within the
general development framework proposed in this paper, should inform
the behaviour of the immune-inspired algorithms. Therefore nonlinear
systems analysis will be essential in the development of robust
algorithms.
However, this is not the full story, since as we have seen above, even
the simplest AIS ? those without any nonlinear interactions ? are essen-
tially stochastic in nature. (In the Markov chain context, we may also
note that absorbing states play the role of attractors.) Hence the full
treatment of AIS will require nonlinear stochastic dynamical systems.
Very little is known about the explicit solutions of nonlinear stochastic
differential equations, although there is a considerable interest in the
linear case [7]. The application of nonlinear stochastic analysis to AIS is
a novel approach which raises many exciting challenges for the future.
5. META-FRAMEWORKS FOR BIO-INSPIRED COMPUTATION
We have so far been speaking particularly of AIS, arguing the case for
the framework in figure 1. This shows potentially many representations
of the same systems under the same observations, each of which may pro-
vide different insights. Such distinct representations, although common,
are seldom examined for unifying properties. Once we have a conceptual
14 STEPNEY, et al.
framework, we can not only make such comparisons, we can go a step
further: to examine and compare the separate conceptual, mathematical
and computational frameworks, to develop more integrated and generic
frameworks, and to expose essential differences.
To achieve this, we can apply the same conceptual model, at a higher
level (figure 3). The key probes here are meta-questions. Just as the
questions at the biological level influence the kinds of models developed,
so the meta-questions influence the kinds of meta-models developed.
5.1 Meta-probes for complex system frameworks
What kind of meta-questions might we ask? Clearly, the questions
asked influence the resulting framework. We have identified some initial
areas thought to affect complex behaviour in general; questions that
address notions such as openness, diversity, interaction, structure, and
scale might lead to models of complex adaptive systems. The idea is to
ask each question (suitably refined and quantified) across the range of
frameworks being incorporated, and to use the answers as part of the
input to build the meta-framework.
Openness: We do not want our computations to halt; we want con-
tinual evolution, continual growth, continual addition of resources: that
is, open, far-from-equilibrium systems. How much openness is necessary?
How is openness controlled by structure and interaction? How is system
unity maintained in the presence of openness?
Diversity (heterogeneity) is present in all complex biological systems,
and occurs in structure, behaviour, and interactions. When can we talk
of an average agent? How much diversity is necessary within a level of
FIGURE 3
An outline conceptual framework for integrating bio-inspired computational domains.
15CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
a structure? between levels? What does it cost? How does it combat
fragility?
Interaction: Agents interact with their environment and with each
other. What are the features of interaction within structural levels?
between levels? What is the balance between computation and
communication?
Structure: Biological systems have structure on a variety of levels, yet
the levels are not crisply delineated. Are the levels we discern artefacts
of our modelling framework? How can we recognise levels? When is
a hierarchy an adequate structural model? How does structure affect
interaction? What are the relationships between physical structures and
information structures? What is the relationship with specialisation of
function? with localisation of function?
Scale: Biological systems have a vast scale, a vast number of com-
ponents. When and how does ?more? become ?different?? What are the
critical points/phase transitions? How small can a system be, and still
be emergent? When is a system too big? How important is multi-scale
modelling? What are the relationships between scale and diversity?
Generic questions apply to each meta-probe question area X: What
is the role of X within a system? What is the balance between X and
not-X at the peak of complexity? How and when does X emerge? How
does X evolve? How does physical embodiment affect X? How can we
exploit X?
5.2 A meta-framework for population models
Many bio-inspired algorithms are based on populations of agents
trained to perform some task, or optimise some function. The most
obvious one is the area of evolutionary algorithms, based on analogy to
populations of organisms breeding and selecting to become ?fitter? [40].
In AIS, there are the positive and negative selection, and clonal selection
algorithms. Swarm algorithms and social insect algorithms [5] are
based on populations of agents whose co-operations result in problem
solving. A neural network could be viewed as a population of neurons
cooperating to perform a recognition task.
Given the number of underlying commonalities, it seems sensible to
abstract a meta-framework from individual population based models.
What are the key properties of population models, and how are they
realised in the various individual models? Here we outline just a few
similarities and differences of these models, which could be used in
16 STEPNEY, et al.
constructing a population based meta-framework. (Since these indi-
vidual frameworks themselves do not yet exist, this section is somewhat
meta-speculative!)
All these models contain a population of individual agents. Members
of the population usually exhibit a range of fitnesses, used when calculat-
ing a new population: fitter individuals have a greater effect on the com-
position of the next generation than do less-fit individuals. The aim is to
find a population that is sufficiently fit for the task at hand.
In evolutionary algorithms (EAs), a population of chromosomes
reproduces in a fitness landscape. Fitter individuals are selected more
frequently, to breed the next generation. When described in these terms,
the clonal selection algorithm looks very similar: the population com-
prises a collection of antibodies, which proliferate in an affinity landscape.
The higher affinity individuals are cloned more, and mutated less, when
producing the next generation. Additionally, the lowest affinity cells are
replaced by random cells (providing automatic diversity maintenance).
In swarm algorithms, a population of particles exists and adapts in a
fitness landscape. Fitter individuals? properties are copied more by the
next generation. In ant colony algorithms, a population of paths exist in a
local fitness (path component length) landscape. The use of components
from fitter (shorter) paths are reinforced by ?pheromones? in the next
generation, which is then constructed by ?ants? following pheromone
trails.
In EAs, clonal AIS, and ant algorithms, the fitness of the entire popu-
lation is evaluated and used for selection and construction of next genera-
tion. Swarm algorithm evaluate the fitness of each individual relative to
the others in its local neighbourhood. (Some EA variants incorporate
niching, which provides a degree of locality.)
In EAs, swarm and ant algorithms, the result is the fittest member
of the final population. In clonal AIS, however, the result is the entire
final population of detectors; the individual detectors are each partial
and unreliable, yet their combined cooperative effect makes the full
robust detector.
Such commonalities and differences as outline above, once exposed
and analysed, can be used to suggest more general algorithms. For
example, the natural diversity maintenance of clonal AIS suggests ways
for similar mechanisms to be added to other population algorithms, in
a less ad hoc manner than currently. Also, many population algorithms
find themselves forced to add some form of elitism to preserve the best
17CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
solution so far: clonal AIS is naturally elitist. One potentially interesting
feature to explore is the relationship between the natural locality of
swarm algorithms, and the locality inherent in danger theory.
Such a combination of models permits many of the meta-probe ques-
tion outlined above to be asked. Diversity is a key question: how to main-
tain diversity within a single population, but additionally, should there
be different ?species?, too? Interaction with the environment (laying and
sensing pheromones) is crucial in the ant algorithms, and with other
agents (at least at the level of copying their behaviour) in swarm algo-
rithms. Co-evolution, with its effect on mutual fitness landscapes, can be
regarded as a form of interaction. What scale, that is, what population
size, is appropriate? The probes also force us to think of new issues: is
openness a relevant aspect? Should we be concerned with flows of agents
into and out of the population (other than by internal mechanisms of
generational breeding)? And is there any way to exploit structure, given
the homogeneity of most population algorithms?
This somewhat simplistic meta-framework sketch is built on the corre-
spondingly simplistic population models. More sophisticated population
models developed in terms of full conceptual frameworks would
doubtless lead to much richer and more powerful meta-frameworks.
5.3 A meta-framework for network models
AIS networks, metabolic networks, auto-catalytic chemical reaction
networks, intra-cellular protein interaction networks, inter-cellular cyto-
kine, hormone and growth factor signalling networks, ecological food
webs, are all examples of biological networks. Indeed, most biological
processes operate through a complicated network of interactions, with
positive and negative feedback control by factors that are themselves
subject to similar controls. These networks function in a distributed
fashion: most components have a variety of roles, and most functions
depend on more than one component. This presumably underpins their
robustness, whilst keeping the malleability required for adaptability and
evolution. How this is achieved in practice is poorly understood.
Currently mathematical and computational descriptions of the
structure of biological networks tend to be static (there is no time compo-
nent to the architecture), closed (no inputs from the environment), and
homogeneous (the types of nodes and connections are uniform, and new
instances, and new kinds, of connections and nodes, are not supported).
It will be necessary to develop novel mathematical approaches to model
18 STEPNEY, et al.
real complex biological networks. Developing these new mathematical
models in the context of the proposed conceptual framework will provide
mechanisms for evaluating their appropriateness and power.
6. CASE STUDY
On-going work by some of the authors [44] is addressing the develop-
ment of a more complete biologically inspired model of computation
than is currently available, and provides a case study upon which to
deploy the meta-probes described in section 5.1. The model is focused on
the generic ability of the ?higher? organisms to maintain their homeo-
static state in a wildly varying environment. Key components of the
organism which promote this ability have been identified as:
The immune system, which provides mechanisms for very long term
adjustment of an organism?s physiological state in a number of ways.
The neural system, which provides mechanisms capable of rapid and
widely varying responses from very specific parts of the organism. These
may involve interacting with the environment and/or internal organs.
The endocrine system, which provides mechanisms for relatively
long term (compared to the neural system) adjustment of behaviour of
the organism. The majority of endocrine system function is restricted to
communication and control within the organism.
Our model is initially intended for use as a control system for complex
electronic and electromechanical systems that would profit from long
term autonomous operation. Autonomous robots are the specific exem-
plar of this type of system which we have chosen to target [43]. Our
system contains direct analogues of these three systems:
An artificial immune system, which will consist of two layers of cells:
an innate layer to pre-process and filter data from condition sensors
distributed throughout the robot, and an adaptive layer capable of
monitoring and adapting to problems signalled by the innate system. The
performance and adaptation of the adaptive layer will be modulated
by the concentrations of hormones generated by the artificial endocrine
system.
An artificial neural system, which will consist of relatively conven-
tional artificial neurons. These will be connected as multi-layer
perceptrons, but the synapses of the neurons will be sensitive to
hormones produced by the artificial endocrine system [43]. Hormone
19CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
concentrations will linearly suppress or excite the activity of synapses
depending on the sign of the sensitivities associated with each hormone
at each synapse. The inputs to the neural system will come from sensors
of the environment and the outputs will control the system actuators.
An artificial endocrine system, which will consist of networks of
cells connected in a similar manner to artificial neural networks. The ter-
minal cells of each endocrine network will however produce and release
?hormone? depending on the inputs that it receives. The hormone con-
centrations in the system will be global properties and will influence the
behaviour of all three of the systems including the endocrine system itself.
The examination of this system in the light of the meta-probes of
section 5.1 reveals a number of interesting properties and some key
compromises.
The system is really only open in the sense that it is intended to operate
for very long periods of time without interruption. There is no current
mechanism proposed for the addition of elements to the system, although
a number of artificial hormone controlled mechanisms are under con-
sideration. Analysis of biological growth control hormones and potential
analogues may provide mechanisms which could be integrated into our
overall structure. At present however this lack of development is the first
major compromise in our structure.
Diversity is present on a number of levels: the division between
neurons, gland cells (the artificial endocrine system) and immune cells
provides one layer of heterogeneity. The presence of multiple types of
immune cell and multiple hormones provides another. All of these com-
ponents behave in different ways and communicate in some common and
some specialised ways. This diversity provides two key advantages: it
allows the processing of diverse signals from a number of sources (both
within the robot itself and from the environment) and the control of the
system on a variety of time-scales in an integrated fashion. The artificial
endocrine system provides a common communication channel capable of
working across this range of time-scales and mechanisms.
Interaction is varied and locally simple. A large number of relatively
low capacity communication channels promotes the emergence of
complex behaviour. The transmission of signals across synapses in the
artificial neural system and artificial endocrine system provides the short-
est time-scale channel and the hormone concentrations provided by the
artificial endocrine system the longest time-scale signal. In the biological
system the immune system generates endocrine signals over potentially
20 STEPNEY, et al.
very long time-scales that are capable of controlling both the neural and
endocrine system; in our artificial system we have chosen to ignore these
signals. This is a further key compromise that restricts the ability of the
artificial immune system to control and avert damage. Further examina-
tion of the role of hormones and cytokines and specifically the stress
response [15,49] may provide clues about how to successfully exploit such
a mechanism.
The structure of the system is crudely seen in the description at the
beginning of this section: neural system composed of probably several
separate neural networks, each composed of hormone sensitive neurons
and synapses; an endocrine system broken down in a very similar way
to the neural system; an immune system composed of two coupled
populations of cells (innate and adaptive). The specialisation of function
within each system affects different aspects of the potential for control
on different time-scales and of different physical mechanisms within the
robot.
The proposed scale of the system presented here is currently limited.
This is mainly due to the major compromise on the openness of the
system. The engineering of a system based on these components will
only be possible for relatively small systems. The inherent modularity of
structure (especially within the neural and endocrine systems) allows
these systems to built out of a number of pre-trained and pre-organised
subcomponents. Ultimately the use of a developmental mechanism
within the system will allow much larger systems and a more blurred
internal structure. For example, cross-linking between the endocrine and
neural networks might be permitted to develop and may well allow more
flexible, robust and effective control to develop.
Whilst the limitations of the system proposed are self-evident and
extensive, we believe that the selection of components and mechanisms
provides a sound basis for effective control of complex electro-
mechanical systems. We also believe that it fits well with the framework
proposed here and that the framework provides a useful tool for the
analysis and further development of the system.
7. DISCUSSION AND CONCLUSION
We have argued that bio-inspired algorithms would benefit from
exploiting more sophisticated biological models, and from being based
21CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
on sound analytical principles; we believe that biology could benefit from
the resulting sophisticated models, too. We have outlined what we believe
to be a suitable conceptual framework including these various compo-
nents. We have suggested how AIS network models might fit into this
framework.
We have additionally sketched how meta-frameworks, based on
the same underlying structure, might be applied at higher levels to unify
various kinds of bio-inspired architectures, and we have suggested how
population based models, including AIS models, might form one such
meta-framework. We do not expect that every individual model will
fit perfectly into an integrated model: part of the development process
will be to expose essential differences as well as to integrate common
abstractions.
One exciting prospect of a unified meta-framework is the possibility
of a novel instantiation, possibly using concepts from across a range of
biological domains, and possibly using concepts from outside biology
(since words like ?Lamarck? and ?teleology? need not be so necessarily
dismissed in the artificial domain). This would allowing the building of
a chimerical computational framework that is inspired by biology, but
not restricted to any one particular biological domain.
8. Acknowledgements
The conceptual framework described in this paper was developed
during the EPSRC-funded EIVIS project. We would like to thank the
other members of the project for their invaluable contributions to some
of the ideas in this paper: Andrew Anderson, Jim Austin, Brian Bell,
Peter Bentley, David Broomhead, Robin Callard, Steve Furber, David
Halliday, Douglas Kell, Alan Murray, Jaroslav Stark, Stefan Wermter,
David Willshaw, Xin Yao, Peter Young.
REFERENCES
[1] Aicklen, U., Bentley, P., Cayzer, P., Kim, J. and McLeod. J. (2003). Danger theory: the
link between AIS and IDS? In Timmis et al. 61, 147?155.
[2] Bersini, H. (1991). Immune network and adaptive control. In Proc. First European
Conference on Artificial Life, 217?226. MIT Press.
[3] Bersini, H. (1992). Reinforcement and recruitment learning for adaptive process
control. In Proc. Int. Fuzzy Association Conference (IFAC/IFIP/IMACS) on Artificial
Intelligence in Real Time Control, 331?337.
22 STEPNEY, et al.
[4] Bersini, H. and Varela, F.J. (1994). The immune learning mechanisms: reinforcement,
recruitment and their applications. In R. Paton, editor, Computing with Biological
Metaphors, 166?192. Chapman & Hall.
[5] Bonabeau, E.W., Dorigo, M. and Theraulaz, G. (1999). Swarm Intelligence: from
natural to artificial systems. Addison Wesley.
[6] Bradley, D.W. and Tyrrell, A.M. (2002). Immunotronics: novel finite state
machine architectures with built in self test using self-nonself differentiation. IEEE
Trans. Evo. Comp., 6(3), 227?238. June.
[7] Brzezaniak, Z. and Zastawniak, T. (1999). Basic Stochastic Processes. Springer.
[8] Cox, D.R. and Miller, H.D. (1965). The Theory of Stochastic Processes. Chapman and
Hall, London.
[9] Cutello, V. and Nicosia, G. (2002). An immunological approach to combinatorial
optimization problems. In F.J. Garijo, J.C. Riquelme, and M. Toro, editors, Advances
in Artificial Intelligence ? IBERAMIA 2002, volume 2527 of LNAI, 361?370. Springer.
[10] de Castro, L.N. and Timmis, J. (2002). Artificial Immune Systems: A New Computa-
tional Intelligence Approach. Springer.
[11] de Castro, L. N. and Von Zuben, F. N. (2000). An evolutionary immune network for
data clustering. In 6th Brazilian Symp. Neural Networks, SBRN ?00, 84?89. IEEE.
[12] de Castro, L.N. and Von Zuben, F.J. (2000). The clonal selection algorithm
with engineering applications. In Workshop on Artificial Immune Systems and Their
Applications, GECCO, 36?37.
[13] de Castro, L.N. and Von Zuben, F.J. (2001). aiNet: an artificial immune network for
data analysis. In H.A. Abbass, R.A. Sarker, and C.S. Newton, editors, Data Mining: a
heuristic approach, chapter XII. Idea Group Publishing.
[14] Farmer, J.D., Packard, N.H. and Perelson, A.S. (1986). The immune system,
adaptation, and machine learning. Physica D, 22, 187?204.
[15] Feder, M. and Hofmann, G. (1999). Heat-shock proteins, molecular chaperones, and
the stress response: evolutionary and ecological physiology. Ann. Rev. Physiol., 61,
243?282.
[16] Forrest, S., Perelson, A., Allen, L. and Cherukuri, R. (1994). Self-nonself discrimina-
tion in a computer. In Proc. IEEE Symp. on Research in Security and Privacy, 202?212.
[17] Freitas, A.A. and Timmis, J. (2003). Revisiting the foundations of artificial immune
systems. In Timmis et al. 61, 229?241.
[18] Gammaitoni, L., Hanggi, P., Jung, P. and Marchesini, F. (1998). Stochastic resonance.
Rev. Mod. Phys., 70(1), 223?287.
[19] Gelfand, I.M. and Fomin, I.M. (1963). Calculus of Variations. Prentice-Hall.
[20] Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine
Learning. Addison Wesley.
[21] Goldstein, B., Faeder, J.R. and Hlavacek, W. (2004). Mathematical models of
immune receptor signalling. Nature Rev. Immunol., 4, 445?456.
[22] Gonzalez, F. and Dasgupta, D. (2003). Anomaly detection using real-valued negative
selection. J. Genetic Prog. and Evolvable Machines, 4, 383?403.
[23] Grimmett, G.R. and Stirzaker, D.R. (1982). Probability and Random Processes.
Oxford University Press.
[24] Haken, H. and Mikhailov, A. (eds) (1993). Interdisciplinary Approaches to Nonlinear
Complex Systems. Springer.
[25] Hightower, R.R., Forrest, S.A. and Perelson, A.S. (1995). The evolution of emergent
organization in immune system gene libraries. In L.J. Eshelman, editor, Proc. 6th Int.
Conf. Genetic Algorithms, 344?350. Morgan Kaufmann.
23CONCEPTUAL FRAMEWORKS FOR ARTIFICIAL IMMUNE SYSTEMS
[26] Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. University of
Michigan Press.
[27] Hone, A. (2004). A piece of the action. Physics World, 17(9), 64.
[28] Hone, A. and Kelsey, A. (2004). Optima, extrema and artificial immune systems. In
Nicosia et al. 46, 80?90.
[29] Hone, A., Kelsey, J. and Timmis, J. (2003). Chasing chaos. In R. Sarker et al., editors,
Proc. Congress on Evolutionary Computation, 413?419. IEEE.
[30] Jerne, N.K. (1974). Towards a network theory of the immune system. Annals
Immunol., 125C, 373?389.
[31] Janeway Jr, C.A. and Medzhitov, R. (2002). Innate immune recognition. Ann. Rev.
Immunol., 20, 197?216.
[32] Kelsey, J. (2004). An immune system-inspired function optimisation algorithm. Master?s
thesis, University of Kent.
[33] Kelsey, J. and Timmis, J. (2003). Immune inspired somatic contiguous hypermutation
for function optimisation. In Cantu-Paz et al., editors, GECCO 2003, volume 2723 of
LNCS, 207?218. Springer.
[34] Kirk, D.E. (1997). Optimal Control Theory: An Introduction. Prentice Hall.
[35] Knight, T.P. and Timmis, J. (2002). A multi-layered immune inspired approach to
data mining. In A. Lotfi, J. Garibaldi, and R. John, editors, Proc. 4th Intl. Conf. Recent
Advances in Soft Computing, 266?271.
[36] Kourilsky, P. and Truffa-Bachi, P. (2001). Cytokine fields and the polarization of the
immune response. Trends Immunol., 22, 502?509.
[37] Matzinger, P. (2002). The danger model: a renewed sense of self. Science, 296, 301?305.
[38] Meade, A.J. and Sonneborn, H.C. (1996). Numerical solution of a calculus of
variations problem using the feedforward neural network architecture. Advances in
Engineering Software, 27, 213?225.
[39] Medzhitov, R. and Janeway Jr, C.A. (2002). Decoding the patterns of self and nonself
by the innate immune system. Science, 296, 298?300.
[40] Mitchell, M. (1996). An Introduction to Genetic Algorithms. MIT Press.
[41] Neal, M. and Timmis, J. (2001). A resource limited artificial immune system for data
analysis. Knowledge Based Systems, 14, 121?130.
[42] Neal, M.J. (2003). Meta-stable memory in an artificial immune network. In Timmis
et al., Proceedings of the 2nd International Conference of Artificial Immune Systems.
LNCS 2787, 168?180.
[43] Neal, M.J. and Timmis, J. (2003). Timidity: a useful mechanism for robot control?
Informatica, 27(4), 197?204.
[44] Neal, M.J. and Timmis, M.J. (2004). Once more unto the breach . . . towards artificial
homeostasis? In L.N. de Castro and F.J. Von Zuben, editors, Recent Advances in
Biologically Inspired Computing, 340?365. IGP.
[45] Nicosia, G. (2004). Combinatorial landscapes, immune algorithms and protein struc-
ture prediction problem. Poster at Mathematical and Statistical Aspects of Molecular
Biology (MASAMB XIV), Isaac Newton Institute, Cambridge.
[46] Nicosia, G., Cutello, V., Bentley, P.J. and Timmis, J. (eds) (2004). ICARIS 2004,
volume 3239 of LNCS. Springer.
[47] Nowak, M.A. and May, R.A. (2000). Virus dynamics. Oxford University Press.
[48] Ott. E. (1993). Chaos in dynamical systems. Cambridge University Press.
[49] Ottaviani, E. and Franceschi, E. (1996). The neuroimmunology of stress from inverte-
brates to man. Progress in Neurobiology, 48, 421?440.
24 STEPNEY, et al.
[50] Padgett, D.A. and Glaser, R. (2003). How stress influences the immune response.
Trends Immunol., 24, 444?448.
[51] Peitgen, H.-O. and Richter, D.H. (1986). The Beauty of Fractals: Images of Complex
Dynamical Systems. Springer.
[52] Perelson, A.S. (1989). Immune network theory. Imm. Rev., 110, 5?36.
[53] Perelson, A.S. (2002). Modelling viral and immune system dynamics. Nature Rev.
Immunol., 2, 28?36.
[54] Perelson, A.S. and Weisbuch, G. (1997). Immunology for physicists. Rev. Mod. Phys.,
69, 1219?1267.
[55] Romanyukha, A.A. and Yashin, A.I. (2003). Age related changes in population of
peripheral T cells: towards a model of immunosenescence. Mechanisms of Ageing and
Development, 124, 433?443.
[56] Scott, A. (1999). Nonlinear Science. Oxford University Press.
[57] Scott, A. (ed.) (2004). Encyclopedia of Nonlinear Science. Routledge.
[58] Sprent, J. and Surh, C.D. (2002). T cell memory. Ann. Rev. Immunol., 20, 551?579.
[59] Taylor, D. and Corne, D. (2003). An investigation of the negative selection algorithm
for fault detection in refrigeration systems. In Timmis et al. 61, 34?45.
[60] Timmis, J. (September 2000). Artificial Immune Systems: a novel data analysis tech-
nique inspired by the Immune Network Theory. PhD thesis, Department of Computer
Science, University of Wales.
[61] Timmis, J., Bentley, P. and Hart, E. (eds) (2003). ICARIS 2003, volume 2787 of LNCS.
Springer.
[62] van den Berg, H.A. (2004). Control of T-cell immunity: design principles without
the wetware. Technical Report UKC/IMS/04/36, University of Kent. preprint.
[63] van den Berg, H.A. and Rand, D. A. (2004). Quantitating T cell responsiveness.
Technical report, University of Warwick. preprint, submitted to Interface.
[64] Varela, F., Coutinho, A., Dupire, B. and Vaz, N.N. (1988). Cognitive networks: im-
mune, neural and otherwise. In A. S. Perelson, editor, Theoretical Immunology, part 2,
359?375. Addison-Wesley.
[65] Villalobos-Arias, M., Coello Coello, C.A. and Hern?ndez-Lerma, O. (2004). Conver-
gence analysis of a multiobjective artificial immune system algorithm. In Nicosia et al.
46, 226?235.